Lea - Discrete probability distributions in Python

WARNING: Lea project has moved to Bitbucket.

The present Lea project is no longer maintained on Google Code. Please continue to follow Lea on Bitbucket, where all the resources have been moved (sources, wiki, issues).

Welcome in Lea!

NEW: 17 July 2015 - Lea 2.1.2 is there (bug fix of withProb method)!

See a presentation of Lea (pdf) done at FOSDEM 15/Python devroom on 31^st January 2015

What is Lea?

Lea is a Python package aiming at working with discrete probability distributions in an intuitive way. It allows you to model a broad range of random phenomenons, like dice throwing, coin tossing, gambling, weather, finance, etc. More generally, Lea may be used for any finite set of discrete values having known probability: numbers, booleans, date/times, symbols, … Each probability distribution is modeled as a plain object, which can be named, displayed, queried or processed to produce new probability distributions.

Lea can be used in any Python program or interactively, in the Python console. As a basic example, the statements below define and display the probability of a fair six-sided die :

```

die = Lea.fromVals(1,2,3,4,5,6) die 1 : 1/6 2 : 1/6 3 : 1/6 4 : 1/6 5 : 1/6 6 : 1/6 ```

and here is how you can model a biased coin, then make a random sample of 10 throws :

```

flip = Lea.fromValFreqsDict({'head': 67, 'tail': 33}) flip head : 67/100 tail : 33/100 flip.random(10) ('head', 'head', 'tail', 'head', 'head', 'head', 'head', 'tail', 'head', 'head') ```

Lea allows you to compute new probability distributions from existing ones, by using different transformation means: arithmetic operators, logical operators, functions, conditions and cartesian product. For example, this is how you can count the probability distribution of number of 'heads' on 2 throws :

```

flipCount = Lea.fromValFreqsDict({1: 67, 0: 33}) flipCount 0 : 33/100 1 : 67/100 flipCount2 = flipCount + flipCount.clone() flipCount2 0 : 1089/10000 1 : 4422/10000 2 : 4489/10000 then, on 4 throws : flipCount4 = flipCount.times(4) 0 : 1185921/100000000 1 : 9631116/100000000 2 : 29331126/100000000 3 : 39700716/100000000 4 : 20151121/100000000 print (flipCount4.asFloat()) 0 : 0.011859 1 : 0.096311 2 : 0.293311 3 : 0.397007 4 : 0.201511 ```

Also, comparison operators can be used to derive boolean probability distributions:

```

flipCount4 >= 3 False : 40148163/100000000 True : 59851837/100000000 (1 <= flipCount4) & (flipCount4 < 4) False : 10668521/50000000 True : 39331479/50000000 ```

Lea provides a large set of operations that allow you to model complex stochastic processes. Advanced operations allow to handle conditional probabilities, including Bayesian networks and Markov chains.

Leapp : a probabilistic programming language

As of version 2, the Lea package includes a small probabilistic programming language (PPL) called Leapp. It provides concise syntax to make use of Lea as easy as possible, … especially for non-Python programmers! Here are some above Python statements revamped in Leapp (lea> is the prompt!):

[Leapp] lea> die = ?(1,2,3,4,5,6) lea> flip = ?{'head': 67%, 'tail': 33%} lea> flip head : 67/100 tail : 33/100 lea> flip$(10) ('head', 'head', 'head', 'head', 'head', 'tail', 'head', 'head', 'tail', 'tail') lea> flipCount = ?{1: 67%, 0: 33%} lea> flipCount2 = flipCount + ?flipCount lea> flipCount4 = ?[4]flipCount lea> :. flipCount4 0 : 0.011859 1 : 0.096311 2 : 0.293311 3 : 0.397007 4 : 0.201511

Do you notice the syntax leap compared to Python statements?

Note that Leapp is not a true programming language. It is just a thin "syntactic sugar" layer on top of Python / Lea. The good news is that you can use standard Python syntax and put Leapp expressions as needed (or the opposite!) ; your favorite Python modules can be used as usual.

Lea features

Here are the main features of Lea :

• scope : finite discrete probability distributions
• can assign probabilities on any hashable Python object
• standard distribution indicators + information theory
• probability stored as integers (no rounding errors)
• probability distribution calculus based on arithmetic, comparison, boolean operators and functions
• generation of random values
• joint tables, marginalisation
• conditional probabilities
• Bayesian networks
• Markov chains (basic)
• Leapp, a light PPL (probabilistic programming language) ⁽*⁾
• comprehensive tutorials (Wiki)
• runs on Python 2 or 3
• open-source project, LGPL license

⁽*⁾ The "probabilistic programming" nature of Lea/Leapp is advocated in the small apologia P("Hello world!") = 0.28.

To learn more, read the Lea tutorial - Leapp flavor or the Lea tutorial - Python flavor.

For installation instructions, see Installation.

Please send your comments, critics, suggestions, bug reports, … in English or French by E-mail to: pie.denis@skynet.be. You are more than welcome / bienvenus !

You can also post issues in the present project site.

Project author, administrator : Pierre Denis (Louvain-la-Neuve, Belgium)