Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called \textit{Type II maximum likelihood} or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call \textit{Fully Bayesian Gaussian Process Regression} (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC) yielding a sampling-based approximation and 2) Variational Inference (VI) where the posterior over hyperparameters is approximated by a factorized Gaussian (mean-field) or a full-rank Gaussian accounting for correlations between hyperparameters. We analyze the predictive performance for fully Bayesian GPR on a range of benchmark data sets.

Robustness to out-of-distribution (OOD) data is an important goal in building reliable machine learning systems. Especially in autonomous systems, wrong predictions for OOD inputs can cause safety critical situations. As a first step towards a solution, we consider the problem of detecting such data in a value-based deep reinforcement learning (RL) setting. Modelling this problem as a one-class classification problem, we propose a framework for uncertainty-based OOD classification: UBOOD. It is based on the effect that an agent's epistemic uncertainty is reduced for situations encountered during training (in-distribution), and thus lower than for unencountered (OOD) situations. Being agnostic towards the approach used for estimating epistemic uncertainty, combinations with different uncertainty estimation methods, e.g. approximate Bayesian inference methods or ensembling techniques are possible. We further present a first viable solution for calculating a dynamic classification threshold, based on the uncertainty distribution of the training data. Evaluation shows that the framework produces reliable classification results when combined with ensemble-based estimators, while the combination with concrete dropout-based estimators fails to reliably detect OOD situations. In summary, UBOOD presents a viable approach for OOD classification in deep RL settings by leveraging the epistemic uncertainty of the agent's value function.

Sequence generation models are commonly refined with reinforcement learning over user-defined metrics. However, high gradient variance hinders the practical use of this method. To stabilize this method, we adapt to contextual generation of categorical sequences a policy gradient estimator, which evaluates a set of correlated Monte Carlo (MC) rollouts for variance control. Due to the correlation, the number of unique rollouts is random and adaptive to model uncertainty; those rollouts naturally become baselines for each other, and hence are combined to effectively reduce gradient variance. We also demonstrate the use of correlated MC rollouts for binary-tree softmax models, which reduce the high generation cost in large vocabulary scenarios by decomposing each categorical action into a sequence of binary actions. We evaluate our methods on both neural program synthesis and image captioning. The proposed methods yield lower gradient variance and consistent improvement over related baselines.

Normalizing flows transform a latent distribution through an invertible neural network for a flexible and pleasingly simple approach to generative modelling, while preserving an exact likelihood. We propose FlowGMM, an end-to-end approach to generative semi supervised learning with normalizing flows, using a latent Gaussian mixture model. FlowGMM is distinct in its simplicity, unified treatment of labelled and unlabelled data with an exact likelihood, interpretability, and broad applicability beyond image data. We show promising results on a wide range of applications, including AG-News and Yahoo Answers text data, tabular data, and semi-supervised image classification. We also show that FlowGMM can discover interpretable structure, provide real-time optimization-free feature visualizations, and specify well calibrated predictive distributions.

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a data-based, probablistic perspective that enables the quantification of predictive uncertainties. One of the outstanding problems has been the introduction of physical constraints in the probabilistic machine learning objectives. The primary utility of such constraints stems from the undisputed physical laws such as conservation of mass, energy etc that they represent. Furthermore and apart from leading to physically realistic predictions, they can significantly reduce the requisite amount of training data which for high-dimensional, multiscale systems are expensive to obtain (Small Data regime). We formulate the coarse-graining process by employing a probabilistic state-space model and account for the aforementioned equality constraints as virtual observables in the associated densities. We demonstrate how probabilistic inference tools can be employed to identify the coarse-grained variables in combination with deep neural nets and their evolution model without ever needing to define a fine-to-coarse (restriction) projection and without needing time-derivatives of state variables. The formulation adopted enables the quantification of a crucial, and often neglected, component in the CG process, i.e. the predictive uncertainty due to information loss. Furthermore, it is capable of reconstructing the evolution of the full, fine-scale system and therefore the observables of interest need not be selected a priori. We demonstrate the efficacy of the proposed framework by applying it to systems of interacting particles and an image series of a nonlinear pendulum. In both cases we identify the underlying coarse dynamics and can generate extrap-olative predicitions including the forming and propagation of a shock for the particle systems and a stable trajectory in the phase space for the pendulum. Keywords: Bayesian machine learning, virtual observables, multiscale modeling, reduced order modeling, coarse graining1. Introduction High-dimensional, nonlinear dynamical systems are ubiquitous in applied physics and engineering. The computational resources needed for their solution can grow exponentially with the dimension of the state-space as well as with the smallest timescale that needs to be resolved as this determines the discretization time-step.

