My favorites | Sign in
Project Home Downloads Wiki Issues Source
Checkout   Browse   Changes    
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
# -*- coding: utf-8 -*-
# Natural Language Toolkit: Probability and Statistics
#
# Copyright (C) 2001-2011 NLTK Project
# Author: Edward Loper <edloper@gradient.cis.upenn.edu>
# Steven Bird <sb@csse.unimelb.edu.au> (additions)
# Trevor Cohn <tacohn@cs.mu.oz.au> (additions)
# Peter Ljunglöf <peter.ljunglof@heatherleaf.se> (additions)
# Liang Dong <ldong@clemson.edu> (additions)
# Geoffrey Sampson <sampson@cantab.net> (additions)
#
# URL: <http://www.nltk.org/>
# For license information, see LICENSE.TXT
#
# $Id$

_NINF = float('-1e300')

"""
Classes for representing and processing probabilistic information.

The L{FreqDist} class is used to encode X{frequency distributions},
which count the number of times that each outcome of an experiment
occurs.

The L{ProbDistI} class defines a standard interface for X{probability
distributions}, which encode the probability of each outcome for an
experiment. There are two types of probability distribution:

- X{derived probability distributions} are created from frequency
distributions. They attempt to model the probability distribution
that generated the frequency distribution.
- X{analytic probability distributions} are created directly from
parameters (such as variance).

The L{ConditionalFreqDist} class and L{ConditionalProbDistI} interface
are used to encode conditional distributions. Conditional probability
distributions can be derived or analytic; but currently the only
implementation of the C{ConditionalProbDistI} interface is
L{ConditionalProbDist}, a derived distribution.

"""

import math
import random
import warnings
from operator import itemgetter
from itertools import imap, islice

from nltk.compat import all

##//////////////////////////////////////////////////////
## Frequency Distributions
##//////////////////////////////////////////////////////

# [SB] inherit from defaultdict?
# [SB] for NLTK 3.0, inherit from collections.Counter?

class FreqDist(dict):
"""
A frequency distribution for the outcomes of an experiment. A
frequency distribution records the number of times each outcome of
an experiment has occurred. For example, a frequency distribution
could be used to record the frequency of each word type in a
document. Formally, a frequency distribution can be defined as a
function mapping from each sample to the number of times that
sample occurred as an outcome.

Frequency distributions are generally constructed by running a
number of experiments, and incrementing the count for a sample
every time it is an outcome of an experiment. For example, the
following code will produce a frequency distribution that encodes
how often each word occurs in a text:

>>> fdist = FreqDist()
>>> for word in tokenize.whitespace(sent):
... fdist.inc(word.lower())

An equivalent way to do this is with the initializer:

>>> fdist = FreqDist(word.lower() for word in tokenize.whitespace(sent))

"""
def __init__(self, samples=None):
"""
Construct a new frequency distribution. If C{samples} is
given, then the frequency distribution will be initialized
with the count of each object in C{samples}; otherwise, it
will be initialized to be empty.

In particular, C{FreqDist()} returns an empty frequency
distribution; and C{FreqDist(samples)} first creates an empty
frequency distribution, and then calls C{update} with the
list C{samples}.

@param samples: The samples to initialize the frequency
distribution with.
@type samples: Sequence
"""
dict.__init__(self)
self._N = 0
self._reset_caches()
if samples:
self.update(samples)

def inc(self, sample, count=1):
"""
Increment this C{FreqDist}'s count for the given
sample.

@param sample: The sample whose count should be incremented.
@type sample: any
@param count: The amount to increment the sample's count by.
@type count: C{int}
@rtype: None
@raise NotImplementedError: If C{sample} is not a
supported sample type.
"""
if count == 0: return
self[sample] = self.get(sample,0) + count

def __setitem__(self, sample, value):
"""
Set this C{FreqDist}'s count for the given sample.

@param sample: The sample whose count should be incremented.
@type sample: any hashable object
@param count: The new value for the sample's count
@type count: C{int}
@rtype: None
@raise TypeError: If C{sample} is not a supported sample type.
"""

self._N += (value - self.get(sample, 0))
dict.__setitem__(self, sample, value)

# Invalidate the caches
self._reset_caches()

def N(self):
"""
@return: The total number of sample outcomes that have been
recorded by this C{FreqDist}. For the number of unique
sample values (or bins) with counts greater than zero, use
C{FreqDist.B()}.
@rtype: C{int}
"""
return self._N

def B(self):
"""
@return: The total number of sample values (or X{bins}) that
have counts greater than zero. For the total
number of sample outcomes recorded, use C{FreqDist.N()}.
(FreqDist.B() is the same as len(FreqDist).)
@rtype: C{int}
"""
return len(self)

# deprecate this -- use keys() instead?
def samples(self):
"""
@return: A list of all samples that have been recorded as
outcomes by this frequency distribution. Use C{count()}
to determine the count for each sample.
@rtype: C{list}
"""
return self.keys()

def hapaxes(self):
"""
@return: A list of all samples that occur once (hapax legomena)
@rtype: C{list}
"""
return [item for item in self if self[item] == 1]

def Nr(self, r, bins=None):
"""
@return: The number of samples with count r.
@rtype: C{int}
@type r: C{int}
@param r: A sample count.
@type bins: C{int}
@param bins: The number of possible sample outcomes. C{bins}
is used to calculate Nr(0). In particular, Nr(0) is
C{bins-self.B()}. If C{bins} is not specified, it
defaults to C{self.B()} (so Nr(0) will be 0).
"""
if r < 0: raise IndexError, 'FreqDist.Nr(): r must be non-negative'

# Special case for Nr(0):
if r == 0:
if bins is None: return 0
else: return bins-self.B()

# We have to search the entire distribution to find Nr. Since
# this is an expensive operation, and is likely to be used
# repeatedly, cache the results.
if self._Nr_cache is None:
self._cache_Nr_values()

if r >= len(self._Nr_cache): return 0
return self._Nr_cache[r]

def _cache_Nr_values(self):
Nr = [0]
for sample in self:
c = self.get(sample, 0)
if c >= len(Nr):
Nr += [0]*(c+1-len(Nr))
Nr[c] += 1
self._Nr_cache = Nr

def count(self, sample):
"""
Return the count of a given sample. The count of a sample is
defined as the number of times that sample outcome was
recorded by this C{FreqDist}. Counts are non-negative
integers. This method has been replaced by conventional
dictionary indexing; use fd[item] instead of fd.count(item).

@return: The count of a given sample.
@rtype: C{int}
@param sample: the sample whose count
should be returned.
@type sample: any.
"""
raise AttributeError, "Use indexing to look up an entry in a FreqDist, e.g. fd[item]"

def _cumulative_frequencies(self, samples=None):
"""
Return the cumulative frequencies of the specified samples.
If no samples are specified, all counts are returned, starting
with the largest.

@return: The cumulative frequencies of the given samples.
@rtype: C{list} of C{float}
@param samples: the samples whose frequencies should be returned.
@type sample: any.
"""
cf = 0.0
if not samples:
samples = self.keys()
for sample in samples:
cf += self[sample]
yield cf

# slightly odd nomenclature freq() if FreqDist does counts and ProbDist does probs,
# here, freq() does probs
def freq(self, sample):
"""
Return the frequency of a given sample. The frequency of a
sample is defined as the count of that sample divided by the
total number of sample outcomes that have been recorded by
this C{FreqDist}. The count of a sample is defined as the
number of times that sample outcome was recorded by this
C{FreqDist}. Frequencies are always real numbers in the range
[0, 1].

@return: The frequency of a given sample.
@rtype: float
@param sample: the sample whose frequency
should be returned.
@type sample: any
"""
if self._N is 0:
return 0
return float(self[sample]) / self._N

def max(self):
"""
Return the sample with the greatest number of outcomes in this
frequency distribution. If two or more samples have the same
number of outcomes, return one of them; which sample is
returned is undefined. If no outcomes have occurred in this
frequency distribution, return C{None}.

@return: The sample with the maximum number of outcomes in this
frequency distribution.
@rtype: any or C{None}
"""
if self._max_cache is None:
self._max_cache = max([(a,b) for (b,a) in self.items()])[1]
return self._max_cache

def plot(self, *args, **kwargs):
"""
Plot samples from the frequency distribution
displaying the most frequent sample first. If an integer
parameter is supplied, stop after this many samples have been
plotted. If two integer parameters m, n are supplied, plot a
subset of the samples, beginning with m and stopping at n-1.
For a cumulative plot, specify cumulative=True.
(Requires Matplotlib to be installed.)

