Bayesian Inference and Information Bottleneck are the two most popular objectives for neural networks, but they can be optimised only via a variational lower bound: the Variational Information Bottleneck (VIB). In this manuscript we show that the two objectives are actually equivalent to the InfoMax: maximise the information between the data and the labels. The InfoMax representation of the two objectives is not relevant only per se, since it helps to understand the role of the network capacity, but also because it allows us to derive a variational objective, the Variational InfoMax (VIM), that maximises them directly without resorting to any lower bound. The theoretical improvement of VIM over VIB is highlighted by the computational experiments, where the model trained by VIM improves the VIB model in three different tasks: accuracy, robustness to noise and representation quality.

Adversarial Machine Learning (AML) is emerging as a major field aimed at the protection of automated ML systems against security threats. The majority of work in this area has built upon a game-theoretic framework by modelling a conflict between an attacker and a defender. After reviewing game-theoretic approaches to AML, we discuss the benefits that a Bayesian Adversarial Risk Analysis perspective brings when defending ML based systems. A research agenda is included.

Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the expectation of interested functions w.r.t. a target distribution. When it comes to high dimensional probability models and large datasets, efficient approximate inference becomes critically important. In this thesis, we propose a new framework for approximate inference, which combines the advantages of these three frameworks and overcomes their limitations. Our proposed four algorithms are motivated by the recent computational progress of Stein's method. Our proposed algorithms are applied to continuous and discrete distributions under the setting when the gradient information of the target distribution is available or unavailable. Theoretical analysis is provided to prove the convergence of our proposed algorithms. Our adaptive IS algorithm iteratively improves the importance proposal by functionally decreasing the KL divergence between the updated proposal and the target. When the gradient of the target is unavailable, our proposed sampling algorithm leverages the gradient of a surrogate model and corrects induced bias with importance weights, which significantly outperforms other gradient-free sampling algorithms. In addition, our theoretical results enable us to perform the goodness-of-fit test on discrete distributions. At the end of the thesis, we propose an importance-weighted method to efficiently aggregate local models in distributed learning with one-shot communication. Results on simulated and real datasets indicate the statistical efficiency and wide applicability of our algorithm.

Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence to approximate the gradient of the KL divergence between data and model distribution. While KL divergence has many desirable properties, other f-divergences have shown advantages in training implicit density generative models such as generative adversarial networks. In this paper, we propose a general variational framework termed f-EBM to train EBMs using any desired f-divergence. We introduce a corresponding optimization algorithm and prove its local convergence property with non-linear dynamical systems theory. Experimental results demonstrate the superiority of f-EBM over contrastive divergence, as well as the benefits of training EBMs using f-divergences other than KL.

The identification of synthetic routes that end with a desired product has been an inherently time-consuming process that is largely dependent on expert knowledge regarding a limited fraction of the entire reaction space. At present, emerging machine-learning technologies are overturning the process of retrosynthetic planning. The objective of this study is to discover synthetic routes backwardly from a given desired molecule to commercially available compounds. The problem is reduced to a combinatorial optimization task with the solution space subject to the combinatorial complexity of all possible pairs of purchasable reactants. We address this issue within the framework of Bayesian inference and computation. The workflow consists of two steps: a deep neural network is trained that forwardly predicts a product of the given reactants with a high level of accuracy, following which this forward model is inverted into the backward one via Bayes' law of conditional probability. Using the backward model, a diverse set of highly probable reaction sequences ending with a given synthetic target is exhaustively explored using a Monte Carlo search algorithm. The Bayesian retrosynthesis algorithm could successfully rediscover 80.3% and 50.0% of known synthetic routes of single-step and two-step reactions within top-10 accuracy, respectively, thereby outperforming state-of-the-art algorithms in terms of the overall accuracy. Remarkably, the Monte Carlo method, which was specifically designed for the presence of diverse multiple routes, often revealed a ranked list of hundreds of reaction routes to the same synthetic target. We investigated the potential applicability of such diverse candidates based on expert knowledge from synthetic organic chemistry.

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Most previous works treat the locations of the inducing variables, i.e. the inducing inputs, as variational hyperparameters, and these are then optimized together with GP covariance hyper-parameters. While some approaches point to the benefits of a Bayesian treatment of GP hyper-parameters, this has been largely overlooked for the inducing inputs. In this work, we show that treating both inducing locations and GP hyper-parameters in a Bayesian way, by inferring their full posterior, further significantly improves performance. Based on stochastic gradient Hamiltonian Monte Carlo, we develop a fully Bayesian approach to scalable GP and deep GP models, and demonstrate its competitive performance through an extensive experimental campaign across several regression and classification problems.

As machine learning algorithms are increasingly deployed for high-impact automated decision making, ethical and increasingly also legal standards demand that they treat all individuals fairly, without discrimination based on their age, gender, race or other sensitive traits. In recent years much progress has been made on ensuring fairness and reducing bias in standard machine learning settings. Yet, for network embedding, with applications in vulnerable domains ranging from social network analysis to recommender systems, current options remain limited both in number and performance. We thus propose DeBayes: a conceptually elegant Bayesian method that is capable of learning debiased embeddings by using a biased prior. Our experiments show that these representations can then be used to perform link prediction that is significantly more fair in terms of popular metrics such as demographic parity and equalized opportunity.

A decentralized Poisson multi-Bernoulli filter is proposed to track multiple vehicles using multiple high-resolution sensors. Independent filters estimate the vehicles' presence, state, and shape using a Gaussian process extent model; a decentralized filter is realized through fusion of the filters posterior densities. An efficient implementation is achieved by parametric state representation, utilization of single hypothesis tracks, and fusion of vehicle information based on a fusion mapping. Numerical results demonstrate the performance.

Probability models have been proposed in the literature to account for "intelligent" behavior in many contexts. In this paper, probability propagation is applied to model agent's motion in potentially complex scenarios that include goals and obstacles. The backward flow provides precious background information to the agent's behavior, viz., inferences coming from the future determine the agent's actions. Probability tensors are layered in time in both directions in a manner similar to convolutional neural networks. The discussion is carried out with reference to a set of simulated grids where, despite the apparent task complexity, a solution, if feasible, is always found. The original model proposed by Attias has been extended to include non-absorbing obstacles, multiple goals and multiple agents. The emerging behaviors are very realistic and demonstrate great potentials of the application of this framework to real environments.

Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear models are often not sufficient to describe the complex relationship between input variables and a response. This relationship can be better described by non-linearities and complex functional interactions. Deep learning models have been extremely successful in terms of prediction although they are often difficult to specify and potentially suffer from overfitting. In this paper, we introduce a class of Bayesian generalized nonlinear regression models with a comprehensive non-linear feature space. Non-linear features are generated hierarchically, similarly to deep learning, but have additional flexibility on the possible types of features to be considered. This flexibility, combined with variable selection, allows us to find a small set of important features and thereby more interpretable models. A genetically modified Markov chain Monte Carlo algorithm is developed to make inference. Model averaging is also possible within our framework. In various applications, we illustrate how our approach is used to obtain meaningful non-linear models. Additionally, we compare its predictive performance with a number of machine learning algorithms.