Topic
Gaussian process
About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.
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14 May 2006
TL;DR: A framework for large margin classification by Gaussian mixture models (GMMs), which have many parallels to support vector machines (SVMs) but use ellipsoids to model classes instead of half-spaces is developed.
Abstract: We develop a framework for large margin classification by Gaussian mixture models (GMMs). Large margin GMMs have many parallels to support vector machines (SVMs) but use ellipsoids to model classes instead of half-spaces. Model parameters are trained discriminatively to maximize the margin of correct classification, as measured in terms of Mahalanobis distances. The required optimization is convex over the model's parameter space of positive semidefinite matrices and can be performed efficiently. Large margin GMMs are naturally suited to large problems in multiway classification; we apply them to phonetic classification and recognition on the TIMIT database. On both tasks, we obtain significant improvement over baseline systems trained by maximum likelihood estimation. For the problem of phonetic classification, our results are competitive with other state-of-the-art classifiers, such as hidden conditional random fields.
152 citations
TL;DR: The Gaussian Process Upper Confidence Bound and Pure exploration algorithm (GP-UCB-PE) is introduced which combines the UCB strategy and Pure Exploration in the same batch of evaluations along the parallel iterations and proves theoretical upper bounds on the regret with batches of size K for this procedure.
Abstract: In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f which is predicted to be the most useful. We focus on the case where the function can be evaluated in parallel with batches of fixed size and analyze the benefit compared to the purely sequential procedure in terms of cumulative regret. We introduce the Gaussian Process Upper Confidence Bound and Pure Exploration algorithm (GP-UCB-PE) which combines the UCB strategy and Pure Exploration in the same batch of evaluations along the parallel iterations. We prove theoretical upper bounds on the regret with batches of size K for this procedure which show the improvement of the order of sqrt{K} for fixed iteration cost over purely sequential versions. Moreover, the multiplicative constants involved have the property of being dimension-free. We also confirm empirically the efficiency of GP-UCB-PE on real and synthetic problems compared to state-of-the-art competitors.
152 citations
Book•
13 Jan 2012TL;DR: The theory of Gaussian processes occupies one of the leading places in modern Probability as discussed by the authors, which is why Gaussian vectors and Gaussian distributions in infinite-dimensional spaces come into play.
Abstract: Theory of random processes needs a kind of normal distribution. This is why Gaussian vectors and Gaussian distributions in infinite-dimensional spaces come into play. By simplicity, importance and wealth of results, theory of Gaussian processes occupies one of the leading places in modern Probability.
152 citations
TL;DR: The effectiveness of theGaussian process approach for the development of a calibration model is demonstrated through its application to two spectroscopic data sets and it is concluded that the Gaussian process exhibits enhanced behaviour.
152 citations
TL;DR: This paper reformulated the rate-distortion problem in terms of the optimal mapping from the unit interval with Lebesgue measure that would induce the desired reproduction probability density and shows how the number of "symbols" grows as the system undergoes phase transitions.
Abstract: In rate-distortion theory, results are often derived and stated in terms of the optimizing density over the reproduction space. In this paper, the problem is reformulated in terms of the optimal mapping from the unit interval with Lebesgue measure that would induce the desired reproduction probability density. This results in optimality conditions that are "random relatives" of the known Lloyd (1982) optimality conditions for deterministic quantizers. The validity of the mapping approach is assured by fundamental isomorphism theorems for measure spaces. We show that for the squared error distortion, the optimal reproduction random variable is purely discrete at supercritical distortion (where the Shannon (1948) lower bound is not tight). The Gaussian source is thus the only source that produces continuous reproduction variables for the entire range of positive rate. To analyze the evolution of the optimal reproduction distribution, we use the mapping formulation and establish an analogy to statistical mechanics. The solutions are given by the distribution at isothermal statistical equilibrium, and are parameterized by the temperature in direct correspondence to the parametric solution of the variational equations in rate-distortion theory. The analysis of an annealing process shows how the number of "symbols" grows as the system undergoes phase transitions. Thus, an algorithm based on the mapping approach often needs but a few variables to find the exact solution, while the Blahut (1972) algorithm would only approach it at the limit of infinite resolution. Finally, a quick "deterministic annealing" algorithm to generate the rate-distortion curve is suggested. The resulting curve is exact as long as continuous phase transitions in the process are accurately followed. >
151 citations