@param title: The title for the graph
@type title: C{str}
@param cumulative: A flag to specify whether the plot is cumulative (default = False)
@type title: C{bool}
"""
try:
import pylab
except ImportError:
raise ValueError('The plot function requires the matplotlib package (aka pylab).'
'See http://matplotlib.sourceforge.net/')

if len(args) == 0:
args = [len(self)]
samples = list(islice(self, *args))

cumulative = _get_kwarg(kwargs, 'cumulative', False)
if cumulative:
freqs = list(self._cumulative_frequencies(samples))
ylabel = "Cumulative Counts"
else:
freqs = [self[sample] for sample in samples]
ylabel = "Counts"
# percents = [f * 100 for f in freqs] only in ProbDist?

pylab.grid(True, color="silver")
if not "linewidth" in kwargs:
kwargs["linewidth"] = 2
if "title" in kwargs:
pylab.title(kwargs["title"])
del kwargs["title"]
pylab.plot(freqs, **kwargs)
pylab.xticks(range(len(samples)), [str(s) for s in samples], rotation=90)
pylab.xlabel("Samples")
pylab.ylabel(ylabel)
pylab.show()

def tabulate(self, *args, **kwargs):
"""
Tabulate the given samples from the frequency distribution (cumulative),
displaying the most frequent sample first. If an integer
parameter is supplied, stop after this many samples have been
plotted. If two integer parameters m, n are supplied, plot a
subset of the samples, beginning with m and stopping at n-1.
(Requires Matplotlib to be installed.)

@param samples: The samples to plot (default is all samples)
@type samples: C{list}
"""
if len(args) == 0:
args = [len(self)]
samples = list(islice(self, *args))

cumulative = _get_kwarg(kwargs, 'cumulative', False)
if cumulative:
freqs = list(self._cumulative_frequencies(samples))
else:
freqs = [self[sample] for sample in samples]
# percents = [f * 100 for f in freqs] only in ProbDist?

for i in range(len(samples)):
print "%4s" % str(samples[i]),
print
for i in range(len(samples)):
print "%4d" % freqs[i],
print

def sorted_samples(self):
raise AttributeError, "Use FreqDist.keys(), or iterate over the FreqDist to get its samples in sorted order (most frequent first)"

def sorted(self):
raise AttributeError, "Use FreqDist.keys(), or iterate over the FreqDist to get its samples in sorted order (most frequent first)"

def _sort_keys_by_value(self):
if not self._item_cache:
self._item_cache = sorted(dict.items(self), key=lambda x:(-x[1], x[0]))

def keys(self):
"""
Return the samples sorted in decreasing order of frequency.

@return: A list of samples, in sorted order
@rtype: C{list} of any
"""
self._sort_keys_by_value()
return map(itemgetter(0), self._item_cache)

def values(self):
"""
Return the samples sorted in decreasing order of frequency.

@return: A list of samples, in sorted order
@rtype: C{list} of any
"""
self._sort_keys_by_value()
return map(itemgetter(1), self._item_cache)

def items(self):
"""
Return the items sorted in decreasing order of frequency.

@return: A list of items, in sorted order
@rtype: C{list} of C{tuple}
"""
self._sort_keys_by_value()
return self._item_cache[:]

def __iter__(self):
"""
Return the samples sorted in decreasing order of frequency.

@return: An iterator over the samples, in sorted order
@rtype: C{iter}
"""
return iter(self.keys())

def iterkeys(self):
"""
Return the samples sorted in decreasing order of frequency.

@return: An iterator over the samples, in sorted order
@rtype: C{iter}
"""
return iter(self.keys())

def itervalues(self):
"""
Return the values sorted in decreasing order.

@return: An iterator over the values, in sorted order
@rtype: C{iter}
"""
return iter(self.values())

def iteritems(self):
"""
Return the items sorted in decreasing order of frequency.

@return: An iterator over the items, in sorted order
@rtype: C{iter} of any
"""
self._sort_keys_by_value()
return iter(self._item_cache)

# sort the supplied samples
# if samples:
# items = [(sample, self[sample]) for sample in set(samples)]

def copy(self):
"""
Create a copy of this frequency distribution.

@return: A copy of this frequency distribution object.
@rtype: C{FreqDist}
"""
return self.__class__(self)

def update(self, samples):
"""
Update the frequency distribution with the provided list of samples.
This is a faster way to add multiple samples to the distribution.

@param samples: The samples to add.
@type samples: C{list}
"""
try:
sample_iter = samples.iteritems()
except:
sample_iter = imap(lambda x: (x,1), samples)
for sample, count in sample_iter:
self.inc(sample, count=count)

def pop(self, other):
self._reset_caches()
return dict.pop(self, other)

def popitem(self, other):
self._reset_caches()
return dict.popitem(self, other)

def clear(self):
self._N = 0
self._reset_caches()
dict.clear(self)

def _reset_caches(self):
self._Nr_cache = None
self._max_cache = None
self._item_cache = None

def __add__(self, other):
clone = self.copy()
clone.update(other)
return clone
def __eq__(self, other):
if not isinstance(other, FreqDist): return False
return self.items() == other.items() # items are already sorted
def __ne__(self, other):
return not (self == other)
def __le__(self, other):
if not isinstance(other, FreqDist): return False
return set(self).issubset(other) and all(self[key] <= other[key] for key in self)
def __lt__(self, other):
if not isinstance(other, FreqDist): return False
return self <= other and self != other
def __ge__(self, other):
if not isinstance(other, FreqDist): return False
return other <= self
def __gt__(self, other):
if not isinstance(other, FreqDist): return False
return other < self

def __repr__(self):
"""
@return: A string representation of this C{FreqDist}.
@rtype: string
"""
return '<FreqDist with %d outcomes>' % self.N()

def __str__(self):
"""
@return: A string representation of this C{FreqDist}.
@rtype: string
"""
items = ['%r: %r' % (s, self[s]) for s in self]
return '<FreqDist: %s>' % ', '.join(items)

def __getitem__(self, sample):
return self.get(sample, 0)

##//////////////////////////////////////////////////////
## Probability Distributions
##//////////////////////////////////////////////////////

class ProbDistI(object):
"""
A probability distribution for the outcomes of an experiment. A
probability distribution specifies how likely it is that an
experiment will have any given outcome. For example, a
probability distribution could be used to predict the probability
that a token in a document will have a given type. Formally, a
probability distribution can be defined as a function mapping from
samples to nonnegative real numbers, such that the sum of every
number in the function's range is 1.0. C{ProbDist}s are often
used to model the probability distribution of the experiment used
to generate a frequency distribution.
"""
SUM_TO_ONE = True
"""True if the probabilities of the samples in this probability
distribution will always sum to one."""

def __init__(self):
if self.__class__ == ProbDistI:
raise AssertionError, "Interfaces can't be instantiated"

def prob(self, sample):
"""
@return: the probability for a given sample. Probabilities
are always real numbers in the range [0, 1].
@rtype: float
@param sample: The sample whose probability
should be returned.
@type sample: any
"""
raise AssertionError()

def logprob(self, sample):
"""
@return: the base 2 logarithm of the probability for a given
sample. Log probabilities range from negitive infinity to
zero.
@rtype: float
@param sample: The sample whose probability
should be returned.
@type sample: any
"""
# Default definition, in terms of prob()
p = self.prob(sample)
if p == 0:
# Use some approximation to infinity. What this does
# depends on your system's float implementation.
return _NINF
else:
return math.log(p, 2)

def max(self):
"""
@return: the sample with the greatest probability. If two or
more samples have the same probability, return one of them;
which sample is returned is undefined.
@rtype: any
"""
raise AssertionError()

# deprecate this (use keys() instead?)
def samples(self):
"""
@return: A list of all samples that have nonzero
probabilities. Use C{prob} to find the probability of
each sample.
@rtype: C{list}
"""
raise AssertionError()

# cf self.SUM_TO_ONE
def discount(self):
"""
@return: The ratio by which counts are discounted on average: c*/c
@rtype: C{float}
"""
return 0.0

# Subclasses should define more efficient implementations of this,
# where possible.
def generate(self):
"""
@return: A randomly selected sample from this probability
distribution. The probability of returning each sample
C{samp} is equal to C{self.prob(samp)}.
"""
p = random.random()
for sample in self.samples():
p -= self.prob(sample)
if p <= 0: return sample
# allow for some rounding error:
if p < .0001:
return sample
# we *should* never get here
if self.SUM_TO_ONE:
warnings.warn("Probability distribution %r sums to %r; generate()"
" is returning an arbitrary sample." % (self, 1-p))
return random.choice(list(self.samples()))

class UniformProbDist(ProbDistI):
"""
A probability distribution that assigns equal probability to each
sample in a given set; and a zero probability to all other
samples.
"""
def __init__(self, samples):
"""
Construct a new uniform probability distribution, that assigns
equal probability to each sample in C{samples}.

