Time series models often deal with extreme events and anomalies, both prevalent in real-world datasets. Such models often need to provide careful probabilistic forecasting, which is vital in risk management for extreme events such as hurricanes and pandemics. However, it is challenging to automatically detect and learn to use extreme events and anomalies for large-scale datasets, which often require manual effort. Hence, we propose an anomaly-aware forecast framework that leverages the previously seen effects of anomalies to improve its prediction accuracy during and after the presence of extreme events. Specifically, the framework automatically extracts anomalies and incorporates them through an attention mechanism to increase its accuracy for future extreme events. Moreover, the framework employs a dynamic uncertainty optimization algorithm that reduces the uncertainty of forecasts in an online manner. The proposed framework demonstrated consistent superior accuracy with less uncertainty on three datasets with different varieties of anomalies over the current prediction models.

We propose and analyze several stochastic gradient algorithms for finding stationary points or local minimum in nonconvex, possibly with nonsmooth regularizer, finite-sum and online optimization problems. First, we propose a simple proximal stochastic gradient algorithm based on variance reduction called ProxSVRG+. We provide a clean and tight analysis of ProxSVRG+, which shows that it outperforms the deterministic proximal gradient descent (ProxGD) for a wide range of minibatch sizes, hence solves an open problem proposed in Reddi et al. (2016b). Also, ProxSVRG+ uses much less proximal oracle calls than ProxSVRG (Reddi et al., 2016b) and extends to the online setting by avoiding full gradient computations. Then, we further propose an optimal algorithm, called SSRGD, based on SARAH (Nguyen et al., 2017) and show that SSRGD further improves the gradient complexity of ProxSVRG+ and achieves the optimal upper bound, matching the known lower bound of (Fang et al., 2018; Li et al., 2021). Moreover, we show that both ProxSVRG+ and SSRGD enjoy automatic adaptation with local structure of the objective function such as the Polyak-\L{}ojasiewicz (PL) condition for nonconvex functions in the finite-sum case, i.e., we prove that both of them can automatically switch to faster global linear convergence without any restart performed in prior work ProxSVRG (Reddi et al., 2016b). Finally, we focus on the more challenging problem of finding an $(\epsilon, \delta)$-local minimum instead of just finding an $\epsilon$-approximate (first-order) stationary point (which may be some bad unstable saddle points). We show that SSRGD can find an $(\epsilon, \delta)$-local minimum by simply adding some random perturbations. Our algorithm is almost as simple as its counterpart for finding stationary points, and achieves similar optimal rates.

Several decades ago the Proximal Point Algorithm (PPA) started to gain a long-lasting attraction for both abstract operator theory and numerical optimization communities. Even in modern applications, researchers still use proximal minimization theory to design scalable algorithms that overcome nonsmoothness. Remarkable works as \cite{Fer:91,Ber:82constrained,Ber:89parallel,Tom:11} established tight relations between the convergence behaviour of PPA and the regularity of the objective function. In this manuscript we derive nonasymptotic iteration complexity of exact and inexact PPA to minimize convex functions under $\gamma-$Holderian growth: $\BigO{\log(1/\epsilon)}$ (for $\gamma \in [1,2]$) and $\BigO{1/\epsilon^{\gamma - 2}}$ (for $\gamma > 2$). In particular, we recover well-known results on PPA: finite convergence for sharp minima and linear convergence for quadratic growth, even under presence of deterministic noise. Moreover, when a simple Proximal Subgradient Method is recurrently called as an inner routine for computing each IPPA iterate, novel computational complexity bounds are obtained for Restarting Inexact PPA. Our numerical tests show improvements over existing restarting versions of the Subgradient Method.

Multi-view unsupervised feature selection (MUFS) has been demonstrated as an effective technique to reduce the dimensionality of multi-view unlabeled data. The existing methods assume that all of views are complete. However, multi-view data are usually incomplete, i.e., a part of instances are presented on some views but not all views. Besides, learning the complete similarity graph, as an important promising technology in existing MUFS methods, cannot achieve due to the missing views. In this paper, we propose a complementary and consensus learning-based incomplete multi-view unsupervised feature selection method (C$^{2}$IMUFS) to address the aforementioned issues. Concretely, C$^{2}$IMUFS integrates feature selection into an extended weighted non-negative matrix factorization model equipped with adaptive learning of view-weights and a sparse $\ell_{2,p}$-norm, which can offer better adaptability and flexibility. By the sparse linear combinations of multiple similarity matrices derived from different views, a complementary learning-guided similarity matrix reconstruction model is presented to obtain the complete similarity graph in each view. Furthermore, C$^{2}$IMUFS learns a consensus clustering indicator matrix across different views and embeds it into a spectral graph term to preserve the local geometric structure. Comprehensive experimental results on real-world datasets demonstrate the effectiveness of C$^{2}$IMUFS compared with state-of-the-art methods.

