arXiv subjects

Varun Gupta

Publications and source records attributed to Varun Gupta.

At least 55 records · Page 3Linked to original sources

arXiv2021

Implementing partisan symmetry: Problems and paradoxes

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.

physics.soc-ph↗

arXiv2021

Online Multivalid Learning: Means, Moments, and Prediction Intervals

We present a general, efficient technique for providing contextual predictions that are "multivalid" in various senses, against an online sequence of adversarially chosen examples $(x,y)$. This means that the resulting estimates correctly predict various statistics of the labels $y$ not just marginally -- as averaged over the sequence of examples -- but also conditionally on $x \in G$ for any $G$ belonging to an arbitrary intersecting collection of groups $\mathcal{G}$. We provide three instantiations of this framework. The first is mean prediction, which corresponds to an online algorithm satisfying the notion of multicalibration from Hebert-Johnson et al. The second is variance and higher moment prediction, which corresponds to an online algorithm satisfying the notion of mean-conditioned moment multicalibration from Jung et al. Finally, we define a new notion of prediction interval multivalidity, and give an algorithm for finding prediction intervals which satisfy it. Because our algorithms handle adversarially chosen examples, they can equally well be used to predict statistics of the residuals of arbitrary point prediction methods, giving rise to very general techniques for quantifying the uncertainty of predictions of black box algorithms, even in an online adversarial setting. When instantiated for prediction intervals, this solves a similar problem as conformal prediction, but in an adversarial environment and with multivalidity guarantees stronger than simple marginal coverage guarantees.

cs.LG↗

arXiv2020

On BPS Strings in ${\mathcal N}=4$ Yang-Mills Theory

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.

hep-th↗

arXiv2020

SiEVE: Semantically Encoded Video Analytics on Edge and Cloud

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.

cs.DC↗

arXiv2020

Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work, and depend linearly on an upper bound on the squared coefficient of variation of the jobs' processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 7.216, respectively. As to the technical contribution, the paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.

cs.DS↗

arXiv2020

Simultaneous Inference for Pairwise Graphical Models with Generalized Score Matching

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 Hyvärinen scoring rule. Hyvärinen 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.

stat.ME↗

arXiv2020

Automated Personalized Feedback Improves Learning Gains in an Intelligent Tutoring System

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.

cs.CL↗

arXiv2020

A Large-Scale, Open-Domain, Mixed-Interface Dialogue-Based ITS for STEM

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.

cs.CY↗

arXiv2020

Estimation of a Low-rank Topic-Based Model for Information Cascades

We consider the problem of estimating the latent structure of a social network based on the observed information diffusion events, or cascades, where the observations for a given cascade consist of only the timestamps of infection for infected nodes but not the source of the infection. Most of the existing work on this problem has focused on estimating a diffusion matrix without any structural assumptions on it. In this paper, we propose a novel model based on the intuition that an information is more likely to propagate among two nodes if they are interested in similar topics which are also prominent in the information content. In particular, our model endows each node with an influence vector (which measures how authoritative the node is on each topic) and a receptivity vector (which measures how susceptible the node is for each topic). We show how this node-topic structure can be estimated from the observed cascades, and prove the consistency of the estimator. Experiments on synthetic and real data demonstrate the improved performance and better interpretability of our model compared to existing state-of-the-art methods.

stat.ML↗

arXiv2019

PERMUTATION Strikes Back: The Power of Recourse in Online Metric Matching

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.

cs.DS↗

arXiv2019

Constrained High Dimensional Statistical Inference

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.

stat.ME↗

arXiv2019

Recovery of simultaneous low rank and two-way sparse coefficient matrices, a nonconvex approach

We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We propose a GDT (Gradient Descent with hard Thresholding) algorithm to efficiently recover matrices with such structure, by minimizing a bi-convex function over a nonconvex set of constraints. We show linear convergence of the iterates obtained by GDT to a region within statistical error of an optimal solution. As an application of our method, we consider multi-task learning problems and show that the statistical error rate obtained by GDT is near optimal compared to minimax rate. Experiments demonstrate competitive performance and much faster running speed compared to existing methods, on both simulations and real data sets.

stat.ML↗

arXiv2019

Learning Influence-Receptivity Network Structure with Guarantee

Traditional works on community detection from observations of information cascade assume that a single adjacency matrix parametrizes all the observed cascades. However, in reality the connection structure usually does not stay the same across cascades. For example, different people have different topics of interest, therefore the connection structure depends on the information/topic content of the cascade. In this paper we consider the case where we observe a sequence of noisy adjacency matrices triggered by information/event with different topic distributions. We propose a novel latent model using the intuition that a connection is more likely to exist between two nodes if they are interested in similar topics, which are common with the information/event. Specifically, we endow each node with two node-topic vectors: an influence vector that measures how influential/authoritative they are on each topic; and a receptivity vector that measures how receptive/susceptible they are to each topic. We show how these two node-topic structures can be estimated from observed adjacency matrices with theoretical guarantee on estimation error, in cases where the topic distributions of the information/event are known, as well as when they are unknown. Experiments on synthetic and real data demonstrate the effectiveness of our model and superior performance compared to state-of-the-art methods.

