arXiv subjects

Vishal Gupta

Publications and source records attributed to Vishal Gupta.

28 records · Page 2Linked to original sources

arXiv2020

Balance Regularized Neural Network Models for Causal Effect Estimation

Estimating individual and average treatment effects from observational data is an important problem in many domains such as healthcare and e-commerce. In this paper, we advocate balance regularization of multi-head neural network architectures. Our work is motivated by representation learning techniques to reduce differences between treated and untreated distributions that potentially arise due to confounding factors. We further regularize the model by encouraging it to predict control outcomes for individuals in the treatment group that are similar to control outcomes in the control group. We empirically study the bias-variance trade-off between different weightings of the regularizers, as well as between inductive and transductive inference.

cs.LG↗

arXiv2020

Data-Pooling in Stochastic Optimization

Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests one can decouple these unrelated problems and solve them separately without loss of generality. We propose a novel data-pooling algorithm called Shrunken-SAA that disproves this intuition. In particular, we prove that combining data across problems can outperform decoupling, even when there is no a priori structure linking the problems and data are drawn independently. Our approach does not require strong distributional assumptions and applies to constrained, possibly non-convex, non-smooth optimization problems such as vehicle-routing, economic lot-sizing or facility location. We compare and contrast our results to a similar phenomenon in statistics (Stein's Phenomenon), highlighting unique features that arise in the optimization setting that are not present in estimation. We further prove that as the number of problems grows large, Shrunken-SAA learns if pooling can improve upon decoupling and the optimal amount to pool, even if the average amount of data per problem is fixed and bounded. Importantly, we highlight a simple intuition based on stability that highlights when and why data-pooling offers a benefit, elucidating this perhaps surprising phenomenon. This intuition further suggests that data-pooling offers the most benefits when there are many problems, each of which has a small amount of relevant data. Finally, we demonstrate the practical benefits of data-pooling using real data from a chain of retail drug stores in the context of inventory management.

math.OC↗

arXiv2017

Fixed function and its application to Medical Science

In the present paper, the concept of contraction has been extended in a refined manner by introducing $\mathfrak{D}$-Contraction defined on a family $\mathfrak{F}$ of bounded functions. Also, a new notion of fixed function has been introduced for a metric space. Some fixed function theorems along with illustrative examples have also been given to verify the effectiveness of our results. In addition, an application to medical science has also been presented. This application is based on best approximation of treatment plan for tumor patients getting intensity modulated radiation therapy(IMRT). In this technique, a proper DDC matrix truncation has been used that significantly improves accuracy of results. In 2013, Z. Tian \textit{et al.} presented a fluence map optimization(FMO) model for dose calculation by splitting the DDC matrix into two components on the basis of a threshold intensity value. Following this concept, a sequence of functions can be constructed through the presented results which contains different dose distributions corresponding to different patients and finally it converges to a fixed function. The fixed function obtained in this application represents the suitable doses of a number of tumor patients at the same time. A nice explanation has also been given to check the authenticity of the application and the results.

math.FA↗

arXiv2016

Robust Sample Average Approximation

Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees, however, do not typically hold in finite samples. In this paper, we propose a modification of SAA, which we term Robust SAA, which retains SAA's tractability and asymptotic properties and, additionally, enjoys strong finite-sample performance guarantees. The key to our method is linking SAA, distributionally robust optimization, and hypothesis testing of goodness-of-fit. Beyond Robust SAA, this connection provides a unified perspective enabling us to characterize the finite sample and asymptotic guarantees of various other data-driven procedures that are based upon distributionally robust optimization. This analysis provides insight into the practical performance of these various methods in real applications. We present examples from inventory management and portfolio allocation, and demonstrate numerically that our approach outperforms other data-driven approaches in these applications.

math.OC↗

arXiv2014

Data-Driven Robust Optimization

The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee. \edit{We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queuing confirm that our data-driven sets significantly outperform traditional robust optimization techniques whenever data is available.

math.OC↗

arXiv2014

A Comparison of Monte Carlo Tree Search and Mathematical Optimization for Large Scale Dynamic Resource Allocation

