Ari Pakman: Oct. 10th

Ari will present the paper "The Horseshoe Estimator for Sparse Signals"

Link: http://faculty.chicagobooth.edu/nicholas.polson/research/papers/Horse.pdf

Abstract:

This paper proposes a new approach to sparse-signal detection called the horseshoe estimator. We show that the horseshoe is a close cousin of the lasso in that it arises from the same class of multivariate scale mixtures of normals, but that it is almost universally superior to the double-exponential prior at handling sparsity. A theoretical framework is proposed for understanding why the horseshoe is a better default “sparsity” estimator than those that arise from powered-exponential priors. Comprehensive numerical evidence is presented to show that the difference in performance can often be large. Most importantly, we show that the horseshoe estimator corresponds quite closely to the answers one would get if one pursued a full Bayesian model-averaging approach using a “two-groups” model: a point mass at zero for noise, and a continuous density for signals. Surprisingly, this correspondence holds both for the estimator itself and for the classification rule induced by a simple threshold applied to the estimator. We show how the resulting thresholded horseshoe can also be viewed as a novel Bayes multiple-testing procedure.

Jonathan Huggins: May 1st

Jonathan Huggins will present his joint work with Frank Wood. Here is an abstract:

We develop a class of non-parametric Bayesian models we call infinite structured explicit duration hidden Markov models (ISEDHMMs). ISEDHMMs are HMMs that possess an unbounded number of states, encode state dwell-time distributions explicitly, and have constraints on what state transitions are allowed. The ISEDHMM framework generalizes explicit duration finite HMMs, infinite HMMs, left-to-right HMMs, and more (all are recoverable by specific choices of ISEDHMM parameters).  This suggests that ISEDHMMs should be applicable to data-analysis problems in a variety of settings.

Carl Smith : March 22

This week in group meeting I will be presenting a somewhat recent paper from Josh Tenenbaum's group entitled "Modelling Relational Data using Bayesian Clustered Tensor Factorization", in which a model for relational data is proposed and explored and argued to be a happy compromise of the pros and cons of clustering methods and factorization models. I plan to present the model itself, some issues it addresses, and some of the results described in the paper.

David Pfau : Nov 17th

Abstract:

I'm presenting joint work with Frank Wood and Nicholas Bartlett on learning simple models for discrete sequence prediction.  We describe a novel Bayesian framework for learning probabilistic deterministic finite automata (PDFA), which are a class of simple generative models for sequences from a discrete alphabet.  We first define a prior over PDFA with a fixed number of states, and then by taking the limit as the number of states becomes unbounded, we show that the prior has a well defined limit, a model we call a Probabilistic Deterministic Infinite Automata (PDIA).  Inference is tractable with MCMC, and we show results from experiments with synthetic grammars, DNA and natural language.  In particular, we find on complex data that averaging predictions over many MCMC samples leads to improved performance, and that the learned models perform as well as 3rd-order Markov models with about 1/10th as many states.  For the curious, a write-up of my work can be found here.

Also, following the talk I'm going to give a brief tutorial on git, a free version control system used in the software community for maintaining large collaborative code bases.  I'd like to set up a git repository for the Paninski group so we can avoid too much code duplication and build on each others' work, and I promise it's actually pretty easy once you learn the basics.