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The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient flow features. In this paper, we introduce nonlinear solver strategies to more robustly and efficiently compute high-speed viscous flows. Specifically, we incorporate an anisotropic grid regularization based on the mesh-implied metric into the nonlinear least-squares solver that inhibits grid motion in directions with small element length scales. Furthermore, we develop an adaptive elementwise regularization strategy that locally scales the regularization terms as needed to maintain grid validity. We apply the proposed MDG-ICE formulation to test cases involving viscous shocks and/or boundary layers, including Mach 17.6 hypersonic viscous flow over a circular cylinder and Mach 5 hypersonic viscous flow over a sphere, which are very challenging test cases for conventional numerical schemes on simplicial grids. Even without artificial dissipation, the computed solutions are free from spurious oscillations and yield highly symmetric surface heat-flux profiles.

Multivariate Time Series (MVTS) anomaly detection is a long-standing and challenging research topic that has attracted tremendous research effort from both industry and academia recently. However, a careful study of the literature makes us realize that 1) the community is active but not as organized as other sibling machine learning communities such as Computer Vision (CV) and Natural Language Processing (NLP), and 2) most proposed solutions are evaluated using either inappropriate or highly flawed protocols, with an apparent lack of scientific foundation. So flawed is one very popular protocol, the so-called point-adjust protocol, that a random guess can be shown to systematically outperform all algorithms developed so far. In this paper, we review and evaluate many recent algorithms using more robust protocols and discuss how a normally good protocol may have weaknesses in the context of MVTS anomaly detection and how to mitigate them. We also share our concerns about benchmark datasets, experiment design and evaluation methodology we observe in many works. Furthermore, we propose a simple, yet challenging, baseline based on Principal Components Analysis (PCA) that surprisingly outperforms many recent Deep Learning (DL) based approaches on popular benchmark datasets. The main objective of this work is to stimulate more effort towards important aspects of the research such as data, experiment design, evaluation methodology and result interpretability, instead of putting the highest weight on the design of increasingly more complex and "fancier" algorithms.

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods hardly scale to high dimensional problems, they have recently been paired with optimization techniques, such as proximal and splitting approaches, to address this issue. Such approaches pave the way to distributed samplers, splitting computations to make inference more scalable and faster. We introduce a distributed Split Gibbs sampler (SGS) to efficiently solve such problems involving distributions with multiple smooth and non-smooth functions composed with linear operators. The proposed approach leverages a recent approximate augmentation technique reminiscent of primal-dual optimization methods. It is further combined with a block-coordinate approach to split the primal and dual variables into blocks, leading to a distributed block-coordinate SGS. The resulting algorithm exploits the hypergraph structure of the involved linear operators to efficiently distribute the variables over multiple workers under controlled communication costs. It accommodates several distributed architectures, such as the Single Program Multiple Data and client-server architectures. Experiments on a large image deblurring problem show the performance of the proposed approach to produce high quality estimates with credibility intervals in a small amount of time. Supplementary material to reproduce the experiments is available online.

Anomaly detection in time series data, to identify points that deviate from normal behaviour, is a common problem in various domains such as manufacturing, medical imaging, and cybersecurity. Recently, Generative Adversarial Networks (GANs) are shown to be effective in detecting anomalies in time series data. The neural network architecture of GANs (i.e. Generator and Discriminator) can significantly improve anomaly detection accuracy. In this paper, we propose a new GAN model, named Adjusted-LSTM GAN (ALGAN), which adjusts the output of an LSTM network for improved anomaly detection in both univariate and multivariate time series data in an unsupervised setting. We evaluate the performance of ALGAN on 46 real-world univariate time series datasets and a large multivariate dataset that spans multiple domains. Our experiments demonstrate that ALGAN outperforms traditional, neural network-based, and other GAN-based methods for anomaly detection in time series data.

