Unstructured data from diverse sources, such as social media and aerial imagery, can provide valuable up-to-date information for intelligent situation assessment. Mining these different information sources could bring major benefits to applications such as situation awareness in disaster zones and mapping the spread of diseases. Such applications depend on classifying the situation across a region of interest, which can be depicted as a spatial "heatmap". Annotating unstructured data using crowdsourcing or automated classifiers produces individual classifications at sparse locations that typically contain many errors. We propose a novel Bayesian approach that models the relevance, error rates and bias of each information source, enabling us to learn a spatial Gaussian Process classifier by aggregating data from multiple sources with varying reliability and relevance. Our method does not require gold-labelled data and can make predictions at any location in an area of interest given only sparse observations. We show empirically that our approach can handle noisy and biased data sources, and that simultaneously inferring reliability and transferring information between neighbouring reports leads to more accurate predictions. We demonstrate our method on two real-world problems from disaster response, showing how our approach reduces the amount of crowdsourced data required and can be used to generate valuable heatmap visualisations from SMS messages and satellite images.

The field of image reconstruction has undergone four waves of methods. The first wave was analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise trade-off for CT. The second wave was iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The FDA-approved methods among these have been based on relatively simple regularization models. The third wave of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low-rank. The fourth wave of methods replaces mathematically designed models of signals and processes with data-driven or adaptive models inspired by the field of machine learning. This paper reviews the progress in image reconstruction methods with focus on the two most recent trends: methods based on sparsity or low-rank models, and data-driven methods based on machine learning techniques.

This paper introduces a generalized representation of Bayesian inference. It is derived axiomatically, recovering existing Bayesian methods as special cases. We use it to prove that variational inference (VI) based on the Kullback-Leibler Divergence with a variational family Q produces the uniquely optimal Q-constrained approximation to the exact Bayesian inference problem. Surprisingly, this implies that standard VI dominates any other Q-constrained approximation to the exact Bayesian inference problem. This means that alternative Q-constrained approximations such as VI targeted at minimizing other divergences and Expectation Propagation can produce better posteriors than VI only by implicitly targeting more appropriate Bayesian inference problems. Inspired by this, we introduce Generalized Variational Inference (GVI), a modular approach for instead solving such alternative inference problems explicitly. We explore some applications of GVI, including robustness and better marginals. Lastly, we derive black box GVI and apply it to Bayesian Neural Networks as well as Deep Gaussian Processes, where GVI comprehensively outperforms competing methods.

Despite some empirical success at correcting exposure bias in machine translation, scheduled sampling algorithms suffer from a major drawback: they incorrectly assume that words in the reference translations and in sampled sequences are aligned at each time step. Our new differentiable sampling algorithm addresses this issue by optimizing the probability that the reference can be aligned with the sampled output, based on a soft alignment predicted by the model itself. As a result, the output distribution at each time step is evaluated with respect to the whole predicted sequence. Experiments on IWSLT translation tasks show that our approach improves BLEU compared to maximum likelihood and scheduled sampling baselines. In addition, our approach is simpler to train with no need for sampling schedule and yields models that achieve larger improvements with smaller beam sizes.

Despite their unprecedented performance in various domains, utilization of Deep Neural Networks (DNNs) in safety-critical environments is severely limited in the presence of even small adversarial perturbations. The present work develops a randomized approach to detecting such perturbations based on minimum uncertainty metrics that rely on sampling at the hidden layers during the DNN inference stage. The sampling probabilities are designed for effective detection of the adversarially corrupted inputs. Being modular, the novel detector of adversaries can be conveniently employed by any pre-trained DNN at no extra training overhead. Selecting which units to sample per hidden layer entails quantifying the amount of DNN output uncertainty from the viewpoint of Bayesian neural networks, where the overall uncertainty is expressed in terms of its layer-wise components - what also promotes scalability. Sampling probabilities are then sought by minimizing uncertainty measures layer-by-layer, leading to a novel convex optimization problem that admits an exact solver with superlinear convergence rate. By simplifying the objective function, low-complexity approximate solvers are also developed. In addition to valuable insights, these approximations link the novel approach with state-of-the-art randomized adversarial detectors. The effectiveness of the novel detectors in the context of competing alternatives is highlighted through extensive tests for various types of adversarial attacks with variable levels of strength.

