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Finding outlying elements in probability distributions can be a hard problem. Taking a real example from Voting Rights Act enforcement, we consider the problem of maximizing the number of simultaneous majority-minority districts in a political districting plan. An unbiased random walk on districting plans is unlikely to find plans that approach this maximum. A common search approach is to use a biased random walk: preferentially select districting plans with more majority-minority districts. Here, we present a third option, called short bursts, in which an unbiased random walk is performed for a small number of steps (called the burst length), then re-started from the most extreme plan that was encountered in the last burst. We give empirical evidence that short-burst runs outperform biased random walks for the problem of maximizing the number of majority-minority districts, and that there are many values of burst length for which we see this improvement. Abstracting from our use case, we also consider short bursts where the underlying state space is a line with various probability distributions, and then explore some features of more complicated state spaces and how these impact the effectiveness of short bursts.

We consider the measures of partisan symmetry proposed for practical use in the political science literature, as clarified and developed in Katz, King, and Rosenblatt (2020). Elementary mathematical manipulation shows the symmetry metrics to have surprising properties that call their meaningfulness into question. To accompany the general analysis, we study measures of partisan symmetry with respect to recent voting patterns in Utah, Texas, and North Carolina, flagging problems in each case. Taken together, these observations should raise major concerns about the available techniques for quantitative scores of partisan symmetry -- including the mean-median score, the partisan bias score, and the more general "partisan symmetry standard" -- as the decennial redistricting begins.

We study singular time-dependent $\frac{1}{8}$-BPS configurations in the abelian sector of ${{\mathcal N}= 4}$ supersymmetric Yang-Mills theory that represent BPS string-like defects in ${{\mathbb R}\times S^3}$ spacetime. Such BPS strings can be described as intersections of the zeros of holomorphic functions in two complex variables with a 3-sphere. We argue that these BPS strings map to $\frac{1}{8}$-BPS surface operators under the state-operator correspondence of the CFT. We show that the string defects are holographically dual to noncompact probe D3-branes in global $AdS_5\times S^5$ that share supersymmetries with a class of dual-giant gravitons. For simple configurations, we demonstrate how to define a good variational problem and propose a regularization scheme that leads to finite energy and global charges on both sides of the holographic correspondence., Comment: v2, 55 pages, 1 figure

Recent advances in computer vision and neural networks have made it possible for more surveillance videos to be automatically searched and analyzed by algorithms rather than humans. This happened in parallel with advances in edge computing where videos are analyzed over hierarchical clusters that contain edge devices, close to the video source. However, the current video analysis pipeline has several disadvantages when dealing with such advances. For example, video encoders have been designed for a long time to please human viewers and be agnostic of the downstream analysis task (e.g., object detection). Moreover, most of the video analytics systems leverage 2-tier architecture where the encoded video is sent to either a remote cloud or a private edge server but does not efficiently leverage both of them. In response to these advances, we present SIEVE, a 3-tier video analytics system to reduce the latency and increase the throughput of analytics over video streams. In SIEVE, we present a novel technique to detect objects in compressed video streams. We refer to this technique as semantic video encoding because it allows video encoders to be aware of the semantics of the downstream task (e.g., object detection). Our results show that by leveraging semantic video encoding, we achieve close to 100% object detection accuracy with decompressing only 3.5% of the video frames which results in more than 100x speedup compared to classical approaches that decompress every video frame.

We present Korbit, a large-scale, open-domain, mixed-interface, dialogue-based intelligent tutoring system (ITS). Korbit uses machine learning, natural language processing and reinforcement learning to provide interactive, personalized learning online. Korbit has been designed to easily scale to thousands of subjects, by automating, standardizing and simplifying the content creation process. Unlike other ITS, a teacher can develop new learning modules for Korbit in a matter of hours. To facilitate learning across a widerange of STEM subjects, Korbit uses a mixed-interface, which includes videos, interactive dialogue-based exercises, question-answering, conceptual diagrams, mathematical exercises and gamification elements. Korbit has been built to scale to millions of students, by utilizing a state-of-the-art cloud-based micro-service architecture. Korbit launched its first course in 2019 on machine learning, and since then over 7,000 students have enrolled. Although Korbit was designed to be open-domain and highly scalable, A/B testing experiments with real-world students demonstrate that both student learning outcomes and student motivation are substantially improved compared to typical online courses., Comment: 6 pages, 1 figure, 1 table, accepted for publication in the 21st International Conference on Artificial Intelligence in Education (AIED 2020)

