A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order operations (e.g., certain optimizations) are considered primitive for the purposes …
The Sarkar-Wang algorithm computes the hat version of the Heegaard Floer homology of a closed oriented three manifold. This paper analyzes the computational complexity of the Sarkar-Wang algorithm; then the algorithm is modified to obtain a better bound. Then the computational complexity of calculating HFK hat from a H…
Model proposes how regulators should oversee complex algorithms in high-stakes applications.
problem Regulating complex algorithms used in high-stakes applications like lending, testing, and hiring.
method Proposes a model where regulators are limited in learning about complex algorithms with misaligned preferences, and explores different regulatory approaches.
result Complex algorithms can improve welfare, but regulation should focus on the source of incentive misalignment for optimal results.
In this work, we address the open problem of finding low-complexity near-optimal multi-armed bandit algorithms for sequential decision making problems. Existing bandit algorithms are either sub-optimal and computationally simple (e.g., UCB1) or optimal and computationally complex (e.g., kl-UCB). We propose a boosting a…
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between m discrete probability distributions supported each on n support points. First, we show that the standard linear programming (LP) represe…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex optimization problem of matrix sensing. Our algorithm is applicable to both noisy and…
We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher…
Study shows a tradeoff between sample complexity and computational efficiency for learning halfspaces with random noise.
problem PAC learning γ-margin halfspaces with Random Classification Noise.
method Established an information-computation tradeoff and provided a simple efficient algorithm with sample complexity O(1/(γ^2 ε^2)). Also, proved lower bounds for SQ algorithms and low-degree polynomial tests.
result Inherent gap between sample complexity and computational efficiency for learning halfspaces with random noise.
We consider streaming, one-pass principal component analysis (PCA), in the high-dimensional regime, with limited memory. Here, p-dimensional samples are presented sequentially, and the goal is to produce the k-dimensional subspace that best approximates these points. Standard algorithms require O(p2) memory; mea…
First proper learning algorithm for Gaussian halfspaces with matching sample and computational complexity.
problem Agnostically learning halfspaces under Gaussian distribution.
method First proper learning algorithm with matching sample and computational complexity.
result First proper learning algorithm for agnostically learning halfspaces under Gaussian distribution with matching sample and computational complexity.
We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most n components. We show that the complexity of the Sinkhorn algorithm for finding an ε-appr…
We study a recent model of collaborative PAC learning where k players with k different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small error on all tasks, there is a collaborative algorithm that finds a single classifi…
We provide theoretical complexity analysis for new algorithms to compute the optimal transport (OT) distance between two discrete probability distributions, and demonstrate their favorable practical performance over state-of-art primal-dual algorithms and their capability in solving other problems in large-scale, such …