We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in $\mathcal{O}(p)$ time. Our GRIEF kernel consists of $p$ eigenfunctions found using a Nystr\"om approximation from a dense Cartesian product grid of inducing points. By exploiting algebraic properties of Kronecker and Khatri-Rao tensor products, computational complexity of the training procedure can be practically independent of the number of inducing points. This allows us to use arbitrarily many inducing points to achieve a globally accurate kernel approximation, even in high-dimensional problems. The fast likelihood evaluation enables type-I or II Bayesian inference on large-scale datasets. We benchmark our algorithms on real-world problems with up to two-million training points and $10^{33}$ inducing points.

Exploration is a difficult challenge in reinforcement learning and even recent state-of-the art curiosity-based methods rely on the simple epsilon-greedy strategy to generate novelty. We argue that pure random walks do not succeed to properly expand the exploration area in most environments and propose to replace single random action choices by random goals selection followed by several steps in their direction. This approach is compatible with any curiosity-based exploration and off-policy reinforcement learning agents and generates longer and safer trajectories than individual random actions. To illustrate this, we present a task-independent agent that learns to reach coordinates in screen frames and demonstrate its ability to explore with the game Super Mario Bros. improving significantly the score of a baseline DQN agent.

Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the algorithm. We show that the proposed framework suffers from several issues; from undefined or pathological behaviour of the true posterior related to use of improper priors, to an ill-defined variational objective due to singularity of the approximating distribution relative to the true posterior. Our analysis of the improper log uniform prior used in variational Gaussian dropout suggests the pathologies are generally irredeemable, and that the algorithm still works only because the variational formulation annuls some of the pathologies. To address the singularity issue, we proffer Quasi-KL (QKL) divergence, a new approximate inference objective for approximation of high-dimensional distributions. We show that motivations for variational Bernoulli dropout based on discretisation and noise have QKL as a limit. Properties of QKL are studied both theoretically and on a simple practical example which shows that the QKL-optimal approximation of a full rank Gaussian with a degenerate one naturally leads to the Principal Component Analysis solution.

Most machine learning classifiers give predictions for new examples accurately, yet without indicating how trustworthy predictions are. In the medical domain, this hampers their integration in decision support systems, which could be useful in the clinical practice. We use a supervised learning approach that combines Ensemble learning with Conformal Predictors to predict conversion from Mild Cognitive Impairment to Alzheimer's Disease. Our goal is to enhance the classification performance (Ensemble learning) and complement each prediction with a measure of credibility (Conformal Predictors). Our results showed the superiority of the proposed approach over a similar ensemble framework with standard classifiers.

We present an instance segmentation algorithm trained and applied to a CCTV recording of beef cattle during a winter finishing period. A fully convolutional network was transformed into an instance segmentation network that learns to label each instance of an animal separately. We introduce a conceptually simple framework that the network uses to output a single prediction for every animal. These results are a contribution towards behaviour analysis in winter finishing beef cattle for early detection of animal welfare-related problems.

We revisit logistic regression and its nonlinear extensions, including multilayer feedforward neural networks, by showing that these classifiers can be viewed as converting input or higher-level features into Dempster-Shafer mass functions and aggregating them by Dempster's rule of combination. The probabilistic outputs of these classifiers are the normalized plausibilities corresponding to the underlying combined mass function. This mass function is more informative than the output probability distribution. In particular, it makes it possible to distinguish between lack of evidence (when none of the features provides discriminant information) from conflicting evidence (when different features support different classes). This expressivity of mass functions allows us to gain insight into the role played by each input feature in logistic regression, and to interpret hidden unit outputs in multilayer neural networks. It also makes it possible to use alternative decision rules, such as interval dominance, which select a set of classes when the available evidence does not unambiguously point to a single class, thus trading reduced error rate for higher imprecision.

Stochastic video prediction is usually framed as an extrapolation problem where the goal is to sample a sequence of consecutive future image frames conditioned on a sequence of observed past frames. For the most part, algorithms for this task generate future video frames sequentially in an autoregressive fashion, which is slow and requires the input and output to be consecutive. We introduce a model that overcomes these drawbacks -- it learns to generate a global latent representation from an arbitrary set of frames within a video. This representation can then be used to simultaneously and efficiently sample any number of temporally consistent frames at arbitrary time-points in the video. We apply our model to synthetic video prediction tasks and achieve results that are comparable to state-of-the-art video prediction models. In addition, we demonstrate the flexibility of our model by applying it to 3D scene reconstruction where we condition on location instead of time. To the best of our knowledge, our model is the first to provide flexible and coherent prediction on stochastic video datasets, as well as consistent 3D scene samples. Please check the project website https://bit.ly/2jX7Vyu to view scene reconstructions and videos produced by our model.

Active learning is relevant and challenging for high-dimensional regression models when the annotation of the samples is expensive. Yet most of the existing sampling methods cannot be applied to large-scale problems, consuming too much time for data processing. In this paper, we propose a fast active learning algorithm for regression, tailored for neural network models. It is based on uncertainty estimation from stochastic dropout output of the network. Experiments on both synthetic and real-world datasets show comparable or better performance (depending on the accuracy metric) as compared to the baselines. This approach can be generalized to other deep learning architectures. It can be used to systematically improve a machine-learning model as it offers a computationally efficient way of sampling additional data.

In this paper we propose two novel bounds for the log-likelihood based on Kullback-Leibler and the R\'{e}nyi divergences, which can be used for variational inference and in particular for the training of Variational AutoEncoders. Our proposal is motivated by the difficulties encountered in training VAEs on continuous datasets with high contrast images, such as those with handwritten digits and characters, where numerical issues often appear unless noise is added, either to the dataset during training or to the generative model given by the decoder. The new bounds we propose, which are obtained from the maximization of the likelihood of an interval for the observations, allow numerically stable training procedures without the necessity of adding any extra source of noise to the data.

Recent developments in deep reinforcement learning have enabled the creation of agents for solving a large variety of games given a visual input. These methods have been proven successful for 2D games, like the Atari games, or for simple tasks, like navigating in mazes. It is still an open question, how to address more complex environments, in which the reward is sparse and the state space is huge. In this paper we propose a divide and conquer deep reinforcement learning solution and we test our agent in the first person shooter (FPS) game of Doom. Our work is based on previous works in deep reinforcement learning and in Doom agents. We also present how our agent is able to perform better in unknown environments compared to a state of the art reinforcement learning algorithm.