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Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component analysis (PCA) that we term dual probabilistic PCA(More)
In this paper we introduce a new underlying probabilistic model for principal component analysis (PCA). Our formulation interprets PCA as a particular Gaussian process prior on a mapping from a latent space to the observed data-space. We show that if the prior's covariance function constrains the mappings to be linear the model is equivalent to PCA, we then(More)
We present a method for the sparse greedy approximation of Bayesian Gaussian process regression, featuring a novel heuristic for very fast forward selection. Our method is essentially as fast as an equivalent one which selects the " support " patterns at random, yet it can outperform random selection on hard curve fitting tasks. More importantly, it leads(More)
We present a framework for sparse Gaussian process (GP) methods which uses forward selection with criteria based on information-theoretic principles, previously suggested for active learning. Our goal is not only to learn d–sparse predictors (which can be evaluated in O(d) rather than O(n), d n, n the number of training points), but also to perform training(More)
We introduce a variational inference framework for training the Gaussian process latent variable model and thus performing Bayesian nonlinear dimensionality reduction. This method allows us to variationally integrate out the input variables of the Gaussian process and compute a lower bound on the exact marginal likelihood of the nonlinear latent variable(More)
The Gaussian process latent variable model (GP-LVM) is a generative approach to nonlinear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a non-linear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most approaches to non-linear dimensionality methods focus on(More)
Data noise is present in many machine learning problems domains, some of these are well studied but others have received less attention. In this paper we propose an algorithm for constructing a kernel Fisher discriminant (KFD) from training examples with noisy labels. The approach allows to associate with each example a probability of the label being(More)
WiFi localization, the task of determining the physical location of a mobile device from wireless signal strengths, has been shown to be an accurate method of indoor and outdoor localization and a powerful building block for location-aware applications. However, most localization techniques require a training set of signal strength readings labeled against(More)