Optimization and Inference

A public-facing hub showing how the site’s math modules reappear in measurement models, hidden variables, posterior questions, regularized recovery, and approximate inference.
Modified

April 26, 2026

Keywords

inference, optimization, latent-variables, posterior, applications

1 Why This Section Exists

Many readers can follow the individual math topics, but still do not have a clean picture of what an inference problem actually is.

This hub is for the moment when you want to answer questions like:

  • what exactly is hidden, observed, or only partially measured?
  • where do likelihoods, priors, regularizers, and posteriors all come from?
  • when should a problem be solved by optimization, sequential estimation, variational approximation, or sampling?

The rule for this section is simple:

every inference page should point back to the exact observed data, hidden variables, and approximation choices it uses

2 What Optimization And Inference Keeps Reusing

Across inverse problems, Bayesian estimation, latent-variable modeling, filtering, and active sensing, the same mathematical objects keep returning:

  • observed data or measurements
  • hidden states, parameters, or latent variables
  • forward models and likelihoods
  • priors, regularizers, or structural assumptions
  • posterior questions, uncertainty summaries, or approximate surrogates

If you can identify those objects quickly, papers about inference stop feeling like separate dialects.

Best Starting Math Probability, Statistics, Optimization

Best Sequential Bridge Signal Processing and Estimation

Best Uncertainty Bridge Stochastic Processes

3 Start Here By Interest

3.1 If You Want The Shortest Math-to-Inference Entry

Start in this order:

  1. Statistics
  2. Optimization
  3. Measurements, Models, and Hidden Variables
  4. Likelihoods, Priors, and MAP Estimation
  5. Filtering, Smoothing, and Hidden-State Inference

3.2 If You Care Most About Posterior Questions And Hidden State

Start with:

  1. Measurements, Models, and Hidden Variables
  2. Likelihoods, Priors, and MAP Estimation
  3. Filtering, Smoothing, and Hidden-State Inference
  4. State Estimation, Smoothing, and Hidden-State Inference
  5. Partial Observability, Belief States, and RL/Control Bridges

3.3 If You Care Most About Approximation And Uncertainty

Start with:

  1. Measurements, Models, and Hidden Variables
  2. Likelihoods, Priors, and MAP Estimation
  3. Variational Inference, ELBO, and Tractable Approximation
  4. Variational Objectives, ELBO, and Information Bounds
  5. Mixing, Ergodicity, and MCMC Bridges

4 First-Pass Route

The cleanest live first-pass route in this section right now is:

  1. Measurements, Models, and Hidden Variables
  2. Likelihoods, Priors, and MAP Estimation
  3. Filtering, Smoothing, and Hidden-State Inference
  4. Variational Inference, ELBO, and Tractable Approximation
  5. Sampling, Mixing, and MCMC for Inference
  6. Bayesian Optimization, Active Sensing, and Information Gathering

Use this hub when you want the shortest translation from pure math into the recurring question:

what hidden quantity am I trying to infer from incomplete or noisy observations, and what computational strategy should I trust?

5 How To Use This Section

  • Use Topics when you want the math itself.
  • Use Applications > Optimization and Inference when you want the translation layer from models and objectives into real inference tasks.
  • Use Paper Lab when the inference objects feel clear and you want paper-reading practice.

6 Sources and Further Reading

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