Pseudo-Marginal Bayesian Inference for Gaussian Processes

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data. Using probit regression as an illustrative working example, this paper presents a general and effective methodology based on the pseudo-marginal approach to Markov chain Monte Carlo that efficiently addresses both of these issues. The results presented in this paper show improvements over existing sampling methods to simulate from the posterior distribution over the parameters defining the covariance function of the Gaussian Process prior. This is particularly important as it offers a powerful tool to carry out full Bayesian inference of Gaussian Process based hierarchic statistical models in general. The results also demonstrate that Monte Carlo based integration of all model parameters is actually feasible in this class of models providing a superior quantification of uncertainty in predictions. Extensive comparisons with respect to state-of-the-art probabilistic classifiers confirm this assertion.Comment: 14 pages double colum

Hybrid Models with Deep and Invertible Features

We propose a neural hybrid model consisting of a linear model defined on a set of features computed by a deep, invertible transformation (i.e. a normalizing flow). An attractive property of our model is that both p(features), the density of the features, and p(targets | features), the predictive distribution, can be computed exactly in a single feed-forward pass. We show that our hybrid model, despite the invertibility constraints, achieves similar accuracy to purely predictive models. Moreover the generative component remains a good model of the input features despite the hybrid optimization objective. This offers additional capabilities such as detection of out-of-distribution inputs and enabling semi-supervised learning. The availability of the exact joint density p(targets, features) also allows us to compute many quantities readily, making our hybrid model a useful building block for downstream applications of probabilistic deep learning.Comment: ICML 201

Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an observed response, a Gaussian process model can easily be implemented using matrix computations that are feasible for datasets of up to about a thousand cases. Hyperparameters that define the covariance function of the Gaussian process can be sampled using Markov chain methods. Regression models where the noise has a t distribution and logistic or probit models for classification applications can be implemented by sampling as well for latent values underlying the observations. Software is now available that implements these methods using covariance functions with hierarchical parameterizations. Models defined in this way can discover high-level properties of the data, such as which inputs are relevant to predicting the response

Online Domain Adaptation for Multi-Object Tracking

Automatically detecting, labeling, and tracking objects in videos depends first and foremost on accurate category-level object detectors. These might, however, not always be available in practice, as acquiring high-quality large scale labeled training datasets is either too costly or impractical for all possible real-world application scenarios. A scalable solution consists in re-using object detectors pre-trained on generic datasets. This work is the first to investigate the problem of on-line domain adaptation of object detectors for causal multi-object tracking (MOT). We propose to alleviate the dataset bias by adapting detectors from category to instances, and back: (i) we jointly learn all target models by adapting them from the pre-trained one, and (ii) we also adapt the pre-trained model on-line. We introduce an on-line multi-task learning algorithm to efficiently share parameters and reduce drift, while gradually improving recall. Our approach is applicable to any linear object detector, and we evaluate both cheap "mini-Fisher Vectors" and expensive "off-the-shelf" ConvNet features. We quantitatively measure the benefit of our domain adaptation strategy on the KITTI tracking benchmark and on a new dataset (PASCAL-to-KITTI) we introduce to study the domain mismatch problem in MOT.Comment: To appear at BMVC 201