Zero-Inflated Poisson Model with Infer.NET

A demonstration of implementing and inferring parameters for a Zero-Inflated Poisson (ZIP) model using Microsoft's Infer.NET probabilistic programming framework on .NET 8.0.

Overview

This project showcases Bayesian inference for a Zero-Inflated Poisson distribution, a statistical model commonly used when count data contains an excess of zeros beyond what a standard Poisson distribution would predict.

What is a Zero-Inflated Poisson Model?

A Zero-Inflated Poisson (ZIP) model is useful for modeling count data with excess zeros. The model assumes that the data generating process has two components:

1. Structural Zeros: Generated by a Bernoulli process (coin flip) that produces zeros with probability π
2. Count Process: When the Bernoulli outcome is "tails," a sample is drawn from a Poisson(λ) distribution, which may also produce zeros

This is analogous to deciding whether to visit a store (coin flip). If you don't go (heads), you buy 0 items. If you do go (tails), the number of items purchased follows a Poisson distribution (which could still be 0 if the item is out of stock).

The Model

The generative story for each data point:

1. Flip a weighted coin with bias π (probability of heads)
2. If heads: return 0 (structural zero)
3. If tails: sample from Poisson(λ) distribution (count process)

Parameters to Infer:

• π (pi): The probability of generating a structural zero (coin bias)
• λ (lambda): The mean of the Poisson distribution

Prior Distributions:

• π ~ Beta(1, 1) - uniform prior over [0, 1]
• λ ~ Gamma(1, 4) - weakly informative prior for the Poisson rate

The model uses Expectation Propagation (EP) as the inference algorithm to compute posterior distributions for both parameters.

Prerequisites

• .NET 8.0 SDK or later
  • Download from: https://dotnet.microsoft.com/download/dotnet/8.0
• Operating System: Windows, macOS, or Linux
• IDE (Optional): Visual Studio 2022, Visual Studio Code, or JetBrains Rider

Dependencies

The project uses the following NuGet packages:

• Microsoft.ML.Probabilistic (v0.4.2301.301) - Core probabilistic programming framework
• Microsoft.ML.Probabilistic.Compiler (v0.4.2301.301) - Compilation support for model inference

These are automatically restored when building the project.

Building the Project

Using .NET CLI

1. Clone the repository:

   git clone https://github.com/yourusername/ZeroInflatedPoisson-Infer.NET.git
   cd ZeroInflatedPoisson-Infer.NET

2. Restore dependencies:

   dotnet restore

3. Build the project:

   dotnet build

   For a release build:

   dotnet build -c Release

Using Visual Studio

1. Open ZeroInflatedPoisson.sln in Visual Studio 2022
2. Press Ctrl+Shift+B to build the solution
3. Dependencies will be restored automatically

Running the Application

Using .NET CLI

From the repository root:

dotnet run --project ZeroInflatedPoisson

Or navigate to the project directory:

cd ZeroInflatedPoisson
dotnet run

Using Visual Studio

1. Set ZeroInflatedPoisson as the startup project (if not already)
2. Press F5 to run with debugging, or Ctrl+F5 to run without debugging

Expected Output

The program will:

1. Generate 1000 synthetic data points from a ZIP model with:
   • True π = 0.3 (30% probability of structural zeros)
   • True λ = 2.0 (Poisson mean)
2. Perform Bayesian inference to estimate these parameters
3. Display the posterior means:

   E(pi) = 0.299...
   E(lambda) = 2.01...
   Press any key ...
   

The inferred values should be close to the true parameters used to generate the data.

Project Structure

ZeroInflatedPoisson-Infer.NET/
├── ZeroInflatedPoisson/
│   ├── Program.cs                  # Main application code
│   └── ZeroInflatedPoisson.csproj  # Project file (.NET 8.0)
├── ZeroInflatedPoisson.sln         # Solution file
├── README.md                       # This file
└── LICENSE                         # MIT License

Understanding the Code

Key Components

1. Data Generation (SampleData method):

   • Simulates data from the ZIP model
   • Used to create synthetic observations for testing inference

2. Model Definition:

   • Uses Infer.NET's modeling API to declare random variables
   • Encodes the ZIP generative process using conditional statements
   • Implements the mixture of structural zeros and Poisson counts

3. Inference:

   • Uses Expectation Propagation (EP) algorithm
   • Computes posterior distributions over unknown parameters
   • Returns Beta and Gamma posterior distributions

Customization

You can modify the following parameters in Program.cs:

int N = 1000;           // Number of data points
double pi = 0.3;        // True coin bias (structural zero probability)
double lambda = 2.0;    // True Poisson mean

Or adjust the prior distributions:

Beta cPrior = new Beta(1, 1);    // Prior for π
Gamma pPrior = new Gamma(1, 4);  // Prior for λ

Applications

Zero-Inflated Poisson models are commonly used in:

• Healthcare: Modeling hospital visits (many people have zero visits)
• Ecology: Counting species occurrences (many sites have zero observations)
• Manufacturing: Defect counts (many items have zero defects)
• Insurance: Claim counts (many policyholders file zero claims)
• Marketing: Purchase counts (many customers make zero purchases)

About Infer.NET

Infer.NET is a framework for running Bayesian inference in graphical models. It can be used for a variety of different probabilistic inference tasks, including:

• Classification
• Regression
• Clustering
• Dimensionality reduction
• Time-series analysis

The framework is developed by Microsoft Research and is open-source under the MIT license.

License

This project is licensed under the MIT License - see the LICENSE file for details.

References

• Infer.NET Documentation
• Infer.NET GitHub Repository
• Zero-Inflated Poisson Regression

Contributing

Contributions are welcome! Please feel free to submit issues or pull requests.

Author

Originally created as a demonstration of Bayesian inference with Infer.NET.
Updated to .NET 8.0 and modern Infer.NET framework (October 2025).