This year, the world changed in the span of a few months, in unprecedented ways that surprised and overwhelmed every country on this planet. The greatest global crisis since World War II and the largest global pandemic since the 1918–19 Spanish Flu fell upon us. Everybody spent a better part of their day looking at the daily rise of the death toll and the rapid, exponential spread of this novel strain of the COVID-19 virus. Millions of people lost their jobs, unemployment rose through the roof, global travel and hospitality industries were all but decimated, international relationships were frayed, healthcare systems were stressed to the limits. Of course, the fight was not one-sided.

We consider a novel variant of the contextual bandit problem (i.e., the multi-armed bandit with side-information, or context, available to a decision-maker) where the reward associated with each context-based decision may not always be observed ("missing rewards"). This new problem is motivated by certain online settings including clinical trial and ad recommendation applications. In order to address the missing rewards setting, we propose to combine the standard contextual bandit approach with an unsupervised learning mechanism such as clustering. Unlike standard contextual bandit methods, by leveraging clustering to estimate missing reward, we are able to learn from each incoming event, even those with missing rewards. Promising empirical results are obtained on several real-life datasets.

We propose a distributionally robust logistic regression model with an unfairness penalty that prevents discrimination with respect to sensitive attributes such as gender or ethnicity. This model is equivalent to a tractable convex optimization problem if a Wasserstein ball centered at the empirical distribution on the training data is used to model distributional uncertainty and if a new convex unfairness measure is used to incentivize equalized opportunities. We demonstrate that the resulting classifier improves fairness at a marginal loss of predictive accuracy on both synthetic and real datasets. We also derive linear programming-based confidence bounds on the level of unfairness of any pre-trained classifier by leveraging techniques from optimal uncertainty quantification over Wasserstein balls.

Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data. This model is the foundation of robust principle component analysis (Candes et al., 2011) (Chandrasekaran et al., 2009), and popularized by dynamic-foreground/static-background separation (Bouwmans et al., 2016) amongst other applications. Compressed sensing, matrix completion, and their variants (Eldar and Kutyniok, 2012) (Foucart and Rauhut, 2013) have established that data satisfying low complexity models can be efficiently measured and recovered from a number of measurements proportional to the model complexity rather than the ambient dimension. This manuscript develops similar guarantees showing that $m\times n$ matrices that can be expressed as the sum of a rank-$r$ matrix and a $s$-sparse matrix can be recovered by computationally tractable methods from $\mathcal{O}(r(m+n-r)+s)\log(mn/s)$ linear measurements. More specifically, we establish that the restricted isometry constants for the aforementioned matrices remain bounded independent of problem size provided $p/mn$, $s/p$, and $r(m+n-r)/p$ reman fixed. Additionally, we show that semidefinite programming and two hard threshold gradient descent algorithms, NIHT and NAHT, converge to the measured matrix provided the measurement operator's RIC's are sufficiently small. Numerical experiments illustrating these results are shown for synthetic problems, dynamic-foreground/static-background separation, and multispectral imaging.

Fully symmetric learning rules for principal component analysis can be derived from a novel objective function suggested in our previous work. We observed that these learning rules suffer from slow convergence for covariance matrices where some principal eigenvalues are close to each other. Here we describe a modified objective function with an additional term which mitigates this convergence problem. We show that the learning rule derived from the modified objective function inherits all fixed points from the original learning rule (but may introduce additional ones). Also the stability of the inherited fixed points remains unchanged. Only the steepness of the objective function is increased in some directions. Simulations confirm that the convergence speed can be noticeably improved, depending on the weight factor of the additional term.

Both pieces of work mentioned in Section 1 rely on confusion We propose a measure to compute class similarity matrices to analyze classification structure (Alsallakh in large-scale classification based on prediction et al., 2018a; Deng et al., 2010). When ordered according to scores. Such measure has not been formally proposed the ImageNet synset hierarchy, this matrix captures the majority in the literature. We show how visualizing of confusions in few diagonal blocks that correspond the class similarity matrix can reveal hierarchical to coarse similarity groups. Each of these blocks, in turn, structures and relationships that govern the can exhibit a nested block pattern that corresponds to narrower classes.

In William Gibson's 2010 novel Zero History, a character preparing to go in a high-stakes raid wears an oddly-patterned t-shirt that renders him invisible on the monitoring CCTVs. It's an idea many science fiction writers have written about, and it has captivated audiences so much because it challenges the notion that AI is unbeatable and all-knowingly. With a simple trick, someone can trick the algorithm? For good or for worse, machine learning algorithms can be tricked by slight changes to inputs, intentional or not, into its system. Recently in 2020, the cyber security firm McAfee showed that Mobileye -- the car intelligence system used by Tesla and other auto manufacturers -- could be fooled into accelerating 50 MPH over the speed limit just by plastering a strip of black tape two inches wide to a speed limit sign.

Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that the methods based on the independence of cause and mechanism, indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.

As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from the signal and data acquisition to modeling and prediction. The optimization problems encountered in practice are often nonconvex. While challenges vary from problem to problem, one common source of nonconvexity is nonlinearity in the data or measurement model. Nonlinear models often exhibit symmetries, creating complicated, nonconvex objective landscapes, with multiple equivalent solutions. Nevertheless, simple methods (e.g., gradient descent) often perform surprisingly well in practice. The goal of this survey is to highlight a class of tractable nonconvex problems, which can be understood through the lens of symmetries. These problems exhibit a characteristic geometric structure: local minimizers are symmetric copies of a single ``ground truth'' solution, while other critical points occur at balanced superpositions of symmetric copies of the ground truth, and exhibit negative curvature in directions that break the symmetry. This structure enables efficient methods to obtain global minimizers. We discuss examples of this phenomenon arising from a wide range of problems in imaging, signal processing, and data analysis. We highlight the key role of symmetry in shaping the objective landscape and discuss the different roles of rotational and discrete symmetries. This area is rich with observed phenomena and open problems; we close by highlighting directions for future research.

Meta learning methods have found success when applied to few shot classification problems, in which they quickly adapt to a small number of labeled examples. Prototypical representations, each representing a particular class, have been of particular importance in this setting, as they provide a compact form to convey information learned from the labeled examples. However, these prototypes are just one method of representing this information, and they are narrow in their scope and ability to classify unseen examples. We propose the implementation of contextualizers, which are generalizable prototypes that adapt to given examples and play a larger role in classification for gradient-based models. We demonstrate how to equip meta learning methods with contextualizers and show that their use can significantly boost performance on a range of few shot learning datasets. We also present figures of merit demonstrating the potential benefits of contextualizers, along with analysis of how models make use of them. Our approach is particularly apt for low-data environments where it is difficult to update parameters without overfitting.