Related papers: Fast Approximation of Persistence Diagrams with Gu…

Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…

In this paper, we propose a variant of Riemannian stochastic recursive gradient method that can achieve second-order convergence guarantee and escape saddle points using simple perturbation. The idea is to perturb the iterates when gradient…

Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…

We provide faster algorithms for approximately solving $\ell_{\infty}$ regression, a fundamental problem prevalent in both combinatorial and continuous optimization. In particular, we provide accelerated coordinate descent methods capable…

Stability of persistence diagrams under slight perturbations is a key characteristic behind the validity and growing popularity of topological data analysis in exploring real-world data. Central to this stability is the use of Bottleneck…

We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…

In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…

Recently, Musco and Woodruff (FOCS, 2017) showed that given an $n \times n$ positive semidefinite (PSD) matrix $A$, it is possible to compute a $(1+\epsilon)$-approximate relative-error low-rank approximation to $A$ by querying…

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

We present maximally-fast numerical algorithms for conserved coarsening systems that are stable and accurate with a growing natural time-step $\Delta t=A t_s^{2/3}$. For non-conserved systems, only effectively finite timesteps are…

Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram…

For a family of graphs $\mathcal{F}$, Weighted $\mathcal{F}$-Deletion is the problem for which the input is a vertex weighted graph $G=(V,E)$ and the goal is to delete $S\subseteq V$ with minimum weight such that $G\setminus…

Saddle point problems, ubiquitous in optimization, extend beyond game theory to diverse domains like power networks and reinforcement learning. This paper presents novel approaches to tackle saddle point problem, with a focus on…

We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming…

Off-policy learning is key to scaling up reinforcement learning as it allows to learn about a target policy from the experience generated by a different behavior policy. Unfortunately, it has been challenging to combine off-policy learning…

Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics…

Effective Resistance (ER) is a fundamental tool in various graph learning tasks. In this paper, we address the problem of efficiently approximating ER on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ with $n$ vertices and $m$ edges.…

This paper presents a generalization of the Wasserstein distance for both persistence diagrams and merge trees [20], [66] that takes advantage of the regions of their topological features in the input domain. Specifically, we redefine the…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…