Normalizing flows are diffeomorphic, typically dimension-preserving, models trained using the likelihood of the model. We use the SurVAE framework to construct dimension reducing surjective flows via a new layer, known as the funnel. We demonstrate its efficacy on a variety of datasets, and show it improves upon or matches the performance of existing flows while having a reduced latent space size. The funnel layer can be constructed from a wide range of transformations including restricted convolution and feed forward layers.

The technologies used in smart homes have recently improved to learn the user preferences from feedback in order to enhance the user convenience and quality of experience. Most smart homes learn a uniform model to represent the thermal preferences of users, which generally fails when the pool of occupants includes people with different sensitivities to temperature, for instance due to age and physiological factors. Thus, a smart home with a single optimal policy may fail to provide comfort when a new user with a different preference is integrated into the home. In this paper, we propose a Bayesian Reinforcement learning framework that can approximate the current occupant state in a partially observable smart home environment using its thermal preference, and then identify the occupant as a new user or someone is already known to the system. Our proposed framework can be used to identify users based on the temperature and humidity preferences of the occupant when performing different activities to enable personalization and improve comfort. We then compare the proposed framework with a baseline long short-term memory learner that learns the thermal preference of the user from the sequence of actions which it takes. We perform these experiments with up to 5 simulated human models each based on hierarchical reinforcement learning. The results show that our framework can approximate the belief state of the current user just by its temperature and humidity preferences across different activities with a high degree of accuracy.

Contrastive learning has become a key component of self-supervised learning approaches for graph-structured data. However, despite their success, existing graph contrastive learning methods are incapable of uncertainty quantification for node representations or their downstream tasks, limiting their application in high-stakes domains. In this paper, we propose a novel Bayesian perspective of graph contrastive learning methods showing random augmentations leads to stochastic encoders. As a result, our proposed method represents each node by a distribution in the latent space in contrast to existing techniques which embed each node to a deterministic vector. By learning distributional representations, we provide uncertainty estimates in downstream graph analytics tasks and increase the expressive power of the predictive model. In addition, we propose a Bayesian framework to infer the probability of perturbations in each view of the contrastive model, eliminating the need for a computationally expensive search for hyperparameter tuning. We empirically show a considerable improvement in performance compared to existing state-of-the-art methods on several benchmark datasets.

In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected. The Graph Neural Network (GNN) has proven to be a very useful tool in a variety of graph learning tasks including node classification, link prediction, and edge classification. However, in most of these tasks, the graph data we are working with may be noisy and may contain spurious edges. That is, there is a lot of uncertainty associated with the underlying graph structure. Recent approaches to modeling uncertainty have been to use a Bayesian framework and view the graph as a random variable with probabilities associated with model parameters. Introducing the Bayesian paradigm to graph-based models, specifically for semi-supervised node classification, has been shown to yield higher classification accuracies. However, the method of graph inference proposed in recent work does not take into account the structure of the graph. In this paper, we propose a novel algorithm called Bayesian Graph Convolutional Network using Neighborhood Random Walk Sampling (BGCN-NRWS), which uses a Markov Chain Monte Carlo (MCMC) based graph sampling algorithm utilizing graph structure, reduces overfitting by using a variational inference layer, and yields consistently competitive classification results compared to the state-of-the-art in semi-supervised node classification.

The main objective of this paper is to outline a theoretical framework to characterise humans' decision-making strategies under uncertainty, in particular active learning in a black-box optimization task and trading-off between information gathering (exploration) and reward seeking (exploitation). Humans' decisions making according to these two objectives can be modelled in terms of Pareto rationality. If a decision set contains a Pareto efficient strategy, a rational decision maker should always select the dominant strategy over its dominated alternatives. A distance from the Pareto frontier determines whether a choice is Pareto rational. To collect data about humans' strategies we have used a gaming application that shows the game field, with previous decisions and observations, as well as the score obtained. The key element in this paper is the representation of behavioural patterns of human learners as a discrete probability distribution. This maps the problem of the characterization of humans' behaviour into a space whose elements are probability distributions structured by a distance between histograms, namely the Wasserstein distance (WST). The distributional analysis gives new insights about human search strategies and their deviations from Pareto rationality. Since the uncertainty is one of the two objectives defining the Pareto frontier, the analysis has been performed for three different uncertainty quantification measures to identify which better explains the Pareto compliant behavioural patterns. Beside the analysis of individual patterns WST has also enabled a global analysis computing the barycenters and WST k-means clustering. A further analysis has been performed by a decision tree to relate non-Paretian behaviour, characterized by exasperated exploitation, to the dynamics of the evolution of the reward seeking process.

