Probabilistic Programming in Python: Bayesian Modeling and Probabilistic Machine Learning with PyTensor
Project description
PyMC (formerly PyMC3) is a Python package for Bayesian statistical modeling focusing on advanced Markov chain Monte Carlo (MCMC) and variational inference (VI) algorithms. Its flexibility and extensibility make it applicable to a large suite of problems.
Check out the PyMC overview, or one of the many examples! For questions on PyMC, head on over to our PyMC Discourse forum.
Features
Intuitive model specification syntax, for example, x ~ N(0,1) translates to x = Normal('x',0,1)
Powerful sampling algorithms, such as the No U-Turn Sampler, allow complex models with thousands of parameters with little specialized knowledge of fitting algorithms.
Variational inference: ADVI for fast approximate posterior estimation as well as mini-batch ADVI for large data sets.
- Relies on PyTensor which provides:
Computation optimization and dynamic C or JAX compilation
NumPy broadcasting and advanced indexing
Linear algebra operators
Simple extensibility
Transparent support for missing value imputation
Linear Regression Example
Plant growth can be influenced by multiple factors, and understanding these relationships is crucial for optimizing agricultural practices.
Imagine we conduct an experiment to predict the growth of a plant based on different environmental variables.
import pymc as pm
# Taking draws from a normal distribution
seed = 42
x_dist = pm.Normal.dist(shape=(100, 3))
x_data = pm.draw(x_dist, random_seed=seed)
# Independent Variables:
# Sunlight Hours: Number of hours the plant is exposed to sunlight daily.
# Water Amount: Daily water amount given to the plant (in milliliters).
# Soil Nitrogen Content: Percentage of nitrogen content in the soil.
# Dependent Variable:
# Plant Growth (y): Measured as the increase in plant height (in centimeters) over a certain period.
# Define coordinate values for all dimensions of the data
coords={
"trial": range(100),
"features": ["sunlight hours", "water amount", "soil nitrogen"],
}
# Define generative model
with pm.Model(coords=coords) as generative_model:
x = pm.Data("x", x_data, dims=["trial", "features"])
# Model parameters
betas = pm.Normal("betas", dims="features")
sigma = pm.HalfNormal("sigma")
# Linear model
mu = x @ betas
# Likelihood
# Assuming we measure deviation of each plant from baseline
plant_growth = pm.Normal("plant growth", mu, sigma, dims="trial")
# Generating data from model by fixing parameters
fixed_parameters = {
"betas": [5, 20, 2],
"sigma": 0.5,
}
with pm.do(generative_model, fixed_parameters) as synthetic_model:
idata = pm.sample_prior_predictive(random_seed=seed) # Sample from prior predictive distribution.
synthetic_y = idata.prior["plant growth"].sel(draw=0, chain=0)
# Infer parameters conditioned on observed data
with pm.observe(generative_model, {"plant growth": synthetic_y}) as inference_model:
idata = pm.sample(random_seed=seed)
summary = pm.stats.summary(idata, var_names=["betas", "sigma"])
print(summary)From the summary, we can see that the mean of the inferred parameters are very close to the fixed parameters
Params |
mean |
sd |
hdi_3% |
hdi_97% |
mcse_mean |
mcse_sd |
ess_bulk |
ess_tail |
r_hat |
|---|---|---|---|---|---|---|---|---|---|
betas[sunlight hours] |
4.972 |
0.054 |
4.866 |
5.066 |
0.001 |
0.001 |
3003 |
1257 |
1 |
betas[water amount] |
19.963 |
0.051 |
19.872 |
20.062 |
0.001 |
0.001 |
3112 |
1658 |
1 |
betas[soil nitrogen] |
1.994 |
0.055 |
1.899 |
2.107 |
0.001 |
0.001 |
3221 |
1559 |
1 |
sigma |
0.511 |
0.037 |
0.438 |
0.575 |
0.001 |
0 |
2945 |
1522 |
1 |
# Simulate new data conditioned on inferred parameters
new_x_data = pm.draw(
pm.Normal.dist(shape=(3, 3)),
random_seed=seed,
)
new_coords = coords | {"trial": [0, 1, 2]}
with inference_model:
pm.set_data({"x": new_x_data}, coords=new_coords)
pm.sample_posterior_predictive(
idata,
predictions=True,
extend_inferencedata=True,
random_seed=seed,
)