@param samples: The samples that should be given uniform
probability.
@type samples: C{list}
@raise ValueError: If C{samples} is empty.
"""
if len(samples) == 0:
raise ValueError('A Uniform probability distribution must '+
'have at least one sample.')
self._sampleset = set(samples)
self._prob = 1.0/len(self._sampleset)
self._samples = list(self._sampleset)

def prob(self, sample):
if sample in self._sampleset: return self._prob
else: return 0
def max(self): return self._samples[0]
def samples(self): return self._samples
def __repr__(self):
return '<UniformProbDist with %d samples>' % len(self._sampleset)

class DictionaryProbDist(ProbDistI):
"""
A probability distribution whose probabilities are directly
specified by a given dictionary. The given dictionary maps
samples to probabilities.
"""
def __init__(self, prob_dict=None, log=False, normalize=False):
"""
Construct a new probability distribution from the given
dictionary, which maps values to probabilities (or to log
probabilities, if C{log} is true). If C{normalize} is
true, then the probability values are scaled by a constant
factor such that they sum to 1.
"""
self._prob_dict = prob_dict.copy()
self._log = log

# Normalize the distribution, if requested.
if normalize:
if log:
value_sum = sum_logs(self._prob_dict.values())
if value_sum <= _NINF:
logp = math.log(1.0/len(prob_dict), 2)
for x in prob_dict.keys():
self._prob_dict[x] = logp
else:
for (x, p) in self._prob_dict.items():
self._prob_dict[x] -= value_sum
else:
value_sum = sum(self._prob_dict.values())
if value_sum == 0:
p = 1.0/len(prob_dict)
for x in prob_dict:
self._prob_dict[x] = p
else:
norm_factor = 1.0/value_sum
for (x, p) in self._prob_dict.items():
self._prob_dict[x] *= norm_factor

def prob(self, sample):
if self._log:
if sample not in self._prob_dict: return 0
else: return 2**(self._prob_dict[sample])
else:
return self._prob_dict.get(sample, 0)

def logprob(self, sample):
if self._log:
return self._prob_dict.get(sample, _NINF)
else:
if sample not in self._prob_dict: return _NINF
elif self._prob_dict[sample] == 0: return _NINF
else: return math.log(self._prob_dict[sample], 2)

def max(self):
if not hasattr(self, '_max'):
self._max = max((p,v) for (v,p) in self._prob_dict.items())[1]
return self._max
def samples(self):
return self._prob_dict.keys()
def __repr__(self):
return '<ProbDist with %d samples>' % len(self._prob_dict)

class MLEProbDist(ProbDistI):
"""
The maximum likelihood estimate for the probability distribution
of the experiment used to generate a frequency distribution. The
X{maximum likelihood estimate} approximates the probability of
each sample as the frequency of that sample in the frequency
distribution.
"""
def __init__(self, freqdist, bins=None):
"""
Use the maximum likelihood estimate to create a probability
distribution for the experiment used to generate C{freqdist}.

@type freqdist: C{FreqDist}
@param freqdist: The frequency distribution that the
probability estimates should be based on.
"""
self._freqdist = freqdist

def freqdist(self):
"""
@return: The frequency distribution that this probability
distribution is based on.
@rtype: C{FreqDist}
"""
return self._freqdist

def prob(self, sample):
return self._freqdist.freq(sample)

def max(self):
return self._freqdist.max()

def samples(self):
return self._freqdist.keys()

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
return '<MLEProbDist based on %d samples>' % self._freqdist.N()

class LidstoneProbDist(ProbDistI):
"""
The Lidstone estimate for the probability distribution of the
experiment used to generate a frequency distribution. The
C{Lidstone estimate} is paramaterized by a real number M{gamma},
which typically ranges from 0 to 1. The X{Lidstone estimate}
approximates the probability of a sample with count M{c} from an
experiment with M{N} outcomes and M{B} bins as
M{(c+gamma)/(N+B*gamma)}. This is equivalant to adding
M{gamma} to the count for each bin, and taking the maximum
likelihood estimate of the resulting frequency distribution.
"""
SUM_TO_ONE = False
def __init__(self, freqdist, gamma, bins=None):
"""
Use the Lidstone estimate to create a probability distribution
for the experiment used to generate C{freqdist}.

@type freqdist: C{FreqDist}
@param freqdist: The frequency distribution that the
probability estimates should be based on.
@type gamma: C{float}
@param gamma: A real number used to paramaterize the
estimate. The Lidstone estimate is equivalant to adding
M{gamma} to the count for each bin, and taking the
maximum likelihood estimate of the resulting frequency
distribution.
@type bins: C{int}
@param bins: The number of sample values that can be generated
by the experiment that is described by the probability
distribution. This value must be correctly set for the
probabilities of the sample values to sum to one. If
C{bins} is not specified, it defaults to C{freqdist.B()}.
"""
if (bins == 0) or (bins is None and freqdist.N() == 0):
name = self.__class__.__name__[:-8]
raise ValueError('A %s probability distribution ' % name +
'must have at least one bin.')
if (bins is not None) and (bins < freqdist.B()):
name = self.__class__.__name__[:-8]
raise ValueError('\nThe number of bins in a %s distribution ' % name +
'(%d) must be greater than or equal to\n' % bins +
'the number of bins in the FreqDist used ' +
'to create it (%d).' % freqdist.N())

self._freqdist = freqdist
self._gamma = float(gamma)
self._N = self._freqdist.N()

if bins is None: bins = freqdist.B()
self._bins = bins

self._divisor = self._N + bins * gamma
if self._divisor == 0.0:
# In extreme cases we force the probability to be 0,
# which it will be, since the count will be 0:
self._gamma = 0
self._divisor = 1

def freqdist(self):
"""
@return: The frequency distribution that this probability
distribution is based on.
@rtype: C{FreqDist}
"""
return self._freqdist

def prob(self, sample):
c = self._freqdist[sample]
return (c + self._gamma) / self._divisor

def max(self):
# For Lidstone distributions, probability is monotonic with
# frequency, so the most probable sample is the one that
# occurs most frequently.
return self._freqdist.max()

def samples(self):
return self._freqdist.keys()

def discount(self):
gb = self._gamma * self._bins
return gb / (self._N + gb)

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
return '<LidstoneProbDist based on %d samples>' % self._freqdist.N()


class LaplaceProbDist(LidstoneProbDist):
"""
The Laplace estimate for the probability distribution of the
experiment used to generate a frequency distribution. The
X{Lidstone estimate} approximates the probability of a sample with
count M{c} from an experiment with M{N} outcomes and M{B} bins as
M{(c+1)/(N+B)}. This is equivalant to adding one to the count for
each bin, and taking the maximum likelihood estimate of the
resulting frequency distribution.
"""
def __init__(self, freqdist, bins=None):
"""
Use the Laplace estimate to create a probability distribution
for the experiment used to generate C{freqdist}.

@type freqdist: C{FreqDist}
@param freqdist: The frequency distribution that the
probability estimates should be based on.
@type bins: C{int}
@param bins: The number of sample values that can be generated
by the experiment that is described by the probability
distribution. This value must be correctly set for the
probabilities of the sample values to sum to one. If
C{bins} is not specified, it defaults to C{freqdist.B()}.
"""
LidstoneProbDist.__init__(self, freqdist, 1, bins)

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
return '<LaplaceProbDist based on %d samples>' % self._freqdist.N()

class ELEProbDist(LidstoneProbDist):
"""
The expected likelihood estimate for the probability distribution
of the experiment used to generate a frequency distribution. The
X{expected likelihood estimate} approximates the probability of a
sample with count M{c} from an experiment with M{N} outcomes and
M{B} bins as M{(c+0.5)/(N+B/2)}. This is equivalant to adding 0.5
to the count for each bin, and taking the maximum likelihood
estimate of the resulting frequency distribution.
"""
def __init__(self, freqdist, bins=None):
"""
Use the expected likelihood estimate to create a probability
distribution for the experiment used to generate C{freqdist}.

@type freqdist: C{FreqDist}
@param freqdist: The frequency distribution that the
probability estimates should be based on.
@type bins: C{int}
@param bins: The number of sample values that can be generated
by the experiment that is described by the probability
distribution. This value must be correctly set for the
probabilities of the sample values to sum to one. If
C{bins} is not specified, it defaults to C{freqdist.B()}.
"""
LidstoneProbDist.__init__(self, freqdist, 0.5, bins)

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
return '<ELEProbDist based on %d samples>' % self._freqdist.N()

class HeldoutProbDist(ProbDistI):
"""
The heldout estimate for the probability distribution of the
experiment used to generate two frequency distributions. These
two frequency distributions are called the "heldout frequency
distribution" and the "base frequency distribution." The
X{heldout estimate} uses uses the X{heldout frequency
distribution} to predict the probability of each sample, given its
frequency in the X{base frequency distribution}.

In particular, the heldout estimate approximates the probability
for a sample that occurs M{r} times in the base distribution as
the average frequency in the heldout distribution of all samples
that occur M{r} times in the base distribution.

This average frequency is M{Tr[r]/(Nr[r]*N)}, where:
- M{Tr[r]} is the total count in the heldout distribution for
all samples that occur M{r} times in the base
distribution.
- M{Nr[r]} is the number of samples that occur M{r} times in
the base distribution.
- M{N} is the number of outcomes recorded by the heldout
frequency distribution.

