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.

We introduce a new and rigorously-formulated PAC-Bayes few-shot meta-learning algorithm that implicitly learns a prior distribution of the model of interest. Our proposed method extends the PAC-Bayes framework from a single task setting to the few-shot learning setting to upper-bound generalisation errors on unseen tasks and samples. We also propose a generative-based approach to model the shared prior and the posterior of task-specific model parameters more expressively compared to the usual diagonal Gaussian assumption. We show that the models trained with our proposed meta-learning algorithm are well calibrated and accurate, with state-of-the-art calibration and classification results on few-shot classification (mini-ImageNet and tiered-ImageNet) and regression (multi-modal task-distribution regression) benchmarks.

Recently latent factor model (LFM) has been drawing much attention in recommender systems due to its good performance and scalability. However, existing LFMs predict missing values in a user-item rating matrix only based on the known ones, and thus the sparsity of the rating matrix always limits their performance. Meanwhile, semi-supervised learning (SSL) provides an effective way to alleviate the label (i.e., rating) sparsity problem by performing label propagation, which is mainly based on the smoothness insight on affinity graphs. However, graph-based SSL suffers serious scalability and graph unreliable problems when directly being applied to do recommendation. In this paper, we propose a novel probabilistic chain graph model (CGM) to marry SSL with LFM. The proposed CGM is a combination of Bayesian network and Markov random field. The Bayesian network is used to model the rating generation and regression procedures, and the Markov random field is used to model the confidence-aware smoothness constraint between the generated ratings. Experimental results show that our proposed CGM significantly outperforms the state-of-the-art approaches in terms of four evaluation metrics, and with a larger performance margin when data sparsity increases.

Automatic Differentiation Variational Inference (ADVI) is a useful tool for efficiently learning probabilistic models in machine learning. Generally approximate posteriors learned by ADVI are forced to be unimodal in order to facilitate use of the reparameterization trick. In this paper, we show how stratified sampling may be used to enable mixture distributions as the approximate posterior, and derive a new lower bound on the evidence analogous to the importance weighted autoencoder (IWAE). We show that this "SIWAE" is a tighter bound than both IWAE and the traditional ELBO, both of which are special instances of this bound. We verify empirically that the traditional ELBO objective disfavors the presence of multimodal posterior distributions and may therefore not be able to fully capture structure in the latent space. Our experiments show that using the SIWAE objective allows the encoder to learn more complex distributions which regularly contain multimodality, resulting in higher accuracy and better calibration in the presence of incomplete, limited, or corrupted data.

Various AI models are increasingly being considered as part of clinical decision-support tools. However, the trustworthiness of such models is rarely considered. Clinicians are more likely to use a model if they can understand and trust its predictions. Key to this is if its underlying reasoning can be explained. A Bayesian network (BN) model has the advantage that it is not a black-box and its reasoning can be explained. In this paper, we propose an incremental explanation of inference that can be applied to'hybrid' BNs, i.e. those that contain both discrete and continuous nodes. The key questions that we answer are: (1) which important evidence supports or contradicts the prediction, and (2) through which intermediate variables does the information flow. The explanation is illustrated using a real clinical case study. A small evaluation study is also conducted.

The data model of standard sparse coding assumes a weighted linear summation of latents to determine the mean of Gaussian observation noise. However, such a linear summation of latents is often at odds with non-Gaussian observables (e.g., means of the Bernoulli distribution have to lie in the unit interval), and also in the Gaussian case it can be difficult to justify for many types of data. Alternative superposition models (i.e., links between latents and observables) have therefore been investigated repeatedly. Here we show that using the maximum instead of a linear sum to link latents to observables allows for the derivation of very general and concise parameter update equations. Concretely, we derive a set of update equations that has the same functional form for all distributions of the exponential family (given that derivatives w.r.t. their parameters can be taken). Our results consequently allow for the development of latent variable models for commonly as well as for unusually distributed data. We numerically verify our analytical result assuming standard Gaussian, Gamma, Poisson, Bernoulli and Exponential distributions and point to some potential applications.