arXiv subjects

Vaishnavi Gupta

Publications and source records attributed to Vaishnavi Gupta.

4 recordsLinked to original sources

arXiv2026

INTHOP: A Second-Order Globally Convergent Method for Nonconvex Optimization

Second-order Newton-type algorithms that leverage the exact Hessian or its approximation are central to solve nonlinear optimization problems. However, their applications in solving large-scale nonconvex problems are hindered by three primary challenges: (1) the high computational cost associated with Hessian evaluations, (2) its inversion, and (3) ensuring descent direction at points where the Hessian becomes indefinite. We propose INTHOP, an interval Hessian-based optimization algorithm for nonconvex problems to deal with these primary challenges. The proposed search direction is based on approximating the original Hessian matrix by a positive definite matrix. The novelty of the proposed method is that the proposed search direction is guaranteed to be descent and requires approximation of Hessian and its inversion only at specific iterations. We prove that the difference between the calculated approximate and exact Hessian is bounded within an interval. Accordingly, the approximate Hessian matrix is reused if the iterates are in that chosen interval while computing the gradients at each iteration. We develop various algorithm variants based on the interval size updating methods and minimum eigenvalue computation methods. We also prove the global convergence of the proposed algorithm. Further, we apply the algorithm to an extensive set of test problems and compare its performance with the existing methods such as steepest descent, quasi-Newton, and Newton method. We show empirically that the proposed method solves more problems in fewer function and gradient evaluations than steepest descent and the quasi-Newton method. While in the comparison to the Newton method, we illustrate that for nonconvex optimization problems, we require substantially less $O(n^3)$ operations.

math.OC↗

arXiv2025

Biorderability of knot quandles of knots up to eight crossings

The paper investigates biorderability of knot quandles of prime knots up to eight crossings. We prove that knot quandles of knots $6_3$, $8_7$, $8_8$, $8_{10}$ and $8_{16}$ can not be biorderable. However, we see that knot quandles of knots $4_1$, $6_1$, $6_2$, $7_6$, $7_7$, $8_1$, $8_2$, $8_3$, $8_4$, $8_5$, $8_6$, $8_9$, $8_{11}$, $8_{12}$, $8_{13}$, $8_{14}$, $8_{17}$, $8_{18}$, $8_{20}$ and $8_{21}$ could be biorderable. We also give linear orders on the generating set of the knot quandle of a knot (among these knots) that could be extendable to biorders on the quandle.

math.GT↗

arXiv2023

Non-Stochastic CDF Estimation Using Threshold Queries

Estimating the empirical distribution of a scalar-valued data set is a basic and fundamental task. In this paper, we tackle the problem of estimating an empirical distribution in a setting with two challenging features. First, the algorithm does not directly observe the data; instead, it only asks a limited number of threshold queries about each sample. Second, the data are not assumed to be independent and identically distributed; instead, we allow for an arbitrary process generating the samples, including an adaptive adversary. These considerations are relevant, for example, when modeling a seller experimenting with posted prices to estimate the distribution of consumers' willingness to pay for a product: offering a price and observing a consumer's purchase decision is equivalent to asking a single threshold query about their value, and the distribution of consumers' values may be non-stationary over time, as early adopters may differ markedly from late adopters. Our main result quantifies, to within a constant factor, the sample complexity of estimating the empirical CDF of a sequence of elements of $[n]$, up to $\varepsilon$ additive error, using one threshold query per sample. The complexity depends only logarithmically on $n$, and our result can be interpreted as extending the existing logarithmic-complexity results for noisy binary search to the more challenging setting where noise is non-stochastic. Along the way to designing our algorithm, we consider a more general model in which the algorithm is allowed to make a limited number of simultaneous threshold queries on each sample. We solve this problem using Blackwell's Approachability Theorem and the exponential weights method. As a side result of independent interest, we characterize the minimum number of simultaneous threshold queries required by deterministic CDF estimation algorithms.

cs.LG↗

arXiv2021

Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods

Many widely used datasets for graph machine learning tasks have generally been homophilous, where nodes with similar labels connect to each other. Recently, new Graph Neural Networks (GNNs) have been developed that move beyond the homophily regime; however, their evaluation has often been conducted on small graphs with limited application domains. We collect and introduce diverse non-homophilous datasets from a variety of application areas that have up to 384x more nodes and 1398x more edges than prior datasets. We further show that existing scalable graph learning and graph minibatching techniques lead to performance degradation on these non-homophilous datasets, thus highlighting the need for further work on scalable non-homophilous methods. To address these concerns, we introduce LINKX -- a strong simple method that admits straightforward minibatch training and inference. Extensive experimental results with representative simple methods and GNNs across our proposed datasets show that LINKX achieves state-of-the-art performance for learning on non-homophilous graphs. Our codes and data are available at https://github.com/CUAI/Non-Homophily-Large-Scale.

cs.LG↗