In order to increase the efficiency of the C{prob} member
function, M{Tr[r]/(Nr[r]*N)} is precomputed for each value of M{r}
when the C{HeldoutProbDist} is created.

@type _estimate: C{list} of C{float}
@ivar _estimate: A list mapping from M{r}, the number of
times that a sample occurs in the base distribution, to the
probability estimate for that sample. C{_estimate[M{r}]} is
calculated by finding the average frequency in the heldout
distribution of all samples that occur M{r} times in the base
distribution. In particular, C{_estimate[M{r}]} =
M{Tr[r]/(Nr[r]*N)}.
@type _max_r: C{int}
@ivar _max_r: The maximum number of times that any sample occurs
in the base distribution. C{_max_r} is used to decide how
large C{_estimate} must be.
"""
SUM_TO_ONE = False
def __init__(self, base_fdist, heldout_fdist, bins=None):
"""
Use the heldout estimate to create a probability distribution
for the experiment used to generate C{base_fdist} and
C{heldout_fdist}.

@type base_fdist: C{FreqDist}
@param base_fdist: The base frequency distribution.
@type heldout_fdist: C{FreqDist}
@param heldout_fdist: The heldout frequency distribution.
@type bins: C{int}
@param bins: The number of sample values that can be generated
by the experiment that is described by the probability
distribution. This value must be correctly set for the
probabilities of the sample values to sum to one. If
C{bins} is not specified, it defaults to C{freqdist.B()}.
"""

self._base_fdist = base_fdist
self._heldout_fdist = heldout_fdist

# The max number of times any sample occurs in base_fdist.
self._max_r = base_fdist[base_fdist.max()]

# Calculate Tr, Nr, and N.
Tr = self._calculate_Tr()
Nr = [base_fdist.Nr(r, bins) for r in range(self._max_r+1)]
N = heldout_fdist.N()

# Use Tr, Nr, and N to compute the probability estimate for
# each value of r.
self._estimate = self._calculate_estimate(Tr, Nr, N)

def _calculate_Tr(self):
"""
@return: the list M{Tr}, where M{Tr[r]} is the total count in
C{heldout_fdist} for all samples that occur M{r}
times in C{base_fdist}.
@rtype: C{list} of C{float}
"""
Tr = [0.0] * (self._max_r+1)
for sample in self._heldout_fdist:
r = self._base_fdist[sample]
Tr[r] += self._heldout_fdist[sample]
return Tr

def _calculate_estimate(self, Tr, Nr, N):
"""
@return: the list M{estimate}, where M{estimate[r]} is the
probability estimate for any sample that occurs M{r} times
in the base frequency distribution. In particular,
M{estimate[r]} is M{Tr[r]/(N[r]*N)}. In the special case
that M{N[r]=0}, M{estimate[r]} will never be used; so we
define M{estimate[r]=None} for those cases.
@rtype: C{list} of C{float}
@type Tr: C{list} of C{float}
@param Tr: the list M{Tr}, where M{Tr[r]} is the total count in
the heldout distribution for all samples that occur M{r}
times in base distribution.
@type Nr: C{list} of C{float}
@param Nr: The list M{Nr}, where M{Nr[r]} is the number of
samples that occur M{r} times in the base distribution.
@type N: C{int}
@param N: The total number of outcomes recorded by the heldout
frequency distribution.
"""
estimate = []
for r in range(self._max_r+1):
if Nr[r] == 0: estimate.append(None)
else: estimate.append(Tr[r]/(Nr[r]*N))
return estimate

def base_fdist(self):
"""
@return: The base frequency distribution that this probability
distribution is based on.
@rtype: C{FreqDist}
"""
return self._base_fdist

def heldout_fdist(self):
"""
@return: The heldout frequency distribution that this
probability distribution is based on.
@rtype: C{FreqDist}
"""
return self._heldout_fdist

def samples(self):
return self._base_fdist.keys()

def prob(self, sample):
# Use our precomputed probability estimate.
r = self._base_fdist[sample]
return self._estimate[r]

def max(self):
# Note: the Heldout estimation is *not* necessarily monotonic;
# so this implementation is currently broken. However, it
# should give the right answer *most* of the time. :)
return self._base_fdist.max()

def discount(self):
raise NotImplementedError()

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
s = '<HeldoutProbDist: %d base samples; %d heldout samples>'
return s % (self._base_fdist.N(), self._heldout_fdist.N())

class CrossValidationProbDist(ProbDistI):
"""
The cross-validation estimate for the probability distribution of
the experiment used to generate a set of frequency distribution.
The X{cross-validation estimate} for the probability of a sample
is found by averaging the held-out estimates for the sample in
each pair of frequency distributions.
"""
SUM_TO_ONE = False
def __init__(self, freqdists, bins):
"""
Use the cross-validation estimate to create a probability
distribution for the experiment used to generate
C{freqdists}.

@type freqdists: C{list} of C{FreqDist}
@param freqdists: A list of the frequency distributions
generated by the experiment.
@type bins: C{int}
@param bins: The number of sample values that can be generated
by the experiment that is described by the probability
distribution. This value must be correctly set for the
probabilities of the sample values to sum to one. If
C{bins} is not specified, it defaults to C{freqdist.B()}.
"""
self._freqdists = freqdists

# Create a heldout probability distribution for each pair of
# frequency distributions in freqdists.
self._heldout_probdists = []
for fdist1 in freqdists:
for fdist2 in freqdists:
if fdist1 is not fdist2:
probdist = HeldoutProbDist(fdist1, fdist2, bins)
self._heldout_probdists.append(probdist)

def freqdists(self):
"""
@rtype: C{list} of C{FreqDist}
@return: The list of frequency distributions that this
C{ProbDist} is based on.
"""
return self._freqdists

def samples(self):
# [xx] nb: this is not too efficient
return set(sum([fd.keys() for fd in self._freqdists], []))

def prob(self, sample):
# Find the average probability estimate returned by each
# heldout distribution.
prob = 0.0
for heldout_probdist in self._heldout_probdists:
prob += heldout_probdist.prob(sample)
return prob/len(self._heldout_probdists)

def discount(self):
raise NotImplementedError()

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
return '<CrossValidationProbDist: %d-way>' % len(self._freqdists)

class WittenBellProbDist(ProbDistI):
"""
The Witten-Bell estimate of a probability distribution. This distribution
allocates uniform probability mass to as yet unseen events by using the
number of events that have only been seen once. The probability mass
reserved for unseen events is equal to:

- M{T / (N + T)}

where M{T} is the number of observed event types and M{N} is the total
number of observed events. This equates to the maximum likelihood estimate
of a new type event occuring. The remaining probability mass is discounted
such that all probability estimates sum to one, yielding:

- M{p = T / Z (N + T)}, if count = 0
- M{p = c / (N + T)}, otherwise
"""

def __init__(self, freqdist, bins=None):
"""
Creates a distribution of Witten-Bell probability estimates. This
distribution allocates uniform probability mass to as yet unseen
events by using the number of events that have only been seen once.
The probability mass reserved for unseen events is equal to:

- M{T / (N + T)}

where M{T} is the number of observed event types and M{N} is the total
number of observed events. This equates to the maximum likelihood
estimate of a new type event occuring. The remaining probability mass
is discounted such that all probability estimates sum to one,
yielding:

- M{p = T / Z (N + T)}, if count = 0
- M{p = c / (N + T)}, otherwise

The parameters M{T} and M{N} are taken from the C{freqdist} parameter
(the C{B()} and C{N()} values). The normalising factor M{Z} is
calculated using these values along with the C{bins} parameter.

@param freqdist: The frequency counts upon which to base the
estimation.
@type freqdist: C{FreqDist}
@param bins: The number of possible event types. This must be
at least as large as the number of bins in the
C{freqdist}. If C{None}, then it's assumed to be
equal to that of the C{freqdist}
@type bins: C{Int}
"""
assert bins == None or bins >= freqdist.B(),\
'Bins parameter must not be less than freqdist.B()'
if bins == None:
bins = freqdist.B()
self._freqdist = freqdist
self._T = self._freqdist.B()
self._Z = bins - self._freqdist.B()
self._N = self._freqdist.N()
# self._P0 is P(0), precalculated for efficiency:
if self._N==0:
# if freqdist is empty, we approximate P(0) by a UniformProbDist:
self._P0 = 1.0 / self._Z
else:
self._P0 = self._T / float(self._Z * (self._N + self._T))

def prob(self, sample):
# inherit docs from ProbDistI
c = self._freqdist[sample]
if c == 0:
return self._P0
else:
return c / float(self._N + self._T)

def max(self):
return self._freqdist.max()

def samples(self):
return self._freqdist.keys()

def freqdist(self):
return self._freqdist

def discount(self):
raise NotImplementedError()

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
return '<WittenBellProbDist based on %d samples>' % self._freqdist.N()


##//////////////////////////////////////////////////////
## Good-Turing Probablity Distributions
##//////////////////////////////////////////////////////

