Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is challenging due to the high dimensionality of the parameter space. In this paper, we construct low-dimensional subspaces of parameter space, such as the first principal components of the stochastic gradient descent (SGD) trajectory, which contain diverse sets of high performing models. In these subspaces, we are able to apply elliptical slice sampling and variational inference, which struggle in the full parameter space. We show that Bayesian model averaging over the induced posterior in these subspaces produces accurate predictions and well calibrated predictive uncertainty for both regression and image classification.

Gaussian processes are expressive, non-parametric statistical models that are well-suited to learn nonlinear dynamical systems. However, large-scale inference in these state space models is a challenging problem. In this paper, we propose CBF-SSM a scalable model that employs a structured variational approximation to maintain temporal correlations. In contrast to prior work, our approach applies to the important class of unstable systems, where state uncertainty grows unbounded over time. For these systems, our method contains a probabilistic, model-based backward pass that infers latent states during training. We demonstrate state-of-the-art performance in our experiments. Moreover, we show that CBF-SSM can be combined with physical models in the form of ordinary differential equations to learn a reliable model of a physical flying robotic vehicle.

In recent years, the use of data-driven modelling and integration of behavioural and psychological factors in discrete choice and travel behaviour analysis have become active areas of research [2, 3, 4]. In the context of data-driven models, behavioural variations describe the correlation between observed choice attributes and unobserved socioeconomic factors using a flexible and tractable model specification. These variations include: decision-protocols, choice sets, unobserved taste variations and unobserved attributes [5]. Under these considerations, recent studies on travel behaviour analysis have so far primarily focused on representing heterogeneity in the error correction function and incorporating it into utility based multinomial logit (MNL) models [3]. Models such as mixed multinomial logit (MMNL) or latent class (LC) model offers flexibility in representing heterogeneity and substitution patterns. In addition, recent conceptual frameworks such as the integrated choice and latent variable (ICLV) use individuals' psychometric indicators to represent unobserved behavioural and perception heterogeneity [6]. It is also possible to apply a generative machine learning to identify informative latent constructs in travel decision making without subjective behaviour indicators [7, 8]. However, the true underlying behavioural patterns are often unknown and usually approximated by some predetermined exogenous indicator variables that would often lead to model misspecification due to lack of complete information, or error in data collection [9]. Furthermore, accurate specification of the underlying distribution assumes individuals have access to all available information regarding the travel activity (e.g.

We offer a graphical interpretation of unfairness in a dataset as the presence of an unfair causal path in the causal Bayesian network representing the data-generation mechanism. We use this viewpoint to revisit the recent debate surrounding the COMPAS pretrial risk assessment tool and, more generally, to point out that fairness evaluation on a model requires careful considerations on the patterns of unfairness underlying the training data. We show that causal Bayesian networks provide us with a powerful tool to measure unfairness in a dataset and to design fair models in complex unfairness scenarios.

In this paper, we consider sequential online prediction (SOP) for streaming data in the presence of outliers and change points. We propose an INstant TEmporal structure Learning (INTEL) algorithm to address this problem.Our INTEL algorithm is developed based on a full consideration to the duality between online prediction and anomaly detection. We first employ a mixture of weighted GP models (WGPs) to cover the expected possible temporal structures of the data. Then, on the basis of the rich modeling capacity of this WGP mixture, we develop an efficient technique to instantly learn (capture) the temporal structure of the data that follows a regime shift. This instant learning is achieved only by adjusting one hyper-parameter value of the mixture model. A weighted generalization of the product of experts (POE) model is used for fusing predictions yielded from multiple GP models. An outlier is declared once a real observation seriously deviates from the fused prediction. If a certain number of outliers are consecutively declared, then a change point is declared. Extensive experiments are performed using a diverse of real datasets. Results show that the proposed algorithm is significantly better than benchmark methods for SOP in the presence of outliers and change points.

