arXiv subjects

Abhimanyu Das

Publications and source records attributed to Abhimanyu Das.

27 records · Page 2Linked to original sources

arXiv2020

Upper Confidence Bounds for Combining Stochastic Bandits

We provide a simple method to combine stochastic bandit algorithms. Our approach is based on a "meta-UCB" procedure that treats each of $N$ individual bandit algorithms as arms in a higher-level $N$-armed bandit problem that we solve with a variant of the classic UCB algorithm. Our final regret depends only on the regret of the base algorithm with the best regret in hindsight. This approach provides an easy and intuitive alternative strategy to the CORRAL algorithm for adversarial bandits, without requiring the stability conditions imposed by CORRAL on the base algorithms. Our results match lower bounds in several settings, and we provide empirical validation of our algorithm on misspecified linear bandit and model selection problems.

cs.LG↗

arXiv2020

Learning the gravitational force law and other analytic functions

Large neural network models have been successful in learning functions of importance in many branches of science, including physics, chemistry and biology. Recent theoretical work has shown explicit learning bounds for wide networks and kernel methods on some simple classes of functions, but not on more complex functions which arise in practice. We extend these techniques to provide learning bounds for analytic functions on the sphere for any kernel method or equivalent infinitely-wide network with the corresponding activation function trained with SGD. We show that a wide, one-hidden layer ReLU network can learn analytic functions with a number of samples proportional to the derivative of a related function. Many functions important in the sciences are therefore efficiently learnable. As an example, we prove explicit bounds on learning the many-body gravitational force function given by Newton's law of gravitation. Our theoretical bounds suggest that very wide ReLU networks (and the corresponding NTK kernel) are better at learning analytic functions as compared to kernel learning with Gaussian kernels. We present experimental evidence that the many-body gravitational force function is easier to learn with ReLU networks as compared to networks with exponential activations.

cs.LG↗

arXiv2020

Converting Hemodialysis (HD) membranes to Extracorporeal Membrane Oxygenation (ECMO) machines

Crises like COVID-19 can create a massive unmet demand for rare blood oxygenation membrane machines for impaired lungs: Extracorporeal Membrane Oxygenation (ECMO) machines. Meanwhile, Hemodialysis (HD) machines, which use membranes to supplement failing kidneys, are extremely common and widespread, with orders of magnitude more available than for ECMO machines. This short study examines whether the membranes for HD can be modified for use in blood oxygenation (ECMO). To do so, it considers mass transfer at the micro-scale level, and calculations for the macro-scale level such as blood pumping rates and O2 supply pressure. Overall, while this conversion may technically be possible, poor gas transport likely requires multiple HD membranes for one patient.

physics.med-ph↗

arXiv2019

On the Learnability of Deep Random Networks

In this paper we study the learnability of deep random networks from both theoretical and practical points of view. On the theoretical front, we show that the learnability of random deep networks with sign activation drops exponentially with its depth. On the practical front, we find that the learnability drops sharply with depth even with the state-of-the-art training methods, suggesting that our stylized theoretical results are closer to reality.

cs.LG↗

arXiv2018

Minimizing Latency in Online Ride and Delivery Services

Motivated by the popularity of online ride and delivery services, we study natural variants of classical multi-vehicle minimum latency problems where the objective is to route a set of vehicles located at depots to serve request located on a metric space so as to minimize the total latency. In this paper, we consider point-to-point requests that come with source-destination pairs and release-time constraints that restrict when each request can be served. The point-to-point requests and release-time constraints model taxi rides and deliveries. For all the variants considered, we show constant-factor approximation algorithms based on a linear programming framework. To the best of our knowledge, these are the first set of results for the aforementioned variants of the minimum latency problems. Furthermore, we provide an empirical study of heuristics based on our theoretical algorithms on a real data set of taxi rides.