# Good-Turing frequency estimation was contributed by Alan Turing and
# his statistical assistant I.J. Good, during their collaboration in
# the WWII. It is a statistical technique for predicting the
# probability of occurrence of objects belonging to an unknown number
# of species, given past observations of such objects and their
# species. (In drawing balls from an urn, the 'objects' would be balls
# and the 'species' would be the distinct colors of the balls (finite
# but unknown in number).
#
# The situation frequency zero is quite common in the original
# Good-Turing estimation. Bill Gale and Geoffrey Sampson present a
# simple and effective approach, Simple Good-Turing. As a smoothing
# curve they simply use a power curve:
#
# Nr = a*r^b (with b < -1 to give the appropriate hyperbolic
# relationsihp)
#
# They estimate a and b by simple linear regression technique on the
# logarithmic form of the equation:
#
# log Nr = a + b*log(r)
#
# However, they suggest that such a simple curve is probably only
# appropriate for high values of r. For low values of r, they use the
# measured Nr directly. (see M&S, p.213)
#
# Gale and Sampson propose to use r while the difference between r and
# r* is 1.96 greather than the standar deviation, and switch to r* if
# it is less or equal:
#
# |r - r*| > 1.96 * sqrt((r + 1)^2 (Nr+1 / Nr^2) (1 + Nr+1 / Nr))
#
# The 1.96 coefficient correspond to a 0.05 significance criterion,
# some implementations can use a coefficient of 1.65 for a 0.1
# significance criterion.
#

class GoodTuringProbDist(ProbDistI):
"""
The Good-Turing estimate of a probability distribution. This method
calculates the probability mass to assign to events with zero or low
counts based on the number of events with higher counts. It does so by
using the smoothed count M{c*}:

- M{c* = (c + 1) N(c + 1) / N(c)} for c >= 1
- M{things with frequency zero in training} = N(1) for c == 0

where M{c} is the original count, M{N(i)} is the number of event types
observed with count M{i}. We can think the count of unseen as the count
of frequency one.
(see Jurafsky & Martin 2nd Edition, p101)

"""
def __init__(self, freqdist, bins=None):
"""
@param freqdist: The frequency counts upon which to base the
estimation.
@type freqdist: C{FreqDist}
@param bins: The number of possible event types. This must be
at least as large as the number of bins in the
C{freqdist}. If C{None}, then it's assumed to be
equal to that of the C{freqdist}
@type bins: C{Int}
"""
assert bins == None or bins >= freqdist.B(),\
'Bins parameter must not be less than freqdist.B()'
if bins == None:
bins = freqdist.B()
self._freqdist = freqdist
self._bins = bins

def prob(self, sample):
count = self._freqdist[sample]

# unseen sample's frequency (count zero) uses frequency one's
if count == 0 and self._freqdist.N() != 0:
p0 = 1.0 * self._freqdist.Nr(1) / self._freqdist.N()
if self._bins == self._freqdist.B():
p0 = 0.0
else:
p0 = p0 / (1.0 * self._bins - self._freqdist.B())

nc = self._freqdist.Nr(count)
ncn = self._freqdist.Nr(count + 1)

# avoid divide-by-zero errors for sparse datasets
if nc == 0 or self._freqdist.N() == 0:
return 0

return 1.0 * (count + 1) * ncn / (nc * self._freqdist.N())

def max(self):
return self._freqdist.max()

def samples(self):
return self._freqdist.keys()

def discount(self):
"""
@return: The probability mass transferred from the
seen samples to the unseen samples.
@rtype: C{float}
"""
return 1.0 * self._freqdist.Nr(1) / self._freqdist.N()

def freqdist(self):
return self._freqdist

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
return '<GoodTuringProbDist based on %d samples>' % self._freqdist.N()



##//////////////////////////////////////////////////////
## Simple Good-Turing Probablity Distributions
##//////////////////////////////////////////////////////

class SimpleGoodTuringProbDist(ProbDistI):
"""
SimpleGoodTuring ProbDist approximates from frequency to freqency of
frequency into a linear line under log space by linear regression.
Details of Simple Good-Turing algorithm can be found in:
(1) Bill Gale and Geoffrey Sampson's joint paper
"Good Turing Smoothing Without Tear", published in
Journal of Quantitative Linguistics, vol. 2 pp. 217-237, 1995
(2) Jurafsky & Martin's Book "Speech and Language Processing"
2e Chap 4.5 p103 (log(Nc) = a + b*log(c))
(3) Website maintained by Geoffrey Sampson:
http://www.grsampson.net/RGoodTur.html

Given a set of pair (xi, yi), where the xi denotes the freqency and
yi denotes the freqency of freqency, we want to minimize their
square variation. E(x) and E(y) represent the mean of xi and yi.

-Slope: b = sigma ((xi-E(x)*(yi-E(y))) / sigma ((xi-E(x))*(xi-E(x)))
-Intercept: a = E(y)- b * E(x)

"""
def __init__(self, freqdist, bins=None):
"""
@param freqdist: The frequency counts upon which to base the
estimation.
@type freqdist: C{FreqDist}
@param bins: The number of possible event types. This must be
at least as large as the number of bins in the
C{freqdist}. If C{None}, then it's assumed to be
equal to that of the C{freqdist}
@type bins: C{Int}
"""
assert bins == None or bins >= freqdist.B(),\
'Bins parameter must not be less than freqdist.B()'
if bins == None:
bins = freqdist.B()
self._freqdist = freqdist
self._bins = bins
r, nr = self._r_Nr()
self.find_best_fit(r, nr)
self._switch(r, nr)
self._renormalize(r, nr)

def _r_Nr(self):
"""
Split the frequency distribution in two list (r, Nr), where Nr(r) > 0
"""
r, nr = [], []
b, i = 0, 0
while b != self._freqdist.B():
nr_i = self._freqdist.Nr(i)
if nr_i > 0:
b += nr_i
r.append(i)
nr.append(nr_i)
i += 1
return (r, nr)

def find_best_fit(self, r, nr):
"""
Use simple linear regression to tune parameters self._slope and
self._intercept in the log-log space based on count and Nr(count)
(Work in log space to avoid floating point underflow.)
"""
# For higher sample frequencies the data points becomes horizontal
# along line Nr=1. To create a more evident linear model in log-log
# space, we average positive Nr values with the surrounding zero
# values. (Church and Gale, 1991)

if not r or not nr:
# Empty r or nr?
return

zr = []
for j in range(len(r)):
if j > 0:
i = r[j-1]
else:
i = 0
if j != len(r) - 1:
k = r[j+1]
else:
k = 2 * r[j] - i
zr_ = 2.0 * nr[j] / (k - i)
zr.append(zr_)

log_r = [math.log(i) for i in r]
log_zr = [math.log(i) for i in zr]

xy_cov = x_var = 0.0
x_mean = 1.0 * sum(log_r) / len(log_r)
y_mean = 1.0 * sum(log_zr) / len(log_zr)
for (x, y) in zip(log_r, log_zr):
xy_cov += (x - x_mean) * (y - y_mean)
x_var += (x - x_mean)**2
if x_var != 0:
self._slope = xy_cov / x_var
else:
self._slope = 0.0
self._intercept = y_mean - self._slope * x_mean

def _switch(self, r, nr):
"""
Calculate the r frontier where we must switch from Nr to Sr
when estimating E[Nr].
"""
for i, r_ in enumerate(r):
if len(r) == i + 1 or r[i+1] != r_ + 1:
# We are at the end of r, or there is a gap in r
self._switch_at = r_
break

Sr = self.smoothedNr
smooth_r_star = (r_ + 1) * Sr(r_+1) / Sr(r_)
unsmooth_r_star = 1.0 * (r_ + 1) * nr[i+1] / nr[i]

std = math.sqrt(self._variance(r_, nr[i], nr[i+1]))
if abs(unsmooth_r_star-smooth_r_star) <= 1.96 * std:
self._switch_at = r_
break

def _variance(self, r, nr, nr_1):
r = float(r)
nr = float(nr)
nr_1 = float(nr_1)
return (r + 1.0)**2 * (nr_1 / nr**2) * (1.0 + nr_1 / nr)

def _renormalize(self, r, nr):
"""
It is necessary to renormalize all the probability estimates to
ensure a proper probability distribution results. This can be done
by keeping the estimate of the probability mass for unseen items as
N(1)/N and renormalizing all the estimates for previously seen items
(as Gale and Sampson (1995) propose). (See M&S P.213, 1999)
"""
prob_cov = 0.0
for r_, nr_ in zip(r, nr):
prob_cov += nr_ * self._prob_measure(r_)
if prob_cov:
self._renormal = (1 - self._prob_measure(0)) / prob_cov

def smoothedNr(self, r):
"""
@return: The number of samples with count r.
@rtype: C{float}
@param r: The amount of freqency.
@type r: C{int}
"""

