Daniel Emaasit
Data Scientist @HaystaxTech, Ph.D. Candidate @UNLV, Bayesian Machine Learning Researcher, Organizer of Data Science Meetups. User of #PyMC3.
Introduction to Probabilistic Machine Learning with PyMC3
Daniel Emaasit
Data Scientist
Haystax Technology
Bayesian Data Science DC Meetup
April 26, 2018
Data Science & Cybersecurity Meetup
Materials
Download slides & code: bit.ly/intro-pml
Application (1/3)
- Optimizing expensive functions in autonomous vehicles (using Bayesian optimization).
Application (2/3)
- Probabilistic approach to ranking & matching gamers.
Application (3/3)
- Supplying internet to remote areas (using Gaussian processes).
Media Attention
Academics flocking to Industry
Intro to Probabilistic Machine Learning
ML: A Probabilistic Perspective (1/3)
- Probabilistic ML:
- An Interdisciplinary field that develops both the mathematical foundations and practical applications of systems that learn models of data. (Ghahramani, 2018)
ML: A Probabilistic Perspective (2/3)
- A Model:
- A model describes data that one could observe from a system (Ghahramani, 2014)
- Use the mathematics of probability theory to express all forms of uncertainty
Generative Process
Inference
ML: A Probabilistic Perspective (3/3)
P(\theta \mid y) = \frac{P(y \mid \theta) \, P(\theta)}{P(y)}
- \(\mathbf{\theta}\) = parameters e.g. coefficients
\(p(\mathbf{\theta})\) = prior over the parameters
\(p(\textbf{y} \mid \mathbf{\theta})\) = likelihood given the covariates & parameters
\(p(\textbf{y})\) = data distribution to ensure normalization
\(p(\mathbf{\theta} \mid \textbf{y})\) = posterior over the parameters, given observed data
where:
Probabilistic ML Vs Traditional ML
| Algorithmic ML | Probabilistic ML | |
|---|---|---|
| Examples | K-Means, Random Forest | GMM, Gaussian Process |
| Specification | Model + Algorithm combined | Model & Inference separate |
| Unknowns | Parameters | Random variables |
| Inference | Optimization (MLE) | Bayes (MCMC, VI) |
| Regularization | Penalty terms | Priors |
| Solution | Best fitting parameter | Full posterior distribution |
Limitations of deep learning
- Deep learning systems give amazing performance on many benchmark tasks but they are generally:
- very data hungry (e.g. often millions of examples)
- very compute-intensive to train and deploy (cloud GPU resources)
- poor at representing uncertainty
- easily fooled by adversarial examples
- finicky to optimize: choice of architecture, learning procedure, etc, require expert knowledge and experimentation
- uninterpretable black-boxes, lacking in transparency, difficult to trust
Probabilistic Programming
Probabilistic Programming (1/2)
- Probabilisic Programming (PP) Languages:
- Software packages that take a model and then automatically generate inference routines (even source code!) e.g Pyro, Stan, Infer.Net, PyMC3, TensorFlow Probability, etc.
Probabilistic Programming (2/2)
- Steps in Probabilisic ML:
- Build the model (Joint probability distribution of all the relevant variables)
- Incorporate the observed data
- Perform inference (to learn distributions of the latent variables)
Demo
Resources to get started
- Winn, J., Bishop, C. M., Diethe, T. (2015). Model-Based Machine Learning. Microsoft Research Cambridge.
- R. McElreath (2012) Statistical Rethinking: A Bayesian Course with Examples in R and Stan (& PyMC3 & brms too)
- Probabilistic Programming and Bayesian Methods for Hackers: Fantastic book with many applied code examples.
Thank You!
Appendix
References
- Ghahramani, Z. (2015). Probabilistic machine learning and artificial intelligence. Nature, 521(7553), 452.
- Bishop, C. M. (2013). Model-based machine learning. Phil. Trans. R. Soc. A, 371(1984), 20120222.
- Murphy, K. P. (2012). Machine learning: a probabilistic perspective. MIT Press.
- Barber, D. (2012). Bayesian reasoning and machine learning. Cambridge University Press.
Introduction to Probabilistic Machine Learning with PyMC3
By Daniel Emaasit
Introduction to Probabilistic Machine Learning with PyMC3
Introduction to Probabilistic Machine Learning with PyMC3
