Particle filters initially appeared as computational tools to perform online state estimation (i.e. "filtering") in non-linear, non-gaussian state space models, with many applications in target tracking and signal processing. They have been generalized to many other settings in Statistics, and now constitute serious competitors to Markov chain Monte Carlo methods, under the name of "Sequential Monte Carlo methods". These algorithms are often advantageous in terms of parallelization on modern hardware, benefit from a solid theoretical validation, and are indeed becoming more and more popular.
In Spring 2016, we are going to read a series of cornerstone articles that have been important in developing Sequential Monte Carlo methods, until we reach some understanding of the current state of the field. This seminar series will be led by Natesh Pillai and myself.
We will meet on Wednesdays 2pm, more or less bi-weekly, in SC 706. The list of dates is given below.
Schedule:
1. 02/03, 2pm
2. 02/17, 2pm
3. 02/24, 2pm
4. 03/09, 2pm
5. 03/23, 2pm
6. 04/06, 2pm
7. 04/13, 2pm (special guest! Patrick Rebeschini!)
8. 04/27, 2pm
That's all, folks!
Please subscribe to our Google groupgle group.
The articles can be found in this Dropbox folder. The list below is subject to changes.
Seminal papers
1.
- Neil J. Gordon, David J. Salmond and Adrian FM Smith. "Novel approach to nonlinear/non-Gaussian Bayesian state estimation." IEE Proceedings F (Radar and Signal Processing). Vol. 140. No. 2. IET Digital Library, 1993.
2.
- Jun Liu and Rong Chen. "Sequential Monte Carlo methods for dynamic systems." Journal of the American statistical association 93(443), 1032-1044, 1998.
- Michael K. Pitt and Neil Shephard. "Filtering via simulation: Auxiliary particle filters". Journal of the American statistical association, 94(446), 590-599, 1999.
(Xufei and Yang volunteered)
From time series to generic sampling
3.
- Nicolas Chopin. "A sequential particle filter method for static models." Biometrika 89(3), 539-552, 2002.
(John volunteered)
- Pierre Del Moral, Arnaud Doucet and Ajay Jasra. "Sequential Monte Carlo samplers." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68(3), 411-436, 2006.
Theoretical Aspects
4.
Relatively easy article, introducing operators acting on probability measures and establishing consistency when N goes to infinity:
- Dan Crisan & Arnaud Doucet. "A survey of convergence results on particle filtering methods for practitioners". IEEE Transactions on Signal Processing, 50(3), 736-746, 2002.
(Shihao volunteered)
Self-contained article on the stability properties of particle methods with respect to the time horizon:
- Frédéric Cérou, Pierre Del Moral, and Arnaud Guyader. "A nonasymptotic theorem for unnormalized Feynman–Kac particle models." Annales de l'IHP Probabilités et statistiques. 47(3): 629-649, 2011
Other recommended papers (that we will not cover).
Early article, self-contained, contains results on time-uniform stability:
- Pierre Del Moral and Alice Guionnet. "On the stability of interacting processes with applications to filtering and genetic algorithms." Annales de l'IHP Probabilités et statistiques. 37(2), 2001.
Reference book on the topic:
- Pierre Del Moral. "Feynman-Kac Formulae". Springer New York, 2004.
Recent developments, with very mild assumptions compared to the above articles, well-written:
- Nick Whiteley. Stability properties of some particle filters. The Annals of Applied Probability, 23(6), 2500-2537, 2013.
Recent developments
5.
- Christophe Andrieu, Arnaud Doucet, and Roman Holenstein. "Particle Markov chain Monte Carlo methods." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72.3: 269-342, 2010.
- Fredrik Lindsten, Michael Jordan and Thomas B. Schön, "Particle Gibbs with Ancestor Sampling", Journal of Machine Learning Research 15 2145-2184, 2014.
(Stephane and Maxime volunteered)
6.
- Liangliang Wang, Alexandre Bouchard-Côté & Arnaud Doucet. "Bayesian Phylogenetic Inference Using a Combinatorial Sequential Monte Carlo Method." Journal of the American statistical association 110(512), 1362-1374, 2015.
(Zhirui volunteered)
- M. Frei and H. Künsch. "Bridging the ensemble Kalman and particle filters." Biometrika 100 (4), 781-800, 2013.
(Espen volunteered)
7. Patrick Rebeschini will be here for this session
- Patrick Rebeschini, and Ramon Van Handel. "Can local particle filters beat the curse of dimensionality?" The Annals of Applied Probability, 25(5), 2809-2866, 2015.
8.
-
Nikolas Kantas, Arnaud Doucet, Sumeetpal S. Singh, Jan Maciejowski, and Nicolas Chopin. "On Particle Methods for Parameter Estimation in State-Space Models", Statistical Science (30:3), 328-351, 2015.
We will end with a discussion of the methods reviewed in this seminar and a discussion on open challenges.
Wikipedia updates
The Wikipedia articles on particle methods are incomplete or nonexistent. Let's try to contribute! We propose to work in small teams, and discuss any change before actually committing them to Wikipedia. Some ideas on what to change are listed below.
- The article on particle filter is long, poorly structured, too technical and yet incomplete. It should be sliced it into smaller bits, separating algorithms and theory into dedicated pages.
- The theory page could be based on the (also poorly structured) page on mean field particle methods. To be more precise, a theory page could contain results on time-uniform stability of particle methods, and on the linear variance non-asymptotic result.
- Particle smoothing algorithms are poorly described. A dedicated page could describe Forward Filtering Backward Smoothing, Two-filter formula and fixed lag smoothing.
- There are no pages on particle methods for parameter inference, i.e. "static problems". There could be a dedicated page describing Iterated Batch Importance Sampling and SMC samplers.
- There are no pages on the various methods to estimate the evidence in Bayesian statistics. There could be a page with links to Importance Sampling, Chib's method, SMC samplers, Nested Sampling (which has a page), thermodynamic integration (which has a page), bridge and path sampling.
- There are no pages describing resampling schemes (although there is a page on stratified sampling, mostly from a statistical survey perspective).
- The page on Auxiliary Particle filter is very short.
- There are no pages describing pseudo-marginal MCMC and particle MCMC methods. There could be a page with pseudo-marginal Metropolis Hastings, with particle MH as a special case, and another page with particle gibbs, with backward sampling, and with ancestor sampling. These would give a Bayesian counterpart to the page on Iterated Filtering.
In all of the above, algorithms should be described in pseudo-code (or even snippets of actual python or R code). Theorems should ideally come with proofs, or specific references to proofs. In general, Wikipedia pages (both theory and methods) should have examples; it's generally good to to have plots, diagrams or pictures; links to software packages that contain the described methods. It's generally good to include as many links as possible (to other Wikipedia pages and elsewhere). By browsing Wikipedia's "featured articles", you can get some inspiration on what is a good scientific Wikipedia article.
Links
- Arnaud Doucet's webpage on SMC algorithms is full of links: http://www.stats.ox.ac.uk/~doucet/smc_resources.html
- Pierre Del Moral's webpage on SMC is also full of links: http://web.maths.unsw.edu.au/~peterdel-moral/simulinks.html
- A list of recent talks at an SMC workshop can be found here: http://smc2015.sciencesconf.org/resource/page/id/