Feature bagging is a well-established ensembling method which aims to reduce prediction variance by combining predictions of many estimators trained on subsets or projections of features. Here, we develop a theory of feature-bagging in noisy least-squares ridge ensembles and simplify the resulting learning curves in the special case of equicorrelated data. Using analytical learning curves, we demonstrate that subsampling shifts the double-descent peak of a linear predictor. This leads us to introduce heterogeneous feature ensembling, with estimators built on varying numbers of feature dimensions, as a computationally efficient method to mitigate double-descent. Then, we compare the performance of a feature-subsampling ensemble to a single linear predictor, describing a trade-off between noise amplification due to subsampling and noise reduction due to ensembling. Our qualitative insights carry over to linear classifiers applied to image classification tasks with realistic datasets constructed using a state-of-the-art deep learning feature map.

Sketching algorithms have recently proven to be a powerful approach both for designing low-space streaming algorithms as well as fast polynomial time approximation schemes (PTAS). In this work, we develop new techniques to extend the applicability of sketching-based approaches to the sparse dictionary learning and the Euclidean $k$-means clustering problems. In particular, we initiate the study of the challenging setting where the dictionary/clustering assignment for each of the $n$ input points must be output, which has surprisingly received little attention in prior work. On the fast algorithms front, we obtain a new approach for designing PTAS's for the $k$-means clustering problem, which generalizes to the first PTAS for the sparse dictionary learning problem. On the streaming algorithms front, we obtain new upper bounds and lower bounds for dictionary learning and $k$-means clustering. In particular, given a design matrix $\mathbf A\in\mathbb R^{n\times d}$ in a turnstile stream, we show an $\tilde O(nr/\epsilon^2 + dk/\epsilon)$ space upper bound for $r$-sparse dictionary learning of size $k$, an $\tilde O(n/\epsilon^2 + dk/\epsilon)$ space upper bound for $k$-means clustering, as well as an $\tilde O(n)$ space upper bound for $k$-means clustering on random order row insertion streams with a natural "bounded sensitivity" assumption. On the lower bounds side, we obtain a general $\tilde\Omega(n/\epsilon + dk/\epsilon)$ lower bound for $k$-means clustering, as well as an $\tilde\Omega(n/\epsilon^2)$ lower bound for algorithms which can estimate the cost of a single fixed set of candidate centers.

Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive, unifying perspective on inverse decision modeling: a framework for learning parameterized representations of sequential decision behavior. First, we formalize the forward problem (as a normative standard), subsuming common classes of control behavior. Second, we use this to formalize the inverse problem (as a descriptive model), generalizing existing work on imitation/reward learning -- while opening up a much broader class of research problems in behavior representation. Finally, we instantiate this approach with an example (inverse bounded rational control), illustrating how this structure enables learning (interpretable) representations of (bounded) rationality -- while naturally capturing intuitive notions of suboptimal actions, biased beliefs, and imperfect knowledge of environments.

Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression (VIR), which not only performs well in imbalanced regression but naturally produces reasonable uncertainty estimation as a byproduct. Different from typical variational autoencoders assuming I.I.D. representations (a data point's representation is not directly affected by other data points), our VIR borrows data with similar regression labels to compute the latent representation's variational distribution; furthermore, different from deterministic regression models producing point estimates, VIR predicts the entire normal-inverse-gamma distributions and modulates the associated conjugate distributions to impose probabilistic reweighting on the imbalanced data, thereby providing better uncertainty estimation. Experiments in several real-world datasets show that our VIR can outperform state-of-the-art imbalanced regression models in terms of both accuracy and uncertainty estimation. Code will soon be available at //github.com/Wang-ML-Lab/variational-imbalanced-regression.

Causal Machine Learning (CausalML) is an umbrella term for machine learning methods that formalize the data-generation process as a structural causal model (SCM). This allows one to reason about the effects of changes to this process (i.e., interventions) and what would have happened in hindsight (i.e., counterfactuals). We categorize work in \causalml into five groups according to the problems they tackle: (1) causal supervised learning, (2) causal generative modeling, (3) causal explanations, (4) causal fairness, (5) causal reinforcement learning. For each category, we systematically compare its methods and point out open problems. Further, we review modality-specific applications in computer vision, natural language processing, and graph representation learning. Finally, we provide an overview of causal benchmarks and a critical discussion of the state of this nascent field, including recommendations for future work.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.