stat.ML↗

arXiv2018

Load Balancing in the Non-Degenerate Slowdown Regime

We analyse Join-the-Shortest-Queue in a contemporary scaling regime known as the Non-Degenerate Slowdown regime. Join-the-Shortest-Queue (JSQ) is a classical load balancing policy for queueing systems with multiple parallel servers. Parallel server queueing systems are regularly analysed and dimensioned by diffusion approximations achieved in the Halfin-Whitt scaling regime. However, when jobs must be dispatched to a server upon arrival, we advocate the Non-Degenerate Slowdown regime (NDS) to compare different load-balancing rules. In this paper we identify novel diffusion approximation and timescale separation that provides insights into the performance of JSQ. We calculate the price of irrevocably dispatching jobs to servers and prove this to within 15% (in the NDS regime) of the rules that may manoeuvre jobs between servers. We also compare ours results for the JSQ policy with the NDS approximations of many modern load balancing policies such as Idle-Queue-First and Power-of-$d$-choices policies which act as low information proxies for the JSQ policy. Our analysis leads us to construct new rules that have identical performance to JSQ but require less communication overhead than power-of-2-choices.

math.PR↗

arXiv2017

DyMo: Dynamic Monitoring of Large Scale LTE-Multicast Systems

LTE evolved Multimedia Broadcast/Multicast Service (eMBMS) is an attractive solution for video delivery to very large groups in crowded venues. However, deployment and management of eMBMS systems is challenging, due to the lack of realtime feedback from the User Equipment (UEs). Therefore, we present the Dynamic Monitoring (DyMo) system for low-overhead feedback collection. DyMo leverages eMBMS for broadcasting Stochastic Group Instructions to all UEs. These instructions indicate the reporting rates as a function of the observed Quality of Service (QoS). This simple feedback mechanism collects very limited QoS reports from the UEs. The reports are used for network optimization, thereby ensuring high QoS to the UEs. We present the design aspects of DyMo and evaluate its performance analytically and via extensive simulations. Specifically, we show that DyMo infers the optimal eMBMS settings with extremely low overhead, while meeting strict QoS requirements under different UE mobility patterns and presence of network component failures. For instance, DyMo can detect the eMBMS Signal-to-Noise Ratio (SNR) experienced by the 0.1% percentile of the UEs with Root Mean Square Error (RMSE) of 0.05% with only 5 to 10 reports per second regardless of the number of UEs.

cs.NI↗

arXiv2016

Interface Formulation and High Order Numerical Solutions of PDEs with Low Regularity

Linear elastic fracture mechanics admit analytic solutions that have low regularity at crack tips. Current numerical methods for partial differential equations (PDEs) of this type suffer from the constraint of such low regularity, and fail to deliver optimal high order rate of convergence. We approach the problem by (i) choosing an artificial interface to enclose the center of the low regularity; and (ii) representing the solution in the interior of artificial interface as unknown linear combination of known modes of low regular solutions. This gives rise to an interface formulation of the original PDE, and the linear combination are represented the interface conditions. By enforcing the smooth component of numerical solution in the interior domain to be approximately zero, a least square problem is obtained for the unknown coefficients. The solution of this least square problem will provide approximate interface conditions for the numerical solution of the PDE in the exterior domain. The potential of our interface formulation is favorably demonstrated by numerical experiments on 1-D and 2-D Poisson equations with low regular solutions. High order numerical solutions of unknown coefficients and PDEs are obtained. This proves the potential of the proposed interface formulation as the theoretical basis for solving linear elastic fracture mechanics problems. We indicate the relations between our interface formulation and domain decomposition methods as well as a regularization strategy for the Poisson-Boltzmann equation with singular charge density.

math.NA↗

arXiv2016

Experimental Evaluation of Large Scale WiFi Multicast Rate Control

WiFi multicast to very large groups has gained attention as a solution for multimedia delivery in crowded areas. Yet, most recently proposed schemes do not provide performance guarantees and none have been tested at scale. To address the issue of providing high multicast throughput with performance guarantees, we present the design and experimental evaluation of the Multicast Dynamic Rate Adaptation (MuDRA) algorithm. MuDRA balances fast adaptation to channel conditions and stability, which is essential for multimedia applications. MuDRA relies on feedback from some nodes collected via a light-weight protocol and dynamically adjusts the rate adaptation response time. Our experimental evaluation of MuDRA on the ORBIT testbed with over 150 nodes shows that MuDRA outperforms other schemes and supports high throughput multicast flows to hundreds of receivers while meeting quality requirements. MuDRA can support multiple high quality video streams, where 90% of the nodes report excellent or very good video quality.

cs.NI↗

arXiv2014

Approximations and Optimal Control for State-dependent Limited Processor Sharing Queues

The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs that can share the server concurrently, with the rest of the jobs waiting in a first-in-first-out (FIFO) buffer. A desirable control scheme should strike the right balance between efficiency (operating at a high service rate) and parallelism (preventing small jobs from getting stuck behind large ones). We employ the framework of heavy-traffic diffusion analysis to devise near optimal control heuristics for such a queueing system. However, while the literature on diffusion control of state-dependent queueing systems begins with a sequence of systems and an exogenously defined drift function, we begin with a finite discrete PS server and propose an axiomatic recipe to explicitly construct a sequence of state-dependent PS servers which then yields a drift function. We establish diffusion approximations and use them to obtain insightful and closed-form approximations for the original system under a static concurrency limit control policy. We extend our study to control policies that dynamically adjust the concurrency limit. We provide two novel numerical algorithms to solve the associated diffusion control problem. Our algorithms can be viewed as "average cost" iteration: The first algorithm uses binary-search on the average cost and can find an $ε$-optimal policy in time $O\left( \log^2 \frac{1}ε \right)$; the second algorithm uses the Newton-Raphson method for root-finding and requires $O\left( \log \frac{1}ε \log\log \frac{1}ε\right)$ time. Numerical experiments demonstrate the accuracy of our approximation for choosing optimal or near-optimal static and dynamic concurrency control heuristics.

eess.SY↗