A reliable evaluation method is essential for building a robust out-of-distribution (OOD) detector. Current robustness evaluation protocols for OOD detectors rely on injecting perturbations to outlier data. However, the perturbations are unlikely to occur naturally or not relevant to the content of data, providing a limited assessment of robustness. In this paper, we propose Evaluation-via-Generation for OOD detectors (EvG), a new protocol for investigating the robustness of OOD detectors under more realistic modes of variation in outliers. EvG utilizes a generative model to synthesize plausible outliers, and employs MCMC sampling to find outliers misclassified as in-distribution with the highest confidence by a detector. We perform a comprehensive benchmark comparison of the performance of state-of-the-art OOD detectors using EvG, uncovering previously overlooked weaknesses.

Verusen is a leading technology company that uses artificial intelligence to provide visibility, digitization and prediction of materials data and inventory for complex supply chains. Intelligent controls enforce inventory procedures to help prevent future inventory spikes, while predictive capabilities optimize allocation and procurement needs. The result is a data foundation you can trust to move quickly to innovate and support related Industry 4.0 initiatives. Verusen is venture-backed by leading investors from San Francisco to Boston, and is a Signature Company at Georgia Tech's Advanced Technology Development Center (ATDC). Verusen is a portfolio company of SAP.iO.

A variety of problems in econometrics and machine learning, including instrumental variable regression and Bellman residual minimization, can be formulated as satisfying a set of conditional moment restrictions (CMR). We derive a general, game-theoretic strategy for satisfying CMR that scales to nonlinear problems, is amenable to gradient-based optimization, and is able to account for finite sample uncertainty. We recover the approaches of Dikkala et al. and Dai et al. as special cases of our general framework before detailing various extensions and how to efficiently solve the game defined by CMR.

We address the problem of unsupervised extractive document summarization, especially for long documents. We model the unsupervised problem as a sparse auto-regression one and approximate the resulting combinatorial problem via a convex, norm-constrained problem. We solve it using a dedicated Frank-Wolfe algorithm. To generate a summary with $k$ sentences, the algorithm only needs to execute $\approx k$ iterations, making it very efficient. We explain how to avoid explicit calculation of the full gradient and how to include sentence embedding information. We evaluate our approach against two other unsupervised methods using both lexical (standard) ROUGE scores, as well as semantic (embedding-based) ones. Our method achieves better results with both datasets and works especially well when combined with embeddings for highly paraphrased summaries.

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about incorrect physics in the presence of random noise and cannot easily handle the situation with incomplete data. In this paper, a new iterative learning algorithm for complex turbulent systems with partial observations is developed that alternates between identifying model structures, recovering unobserved variables, and estimating parameters. First, a causality-based learning approach is utilized for the sparse identification of model structures, which takes into account certain physics knowledge that is pre-learned from data. It has unique advantages in coping with indirect coupling between features and is robust to the stochastic noise. A practical algorithm is designed to facilitate the causal inference for high-dimensional systems. Next, a systematic nonlinear stochastic parameterization is built to characterize the time evolution of the unobserved variables. Closed analytic formula via an efficient nonlinear data assimilation is exploited to sample the trajectories of the unobserved variables, which are then treated as synthetic observations to advance a rapid parameter estimation. Furthermore, the localization of the state variable dependence and the physics constraints are incorporated into the learning procedure, which mitigate the curse of dimensionality and prevent the finite time blow-up issue. Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable stochastic parameterizations for many complex nonlinear systems with chaotic dynamics, spatiotemporal multiscale structures, intermittency, and extreme events.

Given a learning problem with real-world tradeoffs, which cost function should the model be trained to optimize? This is the metric selection problem in machine learning. Despite its practical interest, there is limited formal guidance on how to select metrics for machine learning applications. This thesis outlines metric elicitation as a principled framework for selecting the performance metric that best reflects implicit user preferences. Once specified, the evaluation metric can be used to compare and train models. In this manuscript, we formalize the problem of Metric Elicitation and devise novel strategies for eliciting classification performance metrics using pairwise preference feedback over classifiers. Specifically, we provide novel strategies for eliciting linear and linear-fractional metrics for binary and multiclass classification problems, which are then extended to a framework that elicits group-fair performance metrics in the presence of multiple sensitive groups. All the elicitation strategies that we discuss are robust to both finite sample and feedback noise, thus are useful in practice for real-world applications. Using the tools and the geometric characterizations of the feasible confusion statistics sets from the binary, multiclass, and multiclass-multigroup classification setups, we further provide strategies to elicit from a wider range of complex, modern multiclass metrics defined by quadratic functions of confusion statistics by exploiting their local linear structure. From application perspective, we also propose to use the metric elicitation framework in optimizing complex black box metrics that is amenable to deep network training. Lastly, to bring theory closer to practice, we conduct a preliminary real-user study that shows the efficacy of the metric elicitation framework in recovering the users' preferred performance metric in a binary classification setup.