Probabilistic Probabilistic Programming Programming A Brief introduction to Probabilistic Programming and Python Late August 2015 [email protected] All opinions my own 

Who am I? Who am I? I work as a Data Scientist for a large Telecommunications Company Masters in Mathematics Interned at Amazon Was a consultant for a while Occasional contributor to Pandas and other projects Co-organizer of the Data Science Meetup in Luxembourg Member of Royal Statistical Society and NumFOCUS @springcoil 

What is Probabilistic Programming What is Probabilistic Programming Basically using random variables instead of variables Allows you to create a generative story rather than a black box A different tool to Machine Learning A different paradigm to frequentist statistics Forces you to be explicit about your 'subjective' assumptions 

Source: Oliver Grisel 

Source: Oliver Grisel 

Bayesian Statistics Bayesian Statistics I studied Mathematics, and encountered in textbooks Bayesians This is a hard area to do by pen and paper, and most integrals can't be solved in exact form Thankfully there was an invention of Monte Carlo Simulations These simulations are used to approximate your likelihood function 

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Some terminology Some terminology 

Attribution: Quantopian blog 

How do you pick your prior? How do you pick your prior? This is a bit of an art You generally base the prior on experience As you add more data this matters less and less 

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Huh but isn't Probabilistic Huh but isn't Probabilistic Programming just Stan and BUGS? Programming just Stan and BUGS? 

No in Python you have PyMC3 No in Python you have PyMC3 A complete rewrite of PyMC2 now in 'Beta' status Based upon Theano Computational techniques for handling gradients Automatic Differentiation and GPU speedup Theano - is also used in deep learning! Currently there is a project to port ' ' from I gave a thorough tutorial on this - Key authors: John Salvatier, Thomas Wiecki, Chris Fonnesbeck BMH PyMC2 to PyMC3 my github 

Case study: Rugby Analytics Case study: Rugby Analytics I wanted to do a model of the Six Nations last year. I wanted to build an understandable model to predict the winner Key Info: Inferring the 'strength' of each team. We only have scoring data, which is noisy hence Bayesian Stats 

What did I do? What did I do? 1. I picked Gamma as a prior for all teams 2. I used a Hierarchical Model because I wanted home advantage to be stronger for stronger teams based 3. From this I was able to create a novel model based only on historical results and scoring intensity 4. I simulated the likelihood function using MCMC 

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Run the model Run the model 

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What actually happened What actually happened The model incorrectly predicted that England would come out on top. Ireland actually won by points difference of 6 points. It really came down to the wire! "Prediction is difficult especially about the future" One of the problems is what we call 'over-shrinkage' and you can delve into the results to see what the errors are, my model was within the errors. 

Lessons learned Lessons learned I can build an explainable model using PyMC2 and PyMC3 Generative stories help you build up interest with your colleagues Communication is the 'last mile' problem of Data Science PyMC3 is cool please use it and please contribute 

Wanna learn more? Wanna learn more? BMH BMH Jake VanDerPlas PyMC3 PyMC3 [email protected] [email protected] 

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