We give a basic introduction to Gaussian Process regression models. We focus on understanding the role of the stochastic process and how it is used to define a distribution over functions. We present the simple equations for incorporating training data and examine how to learn the hyperparameters using the marginal likelihood. We explain the practical advantages of Gaussian Process and end with conclusions and a look at the current trends in GP work.

This note is a response to [7] in which it is claimed that [13, Proposition 11] is false. We demonstrate here that this assertion in [7] is false, and is based on a misreading of the notion of set membership in [13, Proposition 11]. We maintain that [13, Proposition 11] is true. * Authors are listed in alphabetical order.

Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis, which is based on a linear transformation between the latent space and the data space. In this article, we introduce a form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization algorithm. GTM provides a principled alternative to the widely used self-organizing map (SOM) of Kohonen (1982) and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multiphase oil pipeline.

International audienceThe PASCAL Visual Object Classes Challenge ran from February to March 2005. The goal of the challenge was to recognize objects from a number of visual object classes in realistic scenes (i.e. not pre-segmented objects). Four object classes were selected: motorbikes, bicycles, cars and people. Twelve teams entered the challenge. In this chapter we provide details of the datasets, algorithms used by the teams, evaluation criteria, and results achieved

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