pm.stats.summary(idata.predictions, kind="stats")The new data conditioned on inferred parameters would look like:
Output |
mean |
sd |
hdi_3% |
hdi_97% |
|---|---|---|---|---|
plant growth[0] |
14.229 |
0.515 |
13.325 |
15.272 |
plant growth[1] |
24.418 |
0.511 |
23.428 |
25.326 |
plant growth[2] |
-6.747 |
0.511 |
-7.740 |
-5.797 |
# Simulate new data, under a scenario where the first beta is zero
with pm.do(
inference_model,
{inference_model["betas"]: inference_model["betas"] * [0, 1, 1]},
) as plant_growth_model:
new_predictions = pm.sample_posterior_predictive(
idata,
predictions=True,
random_seed=seed,
)
pm.stats.summary(new_predictions, kind="stats")The new data, under the above scenario would look like:
Output |
mean |
sd |
hdi_3% |
hdi_97% |
|---|---|---|---|---|
plant growth[0] |
12.149 |
0.515 |
11.193 |
13.135 |
plant growth[1] |
29.809 |
0.508 |
28.832 |
30.717 |
plant growth[2] |
-0.131 |
0.507 |
-1.121 |
0.791 |
Getting started
If you already know about Bayesian statistics:
The PyMC tutorial
PyMC examples and the API reference
Learn Bayesian statistics with a book together with PyMC
Bayesian Analysis with Python (third edition) by Osvaldo Martin: Great introductory book.
Probabilistic Programming and Bayesian Methods for Hackers: Fantastic book with many applied code examples.
PyMC port of the book “Doing Bayesian Data Analysis” by John Kruschke as well as the first edition.
PyMC port of the book “Bayesian Cognitive Modeling” by Michael Lee and EJ Wagenmakers: Focused on using Bayesian statistics in cognitive modeling.
Audio & Video
Here is a YouTube playlist gathering several talks on PyMC.
You can also find all the talks given at PyMCon 2020 here.
The “Learning Bayesian Statistics” podcast helps you discover and stay up-to-date with the vast Bayesian community. Bonus: it’s hosted by Alex Andorra, one of the PyMC core devs!
Installation
To install PyMC on your system, follow the instructions on the installation guide.
Citing PyMC
Please choose from the following:
PyMC: A Modern and Comprehensive Probabilistic Programming Framework in Python, Abril-Pla O, Andreani V, Carroll C, Dong L, Fonnesbeck CJ, Kochurov M, Kumar R, Lao J, Luhmann CC, Martin OA, Osthege M, Vieira R, Wiecki T, Zinkov R. (2023)
DOIs for specific versions are shown on Zenodo and under Releases
Contact
We are using discourse.pymc.io as our main communication channel.
To ask a question regarding modeling or usage of PyMC we encourage posting to our Discourse forum under the “Questions” Category. You can also suggest feature in the “Development” Category.
You can also follow us on these social media platforms for updates and other announcements:
To report an issue with PyMC please use the issue tracker.
Finally, if you need to get in touch for non-technical information about the project, send us an e-mail.
License
Software using PyMC
General purpose
Bambi: BAyesian Model-Building Interface (BAMBI) in Python.
calibr8: A toolbox for constructing detailed observation models to be used as likelihoods in PyMC.
gumbi: A high-level interface for building GP models.
SunODE: Fast ODE solver, much faster than the one that comes with PyMC.
pymc-learn: Custom PyMC models built on top of pymc3_models/scikit-learn API
Domain specific
Exoplanet: a toolkit for modeling of transit and/or radial velocity observations of exoplanets and other astronomical time series.
beat: Bayesian Earthquake Analysis Tool.
CausalPy: A package focussing on causal inference in quasi-experimental settings.
Please contact us if your software is not listed here.
Papers citing PyMC
See Google Scholar here and here for a continuously updated list.
Contributors
See the GitHub contributor page. Also read our Code of Conduct guidelines for a better contributing experience.
Support
PyMC is a non-profit project under NumFOCUS umbrella. If you want to support PyMC financially, you can donate here.
Professional Consulting Support
You can get professional consulting support from PyMC Labs.
Sponsors
Thanks to our contributors
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