Dynamic resource allocation (DRA) problems are an important class of dynamic stochastic optimization problems that arise in a variety of important real-world applications. DRA problems are notoriously difficult to solve to optimality since they frequently combine stochastic elements with intractably large state and action spaces. Although the artificial intelligence and operations research communities have independently proposed two successful frameworks for solving dynamic stochastic optimization problems---Monte Carlo tree search (MCTS) and mathematical optimization (MO), respectively---the relative merits of these two approaches are not well understood. In this paper, we adapt both MCTS and MO to a problem inspired by tactical wildfire and management and undertake an extensive computational study comparing the two methods on large scale instances in terms of both the state and the action spaces. We show that both methods are able to greatly improve on a baseline, problem-specific heuristic. On smaller instances, the MCTS and MO approaches perform comparably, but the MO approach outperforms MCTS as the size of the problem increases for a fixed computational budget.

math.OC↗

arXiv2014

Data-Driven Estimation in Equilibrium Using Inverse Optimization

Equilibrium modeling is common in a variety of fields such as game theory and transportation science. The inputs for these models, however, are often difficult to estimate, while their outputs, i.e., the equilibria they are meant to describe, are often directly observable. By combining ideas from inverse optimization with the theory of variational inequalities, we develop an efficient, data-driven technique for estimating the parameters of these models from observed equilibria. We use this technique to estimate the utility functions of players in a game from their observed actions and to estimate the congestion function on a road network from traffic count data. A distinguishing feature of our approach is that it supports both parametric and \emph{nonparametric} estimation by leveraging ideas from statistical learning (kernel methods and regularization operators). In computational experiments involving Nash and Wardrop equilibria in a nonparametric setting, we find that a) we effectively estimate the unknown demand or congestion function, respectively, and b) our proposed regularization technique substantially improves the out-of-sample performance of our estimators.

math.OC↗

arXiv2010

Personalized Data Set for Analysis

Data Management portfolio within an organization has seen an upsurge in initiatives for compliance, security, repurposing and storage within and outside the organization. When such initiatives are being put to practice care must be taken while granting access to data repositories for analysis and mining activities. Also, initiatives such as Master Data Management, cloud computing and self service business intelligence have raised concerns in the arena of regulatory compliance and data privacy, especially when a large data set of an organization are being outsourced for testing, consolidation and data management. Here, an approach is presented where a new service layer is introduced, by data governance group, in the architecture for data management and can be used for preserving privacy of sensitive information.

cs.DB↗

arXiv2005

Quantifying Influenza Vaccine Efficacy and Antigenic Distance

We introduce a new measure of antigenic distance between influenza A vaccine and circulating strains. The measure correlates well with efficacies of the H3N2 influenza A component of the annual vaccine between 1971 and 2004, as do results of a theory of the immune response to influenza following vaccination. This new measure of antigenic distance is correlated with vaccine efficacy to a greater degree than are current state-of-the-art phylogenetic sequence analyzes or ferret antisera inhibition assays. We suggest that this new measure of antigenic distance be used in the design of the annual influenza vaccine and in the interpretation of vaccine efficacy monitoring.

q-bio.BM↗

arXiv2004

Length, Protein-Protein Interactions, and Complexity

The evolutionary reason for the increase in gene length from archaea to prokaryotes to eukaryotes observed in large scale genome sequencing efforts has been unclear. We propose here that the increasing complexity of protein-protein interactions has driven the selection of longer proteins, as longer proteins are more able to distinguish among a larger number of distinct interactions due to their greater average surface area. Annotated protein sequences available from the SWISS-PROT database were analyzed for thirteen eukaryotes, eight bacteria, and two archaea species. The number of subcellular locations to which each protein is associated is used as a measure of the number of interactions to which a protein participates. Two databases of yeast protein-protein interactions were used as another measure of the number of interactions to which each \emph{S. cerevisiae} protein participates. Protein length is shown to correlate with both number of subcellular locations to which a protein is associated and number of interactions as measured by yeast two-hybrid experiments. Protein length is also shown to correlate with the probability that the protein is encoded by an essential gene. Interestingly, average protein length and number of subcellular locations are not significantly different between all human proteins and protein targets of known, marketed drugs. Increased protein length appears to be a significant mechanism by which the increasing complexity of protein-protein interaction networks is accommodated within the natural evolution of species. Consideration of protein length may be a valuable tool in drug design, one that predicts different strategies for inhibiting interactions in aberrant and normal pathways.

q-bio.MN↗