Uncertainty: Probabilistic Models with Pomegranate 1.1.2

Overview

This repository contains a small collection of self-contained Python examples that demonstrate core probabilistic models using the pomegranate library (version 1.1.2):

• A Markov chain over weather states (sun/rain)
• A Hidden Markov Model (HMM) for inferring hidden weather from umbrella observations
• A Bayesian network for reasoning about rain, track maintenance, train delays, and missed appointments

The code is written as minimal, readable scripts intended for teaching and experimentation, and has been migrated to the newer pomegranate 1.1.x API with integer-encoded categorical variables.

Learning objectives

Working through this project you can learn how to:

• Represent simple discrete probabilistic models (Markov chains, HMMs, Bayesian networks)
• Encode categorical variables as integer indices compatible with pomegranate 1.1.x
• Compute likelihoods and perform inference with pomegranate
• Sample from probabilistic models and interpret the results in human-readable form

Requirements and installation

This project targets Python 3.11+ (the examples were developed against a recent CPython and pomegranate 1.1.2).

Core dependencies (see requirements.txt):

• pomegranate==1.1.2
• torch
• numpy==2.3.5

To set up a virtual environment and install dependencies:

python -m venv .venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate
pip install -r requirements.txt

Note: pomegranate 1.1.x uses PyTorch under the hood, so installing torch first (or via requirements.txt) is required.

Project structure

.
├── bayesnet/      # Bayesian network model and related examples
│   ├── model.py        # Defines the BN structure and conditional distributions
│   ├── likelihood.py   # Computes likelihood of an observation under the BN
│   ├── inference.py    # Performs inference with partial evidence using MaskedTensor
│   └── sample.py       # Draws samples and performs simple rejection sampling
├── chain/         # Markov chain (non-hidden) example
│   └── model.py        # Simple 2-state weather Markov chain and sampling
├── hmm/           # Hidden Markov Model example
│   ├── model.py        # Defines a 2-state HMM and emission/transition structure
│   └── sequence.py     # Encodes observations and decodes most likely state sequence
├── requirements.txt
└── lecture.pdf    # Slide deck or notes (not required to run the code)

Usage: running the examples

All scripts are designed to be run directly from the repository root with Python.

Markov chain example

A simple 2-state Markov chain over weather states (sun/rain):

python -m chain.model

This will:

• Construct a Markov chain with start distribution P(X_0) and transition matrix P(X_t | X_{t-1})
• Sample 50 states from the chain and print them as integer indices (0 for "sun", 1 for "rain")

You can map indices back to labels using chain.model.STATES if you modify or extend the example.

Hidden Markov Model example

A 2-state HMM where the hidden weather (sun/rain) generates observable umbrella usage:

python -m hmm.sequence

This will:

• Define a fixed observed sequence of umbrella usage (strings)
• Encode observations to integer categories using hmm.model.OBSERVATION_STATES
• Use a DenseHMM to predict the most likely sequence of hidden weather states
• Decode and print human-readable weather labels using hmm.model.WEATHER_STATES

Bayesian network examples

The Bayesian network models the relationships:

• rain → maintenance → train → appointment
• With additional edges rain → train and rain → maintenance

All variables are discrete and integer-encoded:

• RAIN_STATES = ["none", "light", "heavy"]
• MAINTENANCE_STATES = ["yes", "no"]
• TRAIN_STATES = ["on time", "delayed"]
• APPOINTMENT_STATES = ["attend", "miss"]

Model definition

python -m bayesnet.model

bayesnet/model.py primarily defines the BN and does not print output by itself, but it is imported by the other scripts.

Likelihood of an observation

python -m bayesnet.likelihood

This script:

• Encodes an observation ["none", "no", "on time", "attend"] into integer indices
• Computes P(rain=none, maintenance=no, train=on time, appointment=attend) using model.probability
• Prints the scalar probability value

Inference with partial evidence

python -m bayesnet.inference

This script:

• Builds a torch.masked.MaskedTensor representing a single sample
• Observes train = "delayed" and leaves other variables unobserved
• Calls model.predict_proba to get marginal distributions for each variable
• Prints a readable distribution over the states of rain, maintenance, train, and appointment

Sampling and rejection sampling

python -m bayesnet.sample

This script:

• Draws many samples from the BN using model.sample
• Decodes integer samples back to string labels
• Uses rejection sampling to approximate the distribution of appointment given that train is "delayed"
• Prints the resulting counts as a collections.Counter

Probabilistic models illustrated

• Markov chain (in chain/): models a sequence of states where the next state depends only on the current state via a transition matrix.
• Hidden Markov Model (HMM) (in hmm/): models a sequence of hidden states (weather) that emit observable symbols (umbrella usage). Inference recovers the most likely hidden sequence.
• Bayesian network (in bayesnet/): a directed acyclic graph over discrete variables that supports computing joint probabilities, conditional probabilities, and posterior distributions given evidence.

All examples use integer-encoded categorical variables to match the pomegranate 1.1.x API.

Migration and version notes

These examples were migrated from older pomegranate APIs to pomegranate 1.1.2 and include several important patterns:

• Use Categorical and ConditionalCategorical from pomegranate.distributions instead of the older DiscreteDistribution and ConditionalProbabilityTable style.
• Use MarkovChain from pomegranate.markov_chain and BayesianNetwork from pomegranate.bayesian_network.
• Use DenseHMM from pomegranate.hmm for hidden Markov models.
• Represent observations and states as integer indices, not strings, when calling probability, sample, predict, and predict_proba.
• For Bayesian network inference with partially observed data, use torch.masked.MaskedTensor as demonstrated in bayesnet/inference.py.

If you run into API or shape errors, check that:

• You are using pomegranate==1.1.2 (or a compatible 1.1.x release)
• Your inputs are integer-encoded with shapes matching what the models expect (see the example scripts)

License

No explicit license is included in this repository. If you intend to reuse or redistribute this code beyond personal or educational purposes, please add an appropriate license file (for example, MIT, BSD, or Apache-2.0) according to your needs.