# Nr = a*r^b (with b < -1 to give the appropriate hyperbolic
# relationship)
# Estimate a and b by simple linear regression technique on
# the logarithmic form of the equation: log Nr = a + b*log(r)

return math.exp(self._intercept + self._slope * math.log(r))

def prob(self, sample):
"""
@param sample: sample of the event
@type sample: C{string}
@return: The sample's probability.
@rtype: C{float}
"""
count = self._freqdist[sample]
p = self._prob_measure(count)
if count == 0:
if self._bins == self._freqdist.B():
p = 0.0
else:
p = p / (1.0 * self._bins - self._freqdist.B())
else:
p = p * self._renormal
return p

def _prob_measure(self, count):
if count == 0 and self._freqdist.N() == 0 :
return 1.0
elif count == 0 and self._freqdist.N() != 0:
return 1.0 * self._freqdist.Nr(1) / self._freqdist.N()

if self._switch_at > count:
Er_1 = 1.0 * self._freqdist.Nr(count+1)
Er = 1.0 * self._freqdist.Nr(count)
else:
Er_1 = self.smoothedNr(count+1)
Er = self.smoothedNr(count)

r_star = (count + 1) * Er_1 / Er
return r_star / self._freqdist.N()

def check(self):
prob_sum = 0.0
for i in range(0, len(self._Nr)):
prob_sum += self._Nr[i] * self._prob_measure(i) / self._renormal
print "Probability Sum:", prob_sum
#assert prob_sum != 1.0, "probability sum should be one!"

def discount(self):
"""
This function returns the total mass of probability transfers from the
seen samples to the unseen samples.
"""
return 1.0 * self.smoothedNr(1) / self._freqdist.N()

def max(self):
return self._freqdist.max()

def samples(self):
return self._freqdist.keys()

def freqdist(self):
return self._freqdist

def __repr__(self):
"""
@rtype: C{string}
@return: A string representation of this C{ProbDist}.
"""
return '<SimpleGoodTuringProbDist based on %d samples>'\
% self._freqdist.N()


class MutableProbDist(ProbDistI):
"""
An mutable probdist where the probabilities may be easily modified. This
simply copies an existing probdist, storing the probability values in a
mutable dictionary and providing an update method.
"""

def __init__(self, prob_dist, samples, store_logs=True):
"""
Creates the mutable probdist based on the given prob_dist and using
the list of samples given. These values are stored as log
probabilities if the store_logs flag is set.

@param prob_dist: the distribution from which to garner the
probabilities
@type prob_dist: ProbDist
@param samples: the complete set of samples
@type samples: sequence of any
@param store_logs: whether to store the probabilities as logarithms
@type store_logs: bool
"""
try:
import numpy
except ImportError:
print "Error: Please install numpy; for instructions see http://www.nltk.org/"
exit()
self._samples = samples
self._sample_dict = dict((samples[i], i) for i in range(len(samples)))
self._data = numpy.zeros(len(samples), numpy.float64)
for i in range(len(samples)):
if store_logs:
self._data[i] = prob_dist.logprob(samples[i])
else:
self._data[i] = prob_dist.prob(samples[i])
self._logs = store_logs

def samples(self):
# inherit documentation
return self._samples

def prob(self, sample):
# inherit documentation
i = self._sample_dict.get(sample)
if i != None:
if self._logs:
return 2**(self._data[i])
else:
return self._data[i]
else:
return 0.0

def logprob(self, sample):
# inherit documentation
i = self._sample_dict.get(sample)
if i != None:
if self._logs:
return self._data[i]
else:
return math.log(self._data[i], 2)
else:
return float('-inf')

def update(self, sample, prob, log=True):
"""
Update the probability for the given sample. This may cause the object
to stop being the valid probability distribution - the user must
ensure that they update the sample probabilities such that all samples
have probabilities between 0 and 1 and that all probabilities sum to
one.

@param sample: the sample for which to update the probability
@type sample: C{any}
@param prob: the new probability
@type prob: C{float}
@param log: is the probability already logged
@type log: C{bool}
"""
i = self._sample_dict.get(sample)
assert i != None
if self._logs:
if log: self._data[i] = prob
else: self._data[i] = math.log(prob, 2)
else:
if log: self._data[i] = 2**(prob)
else: self._data[i] = prob

##//////////////////////////////////////////////////////
## Probability Distribution Operations
##//////////////////////////////////////////////////////

def log_likelihood(test_pdist, actual_pdist):
if (not isinstance(test_pdist, ProbDistI) or
not isinstance(actual_pdist, ProbDistI)):
raise ValueError('expected a ProbDist.')
# Is this right?
return sum(actual_pdist.prob(s) * math.log(test_pdist.prob(s), 2)
for s in actual_pdist.keys())

def entropy(pdist):
probs = [pdist.prob(s) for s in pdist.samples()]
return -sum([p * math.log(p,2) for p in probs])

##//////////////////////////////////////////////////////
## Conditional Distributions
##//////////////////////////////////////////////////////

class ConditionalFreqDist(object):
"""
A collection of frequency distributions for a single experiment
run under different conditions. Conditional frequency
distributions are used to record the number of times each sample
occurred, given the condition under which the experiment was run.
For example, a conditional frequency distribution could be used to
record the frequency of each word (type) in a document, given its
length. Formally, a conditional frequency distribution can be
defined as a function that maps from each condition to the
C{FreqDist} for the experiment under that condition.

The frequency distribution for each condition is accessed using
the indexing operator:

>>> cfdist[3]
<FreqDist with 73 outcomes>
>>> cfdist[3].freq('the')
0.4
>>> cfdist[3]['dog']
2

When the indexing operator is used to access the frequency
distribution for a condition that has not been accessed before,
C{ConditionalFreqDist} creates a new empty C{FreqDist} for that
condition.

Conditional frequency distributions are typically constructed by
repeatedly running an experiment under a variety of conditions,
and incrementing the sample outcome counts for the appropriate
conditions. For example, the following code will produce a
conditional frequency distribution that encodes how often each
word type occurs, given the length of that word type:

>>> cfdist = ConditionalFreqDist()
>>> for word in tokenize.whitespace(sent):
... condition = len(word)
... cfdist[condition].inc(word)

An equivalent way to do this is with the initializer:

>>> cfdist = ConditionalFreqDist((len(word), word) for word in tokenize.whitespace(sent))

"""
def __init__(self, cond_samples=None):
"""
Construct a new empty conditional frequency distribution. In
particular, the count for every sample, under every condition,
is zero.

@param cond_samples: The samples to initialize the conditional
frequency distribution with
@type cond_samples: Sequence of (condition, sample) tuples
"""
self._fdists = {}
if cond_samples:
for (cond, sample) in cond_samples:
self[cond].inc(sample)

def __getitem__(self, condition):
"""
@return: The frequency distribution that encodes the frequency
of each sample outcome, given that the experiment was run
under the given condition. If the frequency distribution for
the given condition has not been accessed before, then this
will create a new empty C{FreqDist} for that condition.
@rtype: C{FreqDist}
@param condition: The condition under which the experiment was run.
@type condition: any
"""
# Create the conditioned freq dist, if it doesn't exist
if condition not in self._fdists:
self._fdists[condition] = FreqDist()
return self._fdists[condition]

def conditions(self):
"""
@return: A list of the conditions that have been accessed for
this C{ConditionalFreqDist}. Use the indexing operator to
access the frequency distribution for a given condition.
Note that the frequency distributions for some conditions
may contain zero sample outcomes.
@rtype: C{list}
"""
return sorted(self._fdists.keys())

def __len__(self):
"""
@return: The number of conditions that have been accessed
for this C{ConditionalFreqDist}.
@rtype: C{int}
"""
return len(self._fdists)

def N(self):
"""
@return: The total number of sample outcomes that have been
recorded by this C{ConditionalFreqDist}.
@rtype: C{int}
"""
return sum(fdist.N() for fdist in self._fdists.values())

def plot(self, *args, **kwargs):
"""
Plot the given samples from the conditional frequency distribution.
For a cumulative plot, specify cumulative=True.
(Requires Matplotlib to be installed.)

@param samples: The samples to plot
@type samples: C{list}
@param title: The title for the graph
@type title: C{str}
@param conditions: The conditions to plot (default is all)
@type conditions: C{list}
"""
try:
import pylab
except ImportError:
raise ValueError('The plot function requires the matplotlib package (aka pylab).'
'See http://matplotlib.sourceforge.net/')

cumulative = _get_kwarg(kwargs, 'cumulative', False)
conditions = _get_kwarg(kwargs, 'conditions', self.conditions())
title = _get_kwarg(kwargs, 'title', '')
samples = _get_kwarg(kwargs, 'samples',
sorted(set(v for c in conditions for v in self[c]))) # this computation could be wasted
if not "linewidth" in kwargs:
kwargs["linewidth"] = 2

for condition in conditions:
if cumulative:
freqs = list(self[condition]._cumulative_frequencies(samples))
ylabel = "Cumulative Counts"
legend_loc = 'lower right'
else:
freqs = [self[condition][sample] for sample in samples]
ylabel = "Counts"
legend_loc = 'upper right'
# percents = [f * 100 for f in freqs] only in ConditionalProbDist?
kwargs['label'] = str(condition)
pylab.plot(freqs, *args, **kwargs)

pylab.legend(loc=legend_loc)
pylab.grid(True, color="silver")
pylab.xticks(range(len(samples)), [str(s) for s in samples], rotation=90)
if title:
pylab.title(title)
pylab.xlabel("Samples")
pylab.ylabel(ylabel)
pylab.show()

def tabulate(self, *args, **kwargs):
"""
Tabulate the given samples from the conditional frequency distribution.

