[Feature]: Tutorial

[mhidalgoaraya]

Feature Summary

Provides a user-facing tutorial demonstrating how to model and perform inference with the Gate node in RxInfer.

Feature Description

Write a tutorial that teaches users what the Gate node represents, how it differs from a naive mean-field mixture, and how to build practical models with it. The tutorial should include runnable code and explain the key conceptual moving parts: selector variable, keyed alternatives, and how messages flow.

Feature Goals

• Make the Gate node understandable without requiring the reader to parse the 2008 paper.
• Provide copy-pasteable examples that are small but real.
• Document best practices and common failure modes if any

Tasks

• Write a conceptual overview:
  • What a “gate” is as a modeling construct for mixtures.
  • What a “gate block” is (one selector, multiple keyed alternatives).
• Provide at least two worked examples:
  • Gaussian mixture with unknown means and a categorical selector.
  • Switching LDS or regime-switching state-space model demo.
• Include visuals:
  • Factor-graph sketches of the gate structure (even simple diagrams help).
  • Plots of inferred regime probabilities over time for the switching example.

Dependencies

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Estimated Timeline

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Related Issues / PRs

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Additional Context

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