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Tom Minka

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7 papers
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7

NeurIPS Conference 2014 Conference Paper

A* Sampling

  • Chris Maddison
  • Daniel Tarlow
  • Tom Minka

The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over continuous space. Central to the method is a stochastic process recently described in mathematical statistics that we call the Gumbel process. We present a new construction of the Gumbel process and A* sampling, a practical generic sampling algorithm that searches for the maximum of a Gumbel process using A* search. We analyze the correctness and convergence time of A* sampling and demonstrate empirically that it makes more efficient use of bound and likelihood evaluations than the most closely related adaptive rejection sampling-based algorithms.

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NeurIPS Conference 2011 Conference Paper

Non-conjugate Variational Message Passing for Multinomial and Binary Regression

  • David Knowles
  • Tom Minka

Variational Message Passing (VMP) is an algorithmic implementation of the Variational Bayes (VB) method which applies only in the special case of conjugate exponential family models. We propose an extension to VMP, which we refer to as Non-conjugate Variational Message Passing (NCVMP) which aims to alleviate this restriction while maintaining modularity, allowing choice in how expectations are calculated, and integrating into an existing message-passing framework: Infer. NET. We demonstrate NCVMP on logistic binary and multinomial regression. In the multinomial case we introduce a novel variational bound for the softmax factor which is tighter than other commonly used bounds whilst maintaining computational tractability.

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NeurIPS Conference 2008 Conference Paper

Gates

  • Tom Minka
  • John Winn

Gates are a new notation for representing mixture models and context-sensitive independence in factor graphs. Factor graphs provide a natural representation for message-passing algorithms, such as expectation propagation. However, message passing in mixture models is not well captured by factor graphs unless the entire mixture is represented by one factor, because the message equations have a containment structure. Gates capture this containment structure graphically, allowing both the independences and the message-passing equations for a model to be readily visualized. Different variational approximations for mixture models can be understood as different ways of drawing the gates in a model. We present general equations for expectation propagation and variational message passing in the presence of gates.

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NeurIPS Conference 2007 Conference Paper

TrueSkill Through Time: Revisiting the History of Chess

  • Pierre Dangauthier
  • Ralf Herbrich
  • Tom Minka
  • Thore Graepel

We extend the Bayesian skill rating system TrueSkill to infer entire time series of skills of players by smoothing through time instead of (cid: 12)ltering. The skill of each participating player, say, every year is represented by a latent skill variable which is a(cid: 11)ected by the relevant game outcomes that year, and coupled with the skill variables of the previous and subsequent year. Inference in the resulting factor graph is carried out by approximate message passing (EP) along the time series of skills. As before the system tracks the uncertainty about player skills, explicitly models draws, can deal with any number of competing entities and can infer individual skills from team results. We extend the system to estimate player-speci(cid: 12)c draw mar- gins. Based on these models we present an analysis of the skill curves of important players in the history of chess over the past 150 years. Results include plots of players’ lifetime skill development as well as the ability to compare the skills of di(cid: 11)erent players across time. Our results indicate that a) the overall playing strength has increased over the past 150 years, and b) that modelling a player’s ability to force a draw provides signi(cid: 12)cantly better predictive power.

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NeurIPS Conference 2003 Conference Paper

Bayesian Color Constancy with Non-Gaussian Models

  • Charles Rosenberg
  • Alok Ladsariya
  • Tom Minka

We present a Bayesian approach to color constancy which utilizes a non- Gaussian probabilistic model of the image formation process. The pa- rameters of this model are estimated directly from an uncalibrated image set and a small number of additional algorithmic parameters are chosen using cross validation. The algorithm is empirically shown to exhibit RMS error lower than other color constancy algorithms based on the Lambertian surface reflectance model when estimating the illuminants of a set of test images. This is demonstrated via a direct performance comparison utilizing a publicly available set of real world test images and code base.

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NeurIPS Conference 2003 Conference Paper

Tree-structured Approximations by Expectation Propagation

  • Yuan Qi
  • Tom Minka

Approximation structure plays an important role in inference on loopy graphs. As a tractable structure, tree approximations have been utilized in the variational method of Ghahramani & Jordan (1997) and the se- quential projection method of Frey et al. (2000). However, belief propa- gation represents each factor of the graph with a product of single-node messages. In this paper, belief propagation is extended to represent fac- tors with tree approximations, by way of the expectation propagation framework. That is, each factor sends a “message” to all pairs of nodes in a tree structure. The result is more accurate inferences and more fre- quent convergence than ordinary belief propagation, at a lower cost than variational trees or double-loop algorithms.

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