Manifold Relevance Determination

In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear(in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private information from multiple views of the data. In contrast to previous approaches, we introduce a relaxation to the discrete segmentation and allow for a "softly" shared latent space. Further, Bayesian techniques allow us to automatically estimate the dimensionality of the latent spaces. The model is capable of capturing structure underlying extremely high dimensional spaces. This is illustrated by modelling unprocessed images with tenths of thousands of pixels. This also allows us to directly generate novel images from the trained model by sampling from the discovered latent spaces. We also demonstrate the model by prediction of human pose in an ambiguous setting. Our Bayesian framework allows us to perform disambiguation in a principled manner by including latent space priors which incorporate the dynamic nature of the data.Comment: ICML201

Tracking known and unknown human activites

Tracking known and unknown human activite

Deep Gaussian Processes

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.Comment: 9 pages, 8 figures. Appearing in Proceedings of the 16th International Conference on Artificial Intelligence and Statistics (AISTATS) 201

Doubly Stochastic Variational Inference for Deep Gaussian Processes

Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs, but inference in these models has proved challenging. Existing approaches to inference in DGP models assume approximate posteriors that force independence between the layers, and do not work well in practice. We present a doubly stochastic variational inference algorithm, which does not force independence between layers. With our method of inference we demonstrate that a DGP model can be used effectively on data ranging in size from hundreds to a billion points. We provide strong empirical evidence that our inference scheme for DGPs works well in practice in both classification and regression.Comment: NIPS 201

Affective Facial Expression Processing via Simulation: A Probabilistic Model

Understanding the mental state of other people is an important skill for intelligent agents and robots to operate within social environments. However, the mental processes involved in `mind-reading' are complex. One explanation of such processes is Simulation Theory - it is supported by a large body of neuropsychological research. Yet, determining the best computational model or theory to use in simulation-style emotion detection, is far from being understood. In this work, we use Simulation Theory and neuroscience findings on Mirror-Neuron Systems as the basis for a novel computational model, as a way to handle affective facial expressions. The model is based on a probabilistic mapping of observations from multiple identities onto a single fixed identity (`internal transcoding of external stimuli'), and then onto a latent space (`phenomenological response'). Together with the proposed architecture we present some promising preliminary resultsComment: Annual International Conference on Biologically Inspired Cognitive Architectures - BICA 201

Transfering Nonlinear Representations using Gaussian Processes with a Shared Latent Space

When a series of problems are related, representations derived fromlearning earlier tasks may be useful in solving later problems. Inthis paper we propose a novel approach to transfer learning withlow-dimensional, non-linear latent spaces. We show how suchrepresentations can be jointly learned across multiple tasks in adiscriminative probabilistic regression framework. When transferred tonew tasks with relatively few training examples, learning can befaster and/or more accurate. Experiments on a digit recognition taskshow significantly improved performance when compared to baselineperformance with the original feature representation or with arepresentation derived from a semi-supervised learning approach

Variational auto-encoded deep Gaussian processes

We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are reparametrized through a multilayer perceptron. The key aspect of this reformulation is that it prevents the proliferation of variational parameters which otherwise grow linearly in proportion to the sample size. We derive a new formulation of the variational lower bound that allows us to distribute most of the computation in a way that enables to handle datasets of the size of mainstream deep learning tasks. We show the efficacy of the method on a variety of challenges including deep unsupervised learning and deep Bayesian optimization