We investigate how automated, data-driven, personalized feedback in a large-scale intelligent tutoring system (ITS) improves student learning outcomes. We propose a machine learning approach to generate personalized feedback, which takes individual needs of students into account. We utilize state-of-the-art machine learning and natural language processing techniques to provide the students with personalized hints, Wikipedia-based explanations, and mathematical hints. Our model is used in Korbit, a large-scale dialogue-based ITS with thousands of students launched in 2019, and we demonstrate that the personalized feedback leads to considerable improvement in student learning outcomes and in the subjective evaluation of the feedback., Comment: To be published in Proceedings of the the 21st International Conference on Artificial Intelligence in Education (AIED 2020)

In the classical Online Metric Matching problem, we are given a metric space with $k$ servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The goal is to find an online matching which minimizes the total cost, i.e., the sum of distances between each client and the server it is matched to. We know deterministic algorithms~\cite{KP93,khuller1994line} that achieve a competitive ratio of $2k-1$, and this bound is tight for deterministic algorithms. The problem has also long been considered in specialized metrics such as the line metric or metrics of bounded doubling dimension, with the current best result on a line metric being a deterministic $O(\log k)$ competitive algorithm~\cite{raghvendra2018optimal}. Obtaining (or refuting) $O(\log k)$-competitive algorithms in general metrics and constant-competitive algorithms on the line metric have been long-standing open questions in this area. In this paper, we investigate the robustness of these lower bounds by considering the Online Metric Matching with Recourse problem where we are allowed to change a small number of previous assignments upon arrival of a new client. Indeed, we show that a small logarithmic amount of recourse can significantly improve the quality of matchings we can maintain. For general metrics, we show a simple \emph{deterministic} $O(\log k)$-competitive algorithm with $O(\log k)$-amortized recourse, an exponential improvement over the $2k-1$ lower bound when no recourse is allowed. We next consider the line metric, and present a deterministic algorithm which is $3$-competitive and has $O(\log k)$-recourse, again a substantial improvement over the best known $O(\log k)$-competitive algorithm when no recourse is allowed.

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained. However, in many problems, there are natural constraints on model parameters and one is interested in whether the parameters are on the boundary of the constraint or not. e.g. non-negativity constraints for transmission rates in network diffusion. In this paper, we provide algorithms to solve this problem of hypothesis testing in high-dimensional statistical models under constrained parameter space. We show that following our testing procedure we are able to get asymptotic designed Type I error under the null. Numerical experiments demonstrate that our algorithm has greater power than the standard algorithms where the constraints are ignored. We demonstrate the effectiveness of our algorithms on two real datasets where we have {\emph{intrinsic}} constraint on the parameters.

Probabilistic graphical models provide a flexible yet parsimonious framework for modeling dependencies among nodes in networks. There is a vast literature on parameter estimation and consistent model selection for graphical models. However, in many of the applications, scientists are also interested in quantifying the uncertainty associated with the estimated parameters and selected models, which current literature has not addressed thoroughly. In this paper, we propose a novel estimator for statistical inference on edge parameters in pairwise graphical models based on generalized Hyv\"arinen scoring rule. Hyv\"arinen scoring rule is especially useful in cases where the normalizing constant cannot be obtained efficiently in a closed form, which is a common problem for graphical models, including Ising models and truncated Gaussian graphical models. Our estimator allows us to perform statistical inference for general graphical models whereas the existing works mostly focus on statistical inference for Gaussian graphical models where finding normalizing constant is computationally tractable. Under mild conditions that are typically assumed in the literature for consistent estimation, we prove that our proposed estimator is $\sqrt{n}$-consistent and asymptotically normal, which allows us to construct confidence intervals and build hypothesis tests for edge parameters. Moreover, we show how our proposed method can be applied to test hypotheses that involve a large number of model parameters simultaneously. We illustrate validity of our estimator through extensive simulation studies on a diverse collection of data-generating processes.