We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive ratio $3 + O(1/m)$, irrespective of the ambient dimension. Additionally, we show that when the sequence of cost functions is $\epsilon$-smooth, OBD has near-optimal dynamic regret and maintains strong per-round accuracy. We demonstrate the generality of our approach by showing that the OBD framework can be used to construct competitive algorithms for a variety of online problems across learning and control, including online variants of ridge regression, logistic regression, maximum likelihood estimation, and LQR control.

Propositional model counting (MC), or #SAT, is the task of counting the number of satisfying assignments for a given propositional formula [14]. Weighted model counting (WMC), or weighted #SAT, additionally incorporates a weight function over the set of all possible assignments. Offering an elegant formalism for encoding various probabilistic inference problems, WMC is a unifying approach for probabilistic inference. In particular, probabilistic graphical models [20], probabilistic planning [10], probabilistic logic programming [25], probabilistic databases [30] and probabilistic ontologies [2] can greatly benefit from advances in WMC. Two important special cases of WMC are weighted #CNF and weighted #DNF, where the former requires the input formula to be in CNF, and the latter to be in DNF. Both of these problems have a wide variety of applications. Inference in probabilistic graphical models typically reduces to solving weighted #CNF instances, while query evaluation in probabilistic databases reduces to solving weighted #DNF instances. The major bottleneck in WMC is its inherent computational complexity.

Traditional cognitive theories systematically apply classical set-theoretic structures to model human judgements and decisions under uncertainty. This is particularly evident in theories of rational decision-making, like expected utility theory, where Bayesian, or Kolmogorovian [1], models of probability directly follow from axioms on agents' preferences [2, 3]. However, several cognitive puzzles have been discovered in empirical tests, which provide evidence of systematic deviations from Kolmogorovian probability structures (see, e.g., [4]). For example, Kahneman and Tversky identified a conjunction fallacy in human probability judgements, namely, the law of monotonicity of Kolmogorovian probability does not generally hold in this kind of judgements [5]. Also, in human decision-making, Tversky and Shafir proved that the law of total Kolmogorovian probability does not hold in the disjunction effect [6], while Allais and Ellsberg indicated that people do not always choose by maximizing an expected utility with respect to a Kolmogorovian probability measure [7]. As a consequence of the puzzles above, traditional theories using Kolmogorovian structures, though normatively compelling, are descriptively flawed, which led several authors to elaborate alternative proposals able to more efficiently and realistically represent human behaviour. This was the starting point of the bounded rationality research programme, initially proposed by Herbert Simon [8] and systematically applied by Kahneman and Tversky [5, 6] to describe concrete judgements and decisions. Bounded rationality models give good predictions in a variety of circumstances.

This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learning-based data-driven multistage optimization with a learning-while-optimizing scheme is presented.

Due to their capacity to condense the spatiotemporal structure of a data set in a format amenable for human interpretation, forecasting, and anomaly detection, causality graphs are routinely estimated in social sciences, natural sciences, and engineering. A popular approach to mathematically formalize causality is based on vector autoregressive (VAR) models, which constitutes an alternative to the well-known but usually intractable Granger causality. Relying on such a VAR causality notion, this paper develops two algorithms with complementary benefits to track time-varying causality graphs in an online fashion. Despite using data in a sequential fashion, both algorithms are shown to asymptotically attain the same average performance as a batch estimator with all data available at once. Moreover, their constant complexity per update renders these algorithms appealing for big-data scenarios. Theoretical and experimental performance analysis support the merits of the proposed algorithms. Remarkably, no probabilistic models or stationarity assumptions need to be introduced, which endows the developed algorithms with considerable generality