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A time series is a sequence of data items; typical examples are streams of temperature measurements, stock ticker data, or gestures recorded with modern virtual reality motion controllers. Quite some research has been devoted to comparing…
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…
In this paper, we study the fundamental problems of maintaining the diameter and a $k$-center clustering of a dynamic point set $P \subset \mathbb{R}^d$, where points may be inserted or deleted over time and the ambient dimension $d$ is not…
Multidimensional time series are sequences of real valued vectors. They occur in different areas, for example handwritten characters, GPS tracking, and gestures of modern virtual reality motion controllers. Within these areas, a common task…
Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement…
We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. Specifically, we are given a set $T$ of $n$ points in $\mathbb{R}^d$ and a parameter $0< \alpha <\frac 1 2$ such that an…
Human demonstrations of trajectories are an important source of training data for many machine learning problems. However, the difficulty of collecting human demonstration data for complex tasks makes learning efficient representations of…
Dynamic Programming suffers from the curse of dimensionality due to large state and action spaces, a challenge further compounded by uncertainties in the environment. To mitigate these issue, we explore an off-policy based Temporal…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
Value functions derived from Markov decision processes arise as a central component of algorithms as well as performance metrics in many statistics and engineering applications of machine learning techniques. Computation of the solution to…
Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial- time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs)…
In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple…
The Median String Problem is W[1]-Hard under the Levenshtein distance, thus, approximation heuristics are used. Perturbation-based heuristics have been proved to be very competitive as regards the ratio approximation accuracy/convergence…
We introduce the combinatorial optimization problem Time Disjoint Walks (TDW), which has applications in collision-free routing of discrete objects (e.g., autonomous vehicles) over a network. This problem takes as input a digraph $G$ with…
In this work, we present a new iterative exact solution algorithm for the weighted fair sequences problem, which is a recently introduced NP-hard sequencing problem with applications in diverse areas such as TV advertisement scheduling,…
In this paper, we consider a variant of the classical algorithmic problem of checking whether a given word $v$ is a subsequence of another word $w$. More precisely, we consider the problem of deciding, given a number $p$ (defining a…
In 2005 Kumar studied the Restricted Disjunctive Temporal Problem (RDTP), a restricted but very expressive class of disjunctive temporal problems (DTPs). It was shown that that RDTPs are solvable in deterministic strongly-polynomial time by…
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…