Christopher M. Bishop

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his book provides an introduction to the eld of pattern recognition and machine earning. It gives an overview of several asic and advanced topics in machine earning theory. The book is definitely aluable to scientists and engineers who re involved in developing machine learnng tools applied to signal and image proessing applications. This book is also(More)
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(More)
Principal component analysis (PCA) is one of the most popular techniques for processing, compressing, and visualizing data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However,(More)
Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However,(More)
Bayesian inference is now widely established as one of the principal foundations for machine learning. In practice, exact inference is rarely possible, and so a variety of approximation techniques have been developed, one of the most widely used being a deterministic framework called variational inference. In this paper we introduce Variational Message(More)
One of the central issues in the use of principal component analysis (PCA) for data modelling is that of choosing the appropriate number of retained components. This problem was recently addressed through the formulation of a Bayesian treatment of PCA (Bishop, 1999a) in terms of a probabilistic latent variable model. A central feature of this approach is(More)