相关论文: Optimal Query Complexities for Dynamic Trace Estim…

Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

We show optimal lower bounds for spanning forest computation in two different models: * One wants a data structure for fully dynamic spanning forest in which updates can insert or delete edges amongst a base set of $n$ vertices. The sole…

The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from…

This paper introduces a simple principle for robust high-dimensional statistical inference via an appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the moment conditions from sub-exponential…

The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a new nuclear norm penalized estimator of $A_0$ and…

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…

Backtracking line search is foundational in numerical optimization. The basic idea is to adjust the step-size of an algorithm by a constant factor until some chosen criterion (e.g. Armijo, Descent Lemma) is satisfied. We propose a novel way…

We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…

We study the problem of scheduling $n$ independent moldable tasks on $m$ processors that arises in large-scale parallel computations. When tasks are monotonic, the best known result is a $(\frac{3}{2}+\epsilon)$-approximation algorithm for…

We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the…

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…

Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…

This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…

Hutchinson estimators are widely employed in training divergence-based likelihoods for diffusion models to ensure optimal transport (OT) properties. However, this estimator often suffers from high variance and scalability concerns. To…

In this paper, we focus our attention on the high-dimensional double sparse linear regression, that is, a combination of element-wise and group-wise sparsity. To address this problem, we propose an IHT-style (iterative hard thresholding)…

Permutation pattern-avoidance is a central concept of both enumerative and extremal combinatorics. In this paper we study the effect of permutation pattern-avoidance on the complexity of optimization problems. In the context of the dynamic…

In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…