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Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a…
Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…
In this work, we study the trade-off between the running time of approximation algorithms and their approximation guarantees. By leveraging a structure of the `hard' instances of the Arora-Rao-Vazirani lemma [JACM'09], we show that the…
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are based on semi-definite programming (\textit{SDP}), which is generally…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the $\ell_1$ setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nearly…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
Large-scale non-convex optimization problems are expensive to solve due to computational and memory costs. To reduce the costs, first-order (computationally efficient) and asynchronous-parallel (memory efficient) algorithms are necessary to…
Continuous-time reinforcement learning (CTRL) provides a principled framework for sequential decision-making in environments where interactions evolve continuously over time. Despite its empirical success, the theoretical understanding of…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…
Momentum Stochastic Gradient Descent (MSGD) algorithm has been widely applied to many nonconvex optimization problems in machine learning, e.g., training deep neural networks, variational Bayesian inference, and etc. Despite its empirical…
In error-tolerant applications, approximate adders have been exploited extensively to achieve energy efficient system designs. Mean error distance is one of the important error metrics used as a performance measure of approximate adders. In…