Imitation Learning (IL) is an effective learning paradigm exploiting the interactions between agents and environments. It does not require explicit reward signals and instead tries to recover desired policies using expert demonstrations. In general, IL methods can be categorized into Behavioral Cloning (BC) and Inverse Reinforcement Learning (IRL). In this work, a novel reward function based on probability density estimation is proposed for IRL, which can significantly reduce the complexity of existing IRL methods. Furthermore, we prove that the theoretically optimal policy derived from our reward function is identical to the expert policy as long as it is deterministic. Consequently, an IRL problem can be gracefully transformed into a probability density estimation problem. Based on the proposed reward function, we present a "watch-try-learn" style framework named Probability Density Estimation based Imitation Learning (PDEIL), which can work in both discrete and continuous action spaces. Finally, comprehensive experiments in the Gym environment show that PDEIL is much more efficient than existing algorithms in recovering rewards close to the ground truth.

Assessing the effects of the energy transition and liberalization of energy markets on resource adequacy is an increasingly important and demanding task. The rising complexity in energy systems requires adequate methods for energy system modeling leading to increased computational requirements. Furthermore, with complexity, uncertainty increases likewise calling for probabilistic assessments and scenario analyses. To adequately and efficiently address these various requirements, new methods from the field of data science are needed to accelerate current methods. With our systematic literature review, we want to close the gap between the three disciplines (1) assessment of security of electricity supply, (2) artificial intelligence, and (3) design of experiments. For this, we conduct a large-scale quantitative review on selected fields of application and methods and make a synthesis that relates the different disciplines to each other. Among other findings, we identify metamodeling of complex security of electricity supply models using AI methods and applications of AI-based methods for forecasts of storage dispatch and (non-)availabilities as promising fields of application that have not sufficiently been covered, yet. We end with deriving a new methodological pipeline for adequately and efficiently addressing the present and upcoming challenges in the assessment of security of electricity supply.

In this work we study the problem of robustly learning a Mallows model. We give an algorithm that can accurately estimate the central ranking even when a constant fraction of its samples are arbitrarily corrupted. Moreover our robustness guarantees are dimension-independent in the sense that our overall accuracy does not depend on the number of alternatives being ranked. Our work can be thought of as a natural infusion of perspectives from algorithmic robust statistics into one of the central inference problems in voting and information-aggregation. Specifically, our voting rule is efficiently computable and its outcome cannot be changed by much by a large group of colluding voters.

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.

A model's interpretability is essential to many practical applications such as clinical decision support systems. In this paper, a novel interpretable machine learning method is presented, which can model the relationship between input variables and responses in humanly understandable rules. The method is built by applying tropical geometry to fuzzy inference systems, wherein variable encoding functions and salient rules can be discovered by supervised learning. Experiments using synthetic datasets were conducted to investigate the performance and capacity of the proposed algorithm in classification and rule discovery. Furthermore, the proposed method was applied to a clinical application that identified heart failure patients that would benefit from advanced therapies such as heart transplant or durable mechanical circulatory support. Experimental results show that the proposed network achieved great performance on the classification tasks. In addition to learning humanly understandable rules from the dataset, existing fuzzy domain knowledge can be easily transferred into the network and used to facilitate model training. From our results, the proposed model and the ability of learning existing domain knowledge can significantly improve the model generalizability. The characteristics of the proposed network make it promising in applications requiring model reliability and justification.

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.