README.md

In henrifnk/NoUTurn: NoUTurn Sampler

NoUTurn

No-U-Turn-Sampler introduced by Hoffman and Gelman in 2014

Library used:

The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo (Hofmann 2014) Topics: Main Paper introducing NUTS Link: http://www.stat.columbia.edu/~gelman/research/published/nuts.pdf

NIPS Learning (2011 Hofmann) [Youtube Video] Topics: Supportiv Presentation of NUTS (especially tree building) Link:

Baysian Data Analysis (Gelman 3rd Edition), Chapter 11, 12 Topics: MCMC, Metropolis(-Hastings), Hamiltonian MC Link: https://statisticalsupportandresearch.files.wordpress.com/2017/11/bayesian_data_analysis.pdf

Markov Chains: Why Walk When You Can Flow? (Richards 2017) Topics: Vizualization Problems of MH and HMC, showing how NUTS can solve them Link: https://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/

Hamiltonian Monte Carlo explained Topics: From MCMC to hamiltonian Monte Carlo with nice vizualizations Link: https://arogozhnikov.github.io/2016/12/19/markov_chain_monte_carlo.html

A Conceptual Introduction to Hamiltonian Monte Carlo (Betancourt 2018), Acknowledges A Topics: Technical implementation of trajectory and transition Link: https://arxiv.org/pdf/1701.02434.pdf

Python: Hamiltonian Monte Carlo from scratch (Moore, 2020) Topics: Code implementation of HMC algorithm in python Link: https://towardsdatascience.com/python-hamiltonian-monte-carlo-from-scratch-955dba96a42d

MCMC from scratch (Moore, 2020) [Colab Reasearch Doc] Topics: Code implementation and Regression for MCMC/ Good Intuition for HMC energy analogy Link: https://colab.research.google.com/drive/1YQBSfS1Nb8a9TAMsV1RjWsiErWqXLbrj#scrollTo=HUoQiEtDX_xL

Slice Sampling (Neal 2003) Topics: Slice Sampler for univariate and multivariate Problems Link: https://projecteuclid.org/download/pdf_1/euclid.aos/1056562461

Stan:A Probabilistic Programmin Language Topics: Stanis a probabilistic programming language for specifying statistical models Link: http://www.stat.columbia.edu/~gelman/research/published/stan-paper-revision-feb2015.pdf

Regression (Fahrmeir, 2013) Topics: Bayesian Generalized Regression

MCMC Interactive Gallery (Chi Feng, 2016) Topics: Vizualization of different MCMC algorithms Link: https://chi-feng.github.io/mcmc-demo/app.html?algorithm=MALA&target=banana

Proposed Structure

1) Brief Intro to MH-Algorithms random walk vs. HMC Idea of supressing local random walk behavior
2) Brief Intro to Hamiltonian HMC with focus on tuning parameters L & \epsilon 
    a) Leapfrog algorithm and physical analogy (frictionless bowl as intuition)
    b) Influence and setting heurictics for the tuning parameters stepsize and Leapfrog-steps (locally adaptive HMC)
       Supply typical problems for wrongly setting L to high/low (like trajectory bites own tail)
3) Introduce the "No-U-Turn" Idea
4) Provide Code for 
    a) naive NUTS algorithm
    b) effective NUTS algorithm
5) Introduce "on the fly" tuning of stepsize
  a) find reasonable epsilon
  b) dual averaging
*Idea 4) and 5)* show developement of algorithm by diffs from Metropolis Hastings to efficient NUTS with dual averaging
6) Synthetic simple examples for Regression and Classification
    a) Benchmarking algorthims (traceplots, convergence diagnostic etc) => Pros and Cons
7) RealWorld example/ Maybe little outlook on apllications like Stan!?

henrifnk/NoUTurn documentation built on Feb. 12, 2021, 11:10 a.m.