cs.DS↗

arXiv2016

STEPS: Predicting place attributes via spatio-temporal analysis

In recent years, a vast amount of research has been conducted on learning people's interests from their actions. Yet their collective actions also allow us to learn something about the world, in particular, infer attributes of places people visit or interact with. Imagine classifying whether a hotel has a gym or a swimming pool, or whether a restaurant has a romantic atmosphere without ever asking its patrons. Algorithms we present can do just that. Many web applications rely on knowing attributes of places, for instance, whether a particular restaurant has WiFi or offers outdoor seating. Such data can be used to support a range of user experiences, from explicit query-driven search to personalized place recommendations. However, obtaining these attributes is generally difficult, with existing approaches relying on crowdsourcing or parsing online reviews, both of which are noisy, biased, and have limited coverage. Here we present a novel approach to classifying place attributes, which learns from patrons' visit patterns based on anonymous observational data. Our method, STEPS, learns from aggregated sequences of place visits. For example, if many people visit the restaurant on a Saturday evening, coming from a luxury hotel or theater, and stay for a long time, then this restaurant is more likely to have a romantic atmosphere. On the other hand, if most people visit the restaurant on weekdays, coming from work or a grocery store, then the restaurant is less likely to be romantic. We show that such transition features are highly predictive of place attributes. In an extensive empirical evaluation, STEPS nearly doubled the coverage of a state of the art approach thanks to learning from observational location data, which allowed our method to reason about many more places.

cs.SI↗

arXiv2011

Submodular meets Spectral: Greedy Algorithms for Subset Selection, Sparse Approximation and Dictionary Selection

We study the problem of selecting a subset of k random variables from a large set, in order to obtain the best linear prediction of another variable of interest. This problem can be viewed in the context of both feature selection and sparse approximation. We analyze the performance of widely used greedy heuristics, using insights from the maximization of submodular functions and spectral analysis. We introduce the submodularity ratio as a key quantity to help understand why greedy algorithms perform well even when the variables are highly correlated. Using our techniques, we obtain the strongest known approximation guarantees for this problem, both in terms of the submodularity ratio and the smallest k-sparse eigenvalue of the covariance matrix. We further demonstrate the wide applicability of our techniques by analyzing greedy algorithms for the dictionary selection problem, and significantly improve the previously known guarantees. Our theoretical analysis is complemented by experiments on real-world and synthetic data sets; the experiments show that the submodularity ratio is a stronger predictor of the performance of greedy algorithms than other spectral parameters.

stat.ML↗

arXiv2011

Estimating the Average of a Lipschitz-Continuous Function from One Sample

We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal is to find a distribution minimizing the expected estimation error against an adversarially chosen Lipschitz continuous function. Our work falls into the broad class of estimating aggregate statistics of a function from a small number of carefully chosen samples. The general problem has a wide range of practical applications in areas as diverse as sensor networks, social sciences and numerical analysis. However, traditional work in numerical analysis has focused on asymptotic bounds, whereas we are interested in the \emph{best} algorithm. For arbitrary discrete metric spaces of bounded doubling dimension, we obtain a PTAS for this problem. In the special case when the points lie on a line, the running time improves to an FPTAS. Both algorithms are based on approximately solving a linear program with an infinite set of constraints, by using an approximate separation oracle. For Lipschitz-continuous functions over $[0,1]$, we calculate the precise achievable error as $1-\frac{\sqrt{3}}{2} \approx 0.134$, which improves upon the \quarter which is best possible for deterministic algorithms.

cs.DS↗

arXiv2002

Fair Stateless Aggregate Traffic Marking using Active Queue Management Techniques

In heterogeneous networks such as today's Internet, the differentiated services architecture promises to provide QoS guarantees through scalable service differentiation. Traffic marking is an important component of this framework. In this paper, we propose two new aggregate markers that are stateless, scalable and fair. We leverage stateless Active Queue Management (AQM) algorithms to enable fair and efficient token distribution among individual flows of an aggregate. The first marker, Probabilistic Aggregate Marker (PAM), uses the Token Bucket burst size to probabilistically mark incoming packets to ensure TCP-friendly and proportionally fair marking. The second marker, Stateless Aggregate Fair Marker (F-SAM) approximates fair queueing techniques to isolate flows while marking packets of the aggregate. It distributes tokens evenly among the flows without maintaining per-flow state. Our simulation results show that our marking strategies show upto 30% improvement over other commonly used markers while marking flow aggregates. These improvements are in terms of better average throughput and fairness indices, in scenarios containing heterogeneous traffic consisting of TCP (both long lived elephants and short lived mice) and misbehaving UDP flows. As a bonus, F-SAM helps the mice to win the war against elephants.

cs.NI↗