Getting Started with Infer.NET: Examples and Best PracticesInfer.NET is a powerful framework for probabilistic programming and Bayesian inference developed originally by Microsoft Research. It allows you to express probabilistic models declaratively in .NET languages (C#, F#) and perform inference to compute posterior distributions, make predictions, or learn model parameters. This guide walks through core concepts, hands‑on examples, and practical best practices to help you use Infer.NET effectively in real projects.
Why use Infer.NET?
- Probabilistic modeling inside .NET: Integrates seamlessly with C# and F# codebases.
- Flexible message-passing inference: Supports expectation propagation (EP) and variational message passing (VMP).
- Rich model expressiveness: Handles discrete, continuous, hierarchical, and latent-variable models.
- Deterministic reproducibility: Same code produces the same results (no stochastic training runs unless you add stochastic steps).
Core concepts
- Model: A set of random variables and their relationships (priors, likelihoods).
- Variable: Represents a random quantity (Variable
, Variable , arrays, matrices). - Range: Indexing for arrays of random variables.
- Observed vs. latent variables: Observed variables take fixed evidence; latent variables are inferred.
- InferenceEngine: The object that runs inference algorithms and returns posterior distributions (e.g., Gaussian, Beta, Dirichlet, Discrete).
- Factors and plates: Factors define relationships and plates represent repeated structure (arrays).
Setup and installation
- .NET SDK: Install .NET SDK (at least .NET 6 or later recommended in modern environments).
- Infer.NET package: Add Infer.NET via NuGet. Example for a .NET project:
dotnet add package Microsoft.ML.Probabilistic - IDE support: Use Visual Studio, Rider, or VS Code. For F# use the appropriate project templates.
Simple example: Bayesian linear regression
This example shows how to build a Bayesian linear regression model with Infer.NET in C# and infer posterior distributions for weights and noise.
using System; using Microsoft.ML.Probabilistic.Models; using Microsoft.ML.Probabilistic.Distributions; class BayesianLinearRegression { static void Main() { // Data: y = X*w + noise double[][] X = { new double[] {1, 2}, new double[] {2, 1}, new double[] {3, 4}, new double[] {4, 3} }; double[] y = {5.1, 5.9, 11.2, 11.8}; int n = y.Length; int d = X[0].Length; var engine = new InferenceEngine(); Range i = new Range(n); Range j = new Range(d); // Priors VariableArray<double> w = Variable.Array<double>(j); w[j] = Variable.GaussianFromMeanAndPrecision(0, 1).ForEach(j); Variable<double> noisePrecision = Variable.GammaFromShapeAndScale(1, 1); VariableArray<double> yVar = Variable.Array<double>(i); var Xvar = Variable.Constant(X); var yObserved = Variable.Constant(y); using (Variable.ForEach(i)) { var wx = Variable.Array<double>(j); wx[j] = w[j] * Xvar[i][j]; var dot = Variable.Sum(wx); yVar[i] = Variable.GaussianFromMeanAndPrecision(dot, noisePrecision); yVar[i].Observe(yObserved[i]); } var posteriorW = engine.Infer<Gaussian[]>(w); var posteriorNoise = engine.Infer<Gamma>(noisePrecision); Console.WriteLine("Posterior means for w:"); for (int k = 0; k < d; k++) Console.WriteLine($"w[{k}] mean = {posteriorW[k].GetMean():F3}, var = {posteriorW[k].GetVariance():F3}"); Console.WriteLine($"Noise precision mean: {posteriorNoise.GetMean():F3}"); } } Notes:
- Variables are declared with types representing distributions.
- Observe data with Observe or Variable.Constant for known arrays.
- Inference returns distribution objects (Gaussian, Gamma) from which you can query means, variances, etc.
Example: Mixture model (Gaussian Mixture)
A Gaussian mixture demonstrates latent discrete assignments and continuous component parameters.
Key steps:
- Define a discrete latent variable for component assignment.
- Define component means and precisions with priors.
- Use Variable.Switch or Variable.Discrete to tie assignments to component-specific likelihoods.
- Run inference to obtain posterior over assignments and component parameters.
(Pseudocode outline; implement in C# similarly to the regression example.)
Handling missing data
Infer.NET naturally handles missing observations by omitting Observe calls for missing entries or using distributions as observed values (e.g., Variable.Random). Use Variable.Masked or treat missing entries as latent variables to infer them jointly with model parameters.
Best practices
- Use appropriate priors: Weakly informative priors often stabilize inference. Avoid overly tight priors unless justified.
- Work in transformed spaces for constrained parameters (e.g., log-scale for positive-only variables) to improve numerical stability.
- Start small: Build and test simpler versions of the model before adding hierarchical layers.
- Monitor convergence: Compare results from different initializations or run sanity checks (posterior predictive checks).
- Use analytic conjugacy where possible: Conjugate pairs (Gaussian–Gaussian, Gamma–Poisson) enable efficient message passing and faster inference.
- Vectorize with Range: Leverage array variables and Range to express repeated structure efficiently.
- Check returned distribution types: Infer.NET may return compound distributions; inspect them to interpret results correctly.
- Performance: Precompute constants, avoid excessive loops in the model, and reuse InferenceEngine instances when possible. Use sparse representations if data are sparse.
- Seed RNG for reproducibility: Set engine.Random = new Random(seed) if using any stochastic components.
Common pitfalls
- Mixing observed and latent array shapes incorrectly — ensure Range sizes match observed data lengths.
- Expectation propagation can produce negative variances in edge cases; switch to VMP or try different priors if unstable.
- Overfitting with too flexible models — use hierarchical priors or regularization via priors.
- Misinterpreting posteriors — understand whether returned distributions are marginal, joint, or conditional.
When to choose Infer.NET vs alternatives
- Choose Infer.NET if you need tight integration with .NET applications, deterministic message-passing inference, or you prefer expressing models in C#/F#.
- Consider PyMC, Stan, or Turing.jl when you need Hamiltonian Monte Carlo (HMC) or a larger community with prebuilt model examples; those tools excel at sampling-based inference for some nonconjugate models.
Comparison (brief):
| Aspect | Infer.NET | Sampling-based tools (PyMC/Stan) |
|---|---|---|
| Inference style | Message passing (EP/VMP) | MCMC (HMC/NUTS) |
| Language | C#, F# (.NET) | Python, R, Julia |
| Determinism | High | Stochastic sampling |
| Performance | Fast for conjugate models | Robust for complex posteriors |
Debugging and validation
- Posterior predictive checks: Simulate from posterior and compare to held-out data.
- Inspect marginal distributions and verify parameter scales.
- Use synthetic data with known parameters to validate model correctness.
- Log intermediate messages or use smaller datasets to trace issues.
Useful resources
- Infer.NET GitHub repository for examples and source.
- Official API documentation for distribution classes and InferenceEngine options.
- Community examples and academic papers on expectation propagation and variational message passing for deeper understanding.
Closing notes
Infer.NET is a versatile tool for probabilistic modeling inside the .NET ecosystem. Start with small, well-specified models, prefer conjugacy where possible, and validate with predictive checks. With careful modeling and the practices above, Infer.NET can be a productive choice for Bayesian inference in production .NET applications.
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