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Index: Advanced MCMC and Latent Discrete Models

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Advanced MCMC and Latent Discrete Models

Routing Summary

This cluster covers sampling when plain NUTS struggles: GPU many-chain samplers (ChEES-HMC, MEADS), funnel geometry and non-centring, marginalising discrete latents, hidden Markov models (forward-backward, Viterbi, Baum-Welch, non-homogeneous HMMs) and stochastic volatility. It has 5 sub-folders and 29 notes, written to cover the methods used in the PyMC worked examples E04, E12, E24, E48, E57, E59, E86 (examples page). Start from a source overview:

Sub-topics

  • Betancourt Girolami 2015 - HMC for Hierarchical Models (6 notes) — COVERS: Betancourt & Girolami (2015, arXiv:1312.0906), Hamiltonian Monte Carlo for Hierarchical Models, explain why hierarchical posteriors have funnel geometry whose curvature varies with position, why random-walk Metropolis and Gibbs degrade into random walks on them, and how Euclidean HMC (with non-centred parameterisations and carefully relaxed adaptation) or Riemannian HMC with the SoftAbs metric…
  • Concept Notes - Discrete Latents and Inference Frontier (3 notes) — COVERS: Concept notes: Bayesian HMMs - Label Switching, Non-Homogeneous Transitions and Dwell Times, Marginalising Discrete Latents - Why NUTS Cannot Sample Discrete Parameters, Stochastic Volatility and the Inference Frontier
  • Hoffman Radul Sountsov 2021 - ChEES-HMC (6 notes) — COVERS: Hoffman, Radul & Sountsov (2021), An Adaptive MCMC Scheme for Setting Trajectory Lengths in Hamiltonian Monte Carlo (AISTATS, PMLR 130), propose ChEES-HMC: plain (non-NUTS) HMC whose maximum trajectory length is tuned by gradient ascent on the Change in the Estimator of the Expected Square, with the same and a jittered length shared by all chains. It matches or beats NUTS per…
  • Hoffman Sountsov 2022 - MEADS (6 notes) — COVERS: Hoffman & Sountsov (2022), Tuning-Free Generalized Hamiltonian Monte Carlo (AISTATS, PMLR 151), propose MEADS (Maximum-Eigenvalue Adaptation of Damping and Step-size): an ensemble-chain adaptation (ECA) scheme that sets every tunable parameter of generalised HMC (step size, damping, slice drift, diagonal preconditioner) each iteration from cross-chain statistics, without perturbing the…
  • Rabiner 1989 - Hidden Markov Models Tutorial (8 notes) — COVERS: Rabiner (1989), A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition (Proc. IEEE 77(2):257-286), is the standard exposition of the HMM and its three problems: evaluation (forward-backward), decoding (posterior argmax and Viterbi) and learning (Baum-Welch EM). It also covers model types (ergodic, left-right), continuous densities, explicit state duration, scaling,…

Motivating PyMC examples

E04, E12, E24, E48, E57, E59, E86 — see the worked examples page; each source Overview lists the examples it supports.

Sources

  • Betancourt Girolami 2015 - Hamiltonian Monte Carlo for Hierarchical Models
  • Hoffman Radul Sountsov 2021 - Adaptive-MCMC Scheme for Setting Trajectory Lengths in HMC
  • Hoffman Sountsov 2022 - Tuning-Free Generalized Hamiltonian Monte Carlo
  • Rabiner 1989 - A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition

See Also

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