Snoek, Jasper, Larochelle, Hugo, Adams, Ryan P.

The use of machine learning algorithms frequently involves careful tuning of learning parameters and model hyperparameters. Unfortunately, this tuning is often a "black art" requiring expert experience, rules of thumb, or sometimes brute-force search. There is therefore great appeal for automatic approaches that can optimize the performance of any given learning algorithm to the problem at hand. In this work, we consider this problem through the framework of Bayesian optimization, in which a learning algorithm's generalization performance is modeled as a sample from a Gaussian process (GP). We show that certain choices for the nature of the GP, such as the type of kernel and the treatment of its hyperparameters, can play a crucial role in obtaining a good optimizer that can achieve expert-level performance.

Rosenberg, Charles, Ladsariya, Alok, Minka, Tom

We present a Bayesian approach to color constancy which utilizes a non-Gaussian probabilistic model of the image formation process. The parameters 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.

Rosenberg, Charles, Ladsariya, Alok, Minka, Tom

Editor's note: The following is an interview with Columbia University Professor Andrew Gelman conducted by Marketing scientist Kevin Gray, in which Gelman spells out the ABCs of Bayesian statistics. Kevin Gray: Most marketing researchers have heard of Bayesian statistics but know little about it. Can you briefly explain in layperson's terms what it is and how it differs from the'ordinary' statistics most of us learned in college? Andrew Gelman: Bayesian statistics uses the mathematical rules of probability to combines data with "prior information" to give inferences which (if the model being used is correct) are more precise than would be obtained by either source of information alone. Classical statistical methods avoid prior distributions.

Ellis, Kevin, Solar-Lezama, Armando, Tenenbaum, Josh

Towards learning programs from data, we introduce the problem of sampling programs from posterior distributions conditioned on that data. Within this setting, we propose an algorithm that uses a symbolic solver to efficiently sample programs. The proposal combines constraint-based program synthesis with sampling via random parity constraints. We give theoretical guarantees on how well the samples approximate the true posterior, and have empirical results showing the algorithm is efficient in practice, evaluating our approach on 22 program learning problems in the domains of text editing and computer-aided programming. Papers published at the Neural Information Processing Systems Conference.