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic Gaussian model observed on a spatial grid, which need not be rectangular. Standard methods are plagued by computational intractability, where designing methods that can be implemented for realistically sized problems has been an issue for a long time. This has motivated the use of the Fourier Transform and the Whittle likelihood approximation. The challenge of frequency-domain methods is to determine and account for observational boundary effects, missing data, and the shape of the observed spatial grid. In this paper we address these effects explicitly by proposing a new quasi-likelihood estimator. We prove consistency and asymptotic normality of our estimator, and show that the proposed method solves boundary issues with Whittle estimation for finite samples, yielding parameter estimates with significantly reduced bias and error. We demonstrate the effectiveness of our method for incomplete lattices, in comparison to other recent methods. Finally, we apply our method to estimate the parameters of a Mat\'ern process used to model data from Venus' topography.

This paper proposes a new architecture of incremen-tal fuzzy inference system (also called Evolving Fuzzy System-EFS). In the context of classifying data stream in non stationary environment, concept drifts problems must be addressed. Several studies have shown that EFS can deal with such environment thanks to their high structural flexibility. These EFS perform well with smooth drift (or incremental drift). The new architecture we propose is focused on improving the processing of brutal changes in the data distribution (often called brutal concept drift). More precisely, a generalized EFS is paired with a module of anticipation to improve the adaptation of new rules after a brutal drift. The proposed architecture is evaluated on three datasets from UCI repository where artificial brutal drifts have been applied. A fit model is also proposed to get a "reactivity time" needed to converge to the steady-state and the score at end. Both characteristics are compared between the same system with and without anticipation and with a similar EFS from state-of-the-art. The experiments demonstrates improvements in both cases.

Causal inference requires theory and prior knowledge to structure analyses, and is not usually thought of as an arena for the application of prediction modelling. However, contemporary causal inference methods, premised on counterfactual or potential outcomes approaches, often include processing steps before the final estimation step. The purposes of this paper are: (i) to overview the recent emergence of prediction underpinning steps in contemporary causal inference methods as a useful perspective on contemporary causal inference methods, and (ii) explore the role of machine learning (as one approach to'best prediction') in causal inference. Causal inference methods covered include propensity scores, inverse probability of treatment weights (IPTWs), G computation and targeted maximum likelihood estimation (TMLE). Machine learning has been used more for propensity scores and TMLE, and there is potential for increased use in G computation and estimation of IPTWs.

Mixtures-of-Experts (MoE) are conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning approaches for prediction, including regression and classification, as well as for clustering. Their estimation in high-dimensional problems is still however challenging. We consider the problem of parameter estimation and feature selection in MoE models with different generalized linear experts models, and propose a regularized maximum likelihood estimation that efficiently encourages sparse solutions for heterogeneous data with high-dimensional predictors. The developed proximal-Newton EM algorithm includes proximal Newton-type procedures to update the model parameter by monotonically maximizing the objective function and allows to perform efficient estimation and feature selection. An experimental study shows the good performance of the algorithms in terms of recovering the actual sparse solutions, parameter estimation, and clustering of heterogeneous regression data, compared to the main state-of-the art competitors.

Although deep neural networks have been widely applied in various domains [19, 25, 27], usually its parameters are learned via the principle of maximum likelihood, hence its success crucially hinges on the availability of large scale datasets. When training rich models on small datasets, explicit regularization techniques are crucial to alleviate overfitting. Previous works have explored various regularization [39] and data augmentation [19, 38] techniques to learn diversified representations. In this paper, we look into an alternative direction by proposing an adaptive and data-dependent regularization method to encourage neurons of the same layer to share statistical strength. The goal of our method is to prevent overfitting when training (large) networks on small dataset. Our key insight stems from the famous argument by Efron [8] in the literature of the empirical Bayes method: It is beneficial to learn from the experience of others. From an algorithmic perspective, we argue that the connection weights of neurons in the same layer (row/column vectors of the weight matrix) will be correlated with each other through the backpropagation learning. Hence, by learning the correlations of the weight matrix, a neuron can "borrow statistical strength" from other neurons in the same layer.