@param samples: The samples to plot
@type samples: C{list}
@param title: The title for the graph
@type title: C{str}
@param conditions: The conditions to plot (default is all)
@type conditions: C{list}
"""

cumulative = _get_kwarg(kwargs, 'cumulative', False)
conditions = _get_kwarg(kwargs, 'conditions', self.conditions())
samples = _get_kwarg(kwargs, 'samples',
sorted(set(v for c in conditions for v in self[c]))) # this computation could be wasted

condition_size = max(len(str(c)) for c in conditions)
print ' ' * condition_size,
for s in samples:
print "%4s" % str(s),
print
for c in conditions:
print "%*s" % (condition_size, str(c)),
if cumulative:
freqs = list(self[c]._cumulative_frequencies(samples))
else:
freqs = [self[c][sample] for sample in samples]

for f in freqs:
print "%4d" % f,
print

def __eq__(self, other):
if not isinstance(other, ConditionalFreqDist): return False
return self.conditions() == other.conditions() \
and all(self[c] == other[c] for c in self.conditions()) # conditions are already sorted
def __ne__(self, other):
return not (self == other)
def __le__(self, other):
if not isinstance(other, ConditionalFreqDist): return False
return set(self.conditions()).issubset(other.conditions()) \
and all(self[c] <= other[c] for c in self.conditions())
def __lt__(self, other):
if not isinstance(other, ConditionalFreqDist): return False
return self <= other and self != other
def __ge__(self, other):
if not isinstance(other, ConditionalFreqDist): return False
return other <= self
def __gt__(self, other):
if not isinstance(other, ConditionalFreqDist): return False
return other < self

def __repr__(self):
"""
@return: A string representation of this
C{ConditionalProbDist}.
@rtype: C{string}
"""
return '<ConditionalProbDist with %d conditions>' % self.__len__()


def __repr__(self):
"""
@return: A string representation of this
C{ConditionalFreqDist}.
@rtype: C{string}
"""
n = len(self._fdists)
return '<ConditionalFreqDist with %d conditions>' % n

class ConditionalProbDistI(object):
"""
A collection of probability distributions for a single experiment
run under different conditions. Conditional probability
distributions are used to estimate the likelihood of each sample,
given the condition under which the experiment was run. For
example, a conditional probability distribution could be used to
estimate the probability of each word type in a document, given
the length of the word type. Formally, a conditional probability
distribution can be defined as a function that maps from each
condition to the C{ProbDist} for the experiment under that
condition.
"""
def __init__(self):
raise AssertionError, 'ConditionalProbDistI is an interface'

def __getitem__(self, condition):
"""
@return: The probability distribution for the experiment run
under the given condition.
@rtype: C{ProbDistI}
@param condition: The condition whose probability distribution
should be returned.
@type condition: any
"""
raise AssertionError

def __len__(self):
"""
@return: The number of conditions that are represented by
this C{ConditionalProbDist}.
@rtype: C{int}
"""
raise AssertionError

def conditions(self):
"""
@return: A list of the conditions that are represented by
this C{ConditionalProbDist}. Use the indexing operator to
access the probability distribution for a given condition.
@rtype: C{list}
"""
raise AssertionError

# For now, this is the only implementation of ConditionalProbDistI;
# but we would want a different implementation if we wanted to build a
# conditional probability distribution analytically (e.g., a gaussian
# distribution), rather than basing it on an underlying frequency
# distribution.
class ConditionalProbDist(ConditionalProbDistI):
"""
A conditional probability distribution modelling the experiments
that were used to generate a conditional frequency distribution.
A C{ConditoinalProbDist} is constructed from a
C{ConditionalFreqDist} and a X{C{ProbDist} factory}:

- The B{C{ConditionalFreqDist}} specifies the frequency
distribution for each condition.
- The B{C{ProbDist} factory} is a function that takes a
condition's frequency distribution, and returns its
probability distribution. A C{ProbDist} class's name (such as
C{MLEProbDist} or C{HeldoutProbDist}) can be used to specify
that class's constructor.

The first argument to the C{ProbDist} factory is the frequency
distribution that it should model; and the remaining arguments are
specified by the C{factory_args} parameter to the
C{ConditionalProbDist} constructor. For example, the following
code constructs a C{ConditionalProbDist}, where the probability
distribution for each condition is an C{ELEProbDist} with 10 bins:

>>> cpdist = ConditionalProbDist(cfdist, ELEProbDist, 10)
>>> print cpdist['run'].max()
'NN'
>>> print cpdist['run'].prob('NN')
0.0813
"""
def __init__(self, cfdist, probdist_factory,
*factory_args, **factory_kw_args):
"""
Construct a new conditional probability distribution, based on
the given conditional frequency distribution and C{ProbDist}
factory.

@type cfdist: L{ConditionalFreqDist}
@param cfdist: The C{ConditionalFreqDist} specifying the
frequency distribution for each condition.
@type probdist_factory: C{class} or C{function}
@param probdist_factory: The function or class that maps
a condition's frequency distribution to its probability
distribution. The function is called with the frequency
distribution as its first argument,
C{factory_args} as its remaining arguments, and
C{factory_kw_args} as keyword arguments.
@type factory_args: (any)
@param factory_args: Extra arguments for C{probdist_factory}.
These arguments are usually used to specify extra
properties for the probability distributions of individual
conditions, such as the number of bins they contain.
@type factory_kw_args: (any)
@param factory_kw_args: Extra keyword arguments for C{probdist_factory}.
"""
self._probdist_factory = probdist_factory
self._cfdist = cfdist
self._factory_args = factory_args
self._factory_kw_args = factory_kw_args

self._pdists = {}
for c in cfdist.conditions():
pdist = probdist_factory(cfdist[c], *factory_args,
**factory_kw_args)
self._pdists[c] = pdist

def __contains__(self, condition):
return condition in self._pdists

def __getitem__(self, condition):
if condition not in self._pdists:
# If it's a condition we haven't seen, create a new prob
# dist from the empty freq dist. Typically, this will
# give a uniform prob dist.
pdist = self._probdist_factory(FreqDist(), *self._factory_args,
**self._factory_kw_args)
self._pdists[condition] = pdist

return self._pdists[condition]

def conditions(self):
return self._pdists.keys()

def __len__(self):
return len(self._pdists)

class DictionaryConditionalProbDist(ConditionalProbDistI):
"""
An alternative ConditionalProbDist that simply wraps a dictionary of
ProbDists rather than creating these from FreqDists.
"""

def __init__(self, probdist_dict):
"""
@param probdist_dict: a dictionary containing the probdists indexed
by the conditions
@type probdist_dict: dict any -> probdist
"""
self._dict = probdist_dict

def __getitem__(self, condition):
# inherit documentation
# this will cause an exception for unseen conditions
return self._dict[condition]

def conditions(self):
# inherit documentation
return self._dict.keys()

##//////////////////////////////////////////////////////
## Adding in log-space.
##//////////////////////////////////////////////////////

# If the difference is bigger than this, then just take the bigger one:
_ADD_LOGS_MAX_DIFF = math.log(1e-30, 2)

def add_logs(logx, logy):
"""
Given two numbers C{logx}=M{log(x)} and C{logy}=M{log(y)}, return
M{log(x+y)}. Conceptually, this is the same as returning
M{log(2**(C{logx})+2**(C{logy}))}, but the actual implementation
avoids overflow errors that could result from direct computation.
"""
if (logx < logy + _ADD_LOGS_MAX_DIFF):
return logy
if (logy < logx + _ADD_LOGS_MAX_DIFF):
return logx
base = min(logx, logy)
return base + math.log(2**(logx-base) + 2**(logy-base), 2)

def sum_logs(logs):
if len(logs) == 0:
# Use some approximation to infinity. What this does
# depends on your system's float implementation.
return _NINF
else:
return reduce(add_logs, logs[1:], logs[0])

##//////////////////////////////////////////////////////
## Probabilistic Mix-in
##//////////////////////////////////////////////////////

class ProbabilisticMixIn(object):
"""
A mix-in class to associate probabilities with other classes
(trees, rules, etc.). To use the C{ProbabilisticMixIn} class,
define a new class that derives from an existing class and from
ProbabilisticMixIn. You will need to define a new constructor for
the new class, which explicitly calls the constructors of both its
parent classes. For example:

>>> class A:
... def __init__(self, x, y): self.data = (x,y)
...
>>> class ProbabilisticA(A, ProbabilisticMixIn):
... def __init__(self, x, y, **prob_kwarg):
... A.__init__(self, x, y)
... ProbabilisticMixIn.__init__(self, **prob_kwarg)

See the documentation for the ProbabilisticMixIn
L{constructor<__init__>} for information about the arguments it
expects.