Describing or calculating the conditional probabilities of multiple events is exponentially expensive. In this work, a natural generalization of Bayesian belief network is proposed by incorporating with tensor network, which is dubbed as Bayesian tensor network (BTN), to efficiently describe the conditional probabilities among multiple sets of events. The complexity of BTN that gives the conditional probabilities of $M$ sets of events scales only polynomially with $M$. To testify its validity, BTN is implemented to capture the conditional probabilities between images and their classifications, where each feature is mapped to a probability distribution of a set of mutually exclusive events. A rotation optimization method is suggested to update BTN, which avoids gradient vanishing problem and exhibits high efficiency. With a simple tree network structures, BTN exhibits competitive performances on fashion-MNIST dataset. Analogous to the tensor network simulations of quantum systems, the validity of BTN implies an "area law" of fluctuations in image recognition problems.

Despite the recent successes of deep learning, such models are still far from some human abilities like learning from few examples, reasoning and explaining decisions. In this paper, we focus on organ annotation in medical images and we introduce a reasoning framework that is based on learning fuzzy relations on a small dataset for generating explanations. Given a catalogue of relations, it efficiently induces the most relevant relations and combines them for building constraints in order to both solve the organ annotation task and generate explanations. We test our approach on a publicly available dataset of medical images where several organs are already segmented. A demonstration of our model is proposed with an example of explained annotations. It was trained on a small training set containing as few as a couple of examples.

Deep neural networks (DNN) are versatile parametric models utilised successfully in a diverse number of tasks and domains. However, they have limitations---particularly from their lack of robustness and over-sensitivity to out of distribution samples. Bayesian Neural Networks, due to their formulation under the Bayesian framework, provide a principled approach to building neural networks that address these limitations. This paper describes a study that empirically evaluates and compares Bayesian Neural Networks to their equivalent point estimate Deep Neural Networks to quantify the predictive uncertainty induced by their parameters, as well as their performance in view of this uncertainty. In this study, we evaluated and compared three point estimate deep neural networks against comparable Bayesian neural network alternatives using two well-known benchmark image classification datasets (CIFAR-10 and SVHN).

As in any interaction process, misunderstandings, ambiguity, and failures to correctly understand the interaction partner are bound to happen in human-robot interaction. We term these failures 'conflicts' and are interested in both conflict detection and conflict resolution. In that, we focus on the robot's perspective. For the robot, conflicts may occur because of errors in its perceptual processes or because of ambiguity stemming from human input. This poster presents a brief system overview, and details Here, we briefly outline the project's motivation and setting, introduce the general processing framework, and then present two kinds of conflicts in some more detail: 1) a failure to identify a relevant object at all; 2) ambiguity emerging from multiple matches in scene perception.

This paper introduces a new approach to learning from i.i.d. data under model miss-specification. This approach casts the problem of learning as minimizing the expected code-length of a Bayesian mixture code. To solve this problem, we build on PAC-Bayes bounds, information theory and a new family of second-order Jensen bounds. The key insight of this paper is that the use of the standard (first-order) Jensen bounds in learning is suboptimal when our model class is miss-specified (i.e. it does not contain the data generating distribution). As a consequence of this insight, this work provides strong theoretical arguments explaining why the Bayesian posterior is not optimal for making predictions that generalize under model miss-specification because the Bayesian posterior is directly related to the use of first-order Jensen bounds. We then argue for the use of second-order Jensen bounds, which leads to new families of learning algorithms. In this work, we introduce novel variational and ensemble learning methods based on the minimization of a novel family of second-order PAC-Bayes bounds over the expected code-length of a Bayesian mixture code. Using this new framework, we also provide novel hypotheses of why parameters in a flat minimum generalize better than parameters in a sharp minimum.