Bayesian neural networks (BNNs) have become a principal approach to alleviate overconfident predictions in deep learning, but they often suffer from scaling issues due to a large number of distribution parameters. In this paper, we discover that the first layer of a deep network possesses multiple disparate optima when solely retrained. This indicates a large posterior variance when the first layer is altered by a Bayesian layer, which motivates us to design a spatial-temporal-fusion BNN (STF-BNN) for efficiently scaling BNNs to large models: (1) first normally train a neural network from scratch to realize fast training; and (2) the first layer is converted to Bayesian and inferred by employing stochastic variational inference, while other layers are fixed. Compared to vanilla BNNs, our approach can greatly reduce the training time and the number of parameters, which contributes to scale BNNs efficiently. We further provide theoretical guarantees on the generalizability and the capability of mitigating overconfidence of STF-BNN. Comprehensive experiments demonstrate that STF-BNN (1) achieves the state-of-the-art performance on prediction and uncertainty quantification; (2) significantly improves adversarial robustness and privacy preservation; and (3) considerably reduces training time and memory costs.

Feature selection pursues two major goals: to improve generalizability and performance of predictive algorithms like classification, regression, or clustering models and to improve data understanding and interpretability. Both aspects are of significant interest in fields like healthcare, where major decisions may be based on data analysis. Here, two sources of information are available: large-scale collections of data from multiple sources and profound knowledge from domain experts. Previous works tend to handle these sources as opposites, see [4], or neglect expert knowledge completely, see [30]. However, a combination of both can be valuable to compensate for underdetermined problem setups from high-dimensional datasets. Moreover, meta-information on the feature set may leverage interpretability. Works such as [21] consider constraints between samples but neglect constraints between features. The extension of L1 regularization to the so-called Group Lasso [43] and its variants [19] account for block structure but cannot handle more complex constraint types. There is a lack of sophisticated probabilistic frameworks that tackle this issue and deliver transparent results.

The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) based on a testing dataset. Whereas, these algorithms are optimized through the minimization of a typically different--more convenient--loss function based on a training set. For classification tasks, this loss function is often the negative log-loss that leads to the well-known cross-entropy risk which is typically better behaved (from a numerical perspective) than the error probability. Conventional studies on the generalization error do not usually take into account the underlying mismatch between losses at training and testing phases. In this work, we introduce an analysis based on point-wise PAC approach over the generalization gap considering the mismatch of testing based on the accuracy metric and training on the negative log-loss. We label this analysis PACMAN. Building on the fact that the mentioned mismatch can be written as a likelihood ratio, concentration inequalities can be used to provide some insights for the generalization problem in terms of some point-wise PAC bounds depending on some meaningful information-theoretic quantities. An analysis of the obtained bounds and a comparison with available results in the literature are also provided.

Uncertainty estimation (UE) techniques -- such as the Gaussian process (GP), Bayesian neural networks (BNN), Monte Carlo dropout (MCDropout) -- aim to improve the interpretability of machine learning models by assigning an estimated uncertainty value to each of their prediction outputs. However, since too high uncertainty estimates can have fatal consequences in practice, this paper analyzes the above techniques. Firstly, we show that GP methods always yield high uncertainty estimates on out of distribution (OOD) data. Secondly, we show on a 2D toy example that both BNNs and MCDropout do not give high uncertainty estimates on OOD samples. Finally, we show empirically that this pitfall of BNNs and MCDropout holds on real world datasets as well. Our insights (i) raise awareness for the more cautious use of currently popular UE methods in Deep Learning, (ii) encourage the development of UE methods that approximate GP-based methods -- instead of BNNs and MCDropout, and (iii) our empirical setups can be used for verifying the OOD performances of any other UE method. The source code is available at https://github.com/epfml/uncertainity-estimation.

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First, the form and the parameters of the kernel function are usually selected blindly, depending seriously on trial-and-error. As a result, there may be serious performance degradation in case of inappropriate selections. Second, at the online monitoring stage, KPCA has much computational burden and poor real-time performance, because the kernel method requires to leverage all the offline training data. In this work, to deal with the two drawbacks, a learnable faster realization of the conventional KPCA is proposed. The core idea is to parameterize all feasible kernel functions using the novel nonlinear DAE-FE (deep autoencoder based feature extraction) framework and propose DAE-PCA (deep autoencoder based principal component analysis) approach in detail. The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs. Furthermore, the online computational efficiency improves by approximately 100 times compared with the conventional KPCA. With the Tennessee Eastman (TE) process benchmark, the effectiveness and superiority of the proposed method is illustrated.