You should generally also redefine the string representation
methods, the comparison methods, and the hashing method.
"""
def __init__(self, **kwargs):
"""
Initialize this object's probability. This initializer should
be called by subclass constructors. C{prob} should generally be
the first argument for those constructors.

@kwparam prob: The probability associated with the object.
@type prob: C{float}
@kwparam logprob: The log of the probability associated with
the object.
@type logprob: C{float}
"""
if 'prob' in kwargs:
if 'logprob' in kwargs:
raise TypeError('Must specify either prob or logprob '
'(not both)')
else:
ProbabilisticMixIn.set_prob(self, kwargs['prob'])
elif 'logprob' in kwargs:
ProbabilisticMixIn.set_logprob(self, kwargs['logprob'])
else:
self.__prob = self.__logprob = None

def set_prob(self, prob):
"""
Set the probability associated with this object to C{prob}.
@param prob: The new probability
@type prob: C{float}
"""
self.__prob = prob
self.__logprob = None

def set_logprob(self, logprob):
"""
Set the log probability associated with this object to
C{logprob}. I.e., set the probability associated with this
object to C{2**(logprob)}.
@param logprob: The new log probability
@type logprob: C{float}
"""
self.__logprob = logprob
self.__prob = None

def prob(self):
"""
@return: The probability associated with this object.
@rtype: C{float}
"""
if self.__prob is None:
if self.__logprob is None: return None
self.__prob = 2**(self.__logprob)
return self.__prob

def logprob(self):
"""
@return: C{log(p)}, where C{p} is the probability associated
with this object.

@rtype: C{float}
"""
if self.__logprob is None:
if self.__prob is None: return None
self.__logprob = math.log(self.__prob, 2)
return self.__logprob

class ImmutableProbabilisticMixIn(ProbabilisticMixIn):
def set_prob(self, prob):
raise ValueError, '%s is immutable' % self.__class__.__name__
def set_logprob(self, prob):
raise ValueError, '%s is immutable' % self.__class__.__name__

## Helper function for processing keyword arguments

def _get_kwarg(kwargs, key, default):
if key in kwargs:
arg = kwargs[key]
del kwargs[key]
else:
arg = default
return arg

##//////////////////////////////////////////////////////
## Demonstration
##//////////////////////////////////////////////////////

def _create_rand_fdist(numsamples, numoutcomes):
"""
Create a new frequency distribution, with random samples. The
samples are numbers from 1 to C{numsamples}, and are generated by
summing two numbers, each of which has a uniform distribution.
"""
import random
fdist = FreqDist()
for x in range(numoutcomes):
y = (random.randint(1, (1+numsamples)/2) +
random.randint(0, numsamples/2))
fdist.inc(y)
return fdist

def _create_sum_pdist(numsamples):
"""
Return the true probability distribution for the experiment
C{_create_rand_fdist(numsamples, x)}.
"""
fdist = FreqDist()
for x in range(1, (1+numsamples)/2+1):
for y in range(0, numsamples/2+1):
fdist.inc(x+y)
return MLEProbDist(fdist)

def demo(numsamples=6, numoutcomes=500):
"""
A demonstration of frequency distributions and probability
distributions. This demonstration creates three frequency
distributions with, and uses them to sample a random process with
C{numsamples} samples. Each frequency distribution is sampled
C{numoutcomes} times. These three frequency distributions are
then used to build six probability distributions. Finally, the
probability estimates of these distributions are compared to the
actual probability of each sample.

@type numsamples: C{int}
@param numsamples: The number of samples to use in each demo
frequency distributions.
@type numoutcomes: C{int}
@param numoutcomes: The total number of outcomes for each
demo frequency distribution. These outcomes are divided into
C{numsamples} bins.
@rtype: C{None}
"""

# Randomly sample a stochastic process three times.
fdist1 = _create_rand_fdist(numsamples, numoutcomes)
fdist2 = _create_rand_fdist(numsamples, numoutcomes)
fdist3 = _create_rand_fdist(numsamples, numoutcomes)

# Use our samples to create probability distributions.
pdists = [
MLEProbDist(fdist1),
LidstoneProbDist(fdist1, 0.5, numsamples),
HeldoutProbDist(fdist1, fdist2, numsamples),
HeldoutProbDist(fdist2, fdist1, numsamples),
CrossValidationProbDist([fdist1, fdist2, fdist3], numsamples),
GoodTuringProbDist(fdist1),
SimpleGoodTuringProbDist(fdist1),
SimpleGoodTuringProbDist(fdist1, 7),
_create_sum_pdist(numsamples),
]

# Find the probability of each sample.
vals = []
for n in range(1,numsamples+1):
vals.append(tuple([n, fdist1.freq(n)] +
[pdist.prob(n) for pdist in pdists]))

# Print the results in a formatted table.
print ('%d samples (1-%d); %d outcomes were sampled for each FreqDist' %
(numsamples, numsamples, numoutcomes))
print '='*9*(len(pdists)+2)
FORMATSTR = ' FreqDist '+ '%8s '*(len(pdists)-1) + '| Actual'
print FORMATSTR % tuple(`pdist`[1:9] for pdist in pdists[:-1])
print '-'*9*(len(pdists)+2)
FORMATSTR = '%3d %8.6f ' + '%8.6f '*(len(pdists)-1) + '| %8.6f'
for val in vals:
print FORMATSTR % val

# Print the totals for each column (should all be 1.0)
zvals = zip(*vals)
def sum(lst): return reduce(lambda x,y:x+y, lst, 0)
sums = [sum(val) for val in zvals[1:]]
print '-'*9*(len(pdists)+2)
FORMATSTR = 'Total ' + '%8.6f '*(len(pdists)) + '| %8.6f'
print FORMATSTR % tuple(sums)
print '='*9*(len(pdists)+2)

# Display the distributions themselves, if they're short enough.
if len(`str(fdist1)`) < 70:
print ' fdist1:', str(fdist1)
print ' fdist2:', str(fdist2)
print ' fdist3:', str(fdist3)
print

print 'Generating:'
for pdist in pdists:
fdist = FreqDist(pdist.generate() for i in range(5000))
print '%20s %s' % (pdist.__class__.__name__[:20], str(fdist)[:55])
print

def gt_demo():
from nltk import corpus
emma_words = corpus.gutenberg.words('austen-emma.txt')
fd = FreqDist(emma_words)
gt = GoodTuringProbDist(fd)
sgt = SimpleGoodTuringProbDist(fd)
katz = SimpleGoodTuringProbDist(fd, 7)
print '%18s %8s %12s %14s %12s' \
% ("word", "freqency", "GoodTuring", "SimpleGoodTuring", "Katz-cutoff" )
for key in fd.keys():
print '%18s %8d %12e %14e %12e' \
% (key, fd[key], gt.prob(key), sgt.prob(key), katz.prob(key))

if __name__ == '__main__':
demo(6, 10)
demo(5, 5000)
gt_demo()

__all__ = ['ConditionalFreqDist', 'ConditionalProbDist',
'ConditionalProbDistI', 'CrossValidationProbDist',
'DictionaryConditionalProbDist', 'DictionaryProbDist', 'ELEProbDist',
'FreqDist', 'GoodTuringProbDist', 'SimpleGoodTuringProbDist', 'HeldoutProbDist',
'ImmutableProbabilisticMixIn', 'LaplaceProbDist', 'LidstoneProbDist',
'MLEProbDist', 'MutableProbDist', 'ProbDistI', 'ProbabilisticMixIn',
'UniformProbDist', 'WittenBellProbDist', 'add_logs',
'log_likelihood', 'sum_logs', 'entropy']

Change log

r8807 by stevenbird1 on Aug 7, 2011   Diff
cast label to be a string for correct
plotting; resolves  issue 671 
Go to: 
Sign in to write a code review

Older revisions

r8804 by StevenBird1 on Jul 28, 2011   Diff
accepted patch contributed by
rico.sennrich to fix issue with
MLEProbDist initializer; resolves
 issue 702 .
r8776 by StevenBird1 on Apr 9, 2011   Diff
Fixed syntax errors for Python 2.4
compatibility.  Resolves  issue 581 .
r8737 by stevenbird1 on Mar 16, 2011   Diff
Fixed stale documentation for
FreqDist.tabulate, resolves  issue 647 
All revisions of this file

File info

Size: 87287 bytes, 2339 lines

File properties

svn:eol-style
native
svn:keywords
Author Date Id Revision
Powered by Google Project Hosting