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We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
In distribution compression, one aims to accurately summarize a probability distribution $\mathbb{P}$ using a small number of representative points. Near-optimal thinning procedures achieve this goal by sampling $n$ points from a Markov…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms…
Multivariate time series alignment is critical for ensuring coherent analysis across variables, but missing values and timestamp inconsistencies make this task highly challenging. Existing approaches often rely on prior imputation, which…
This paper discusses the problem of covering and hitting a set of line segments $\cal L$ in ${\mathbb R}^2$ by a pair of axis-parallel squares such that the side length of the larger of the two squares is minimized. We also discuss the…
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms…
Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
In this paper, we consider the problems for covering multiple intervals on a line. Given a set $B$ of $m$ line segments (called "barriers") on a horizontal line $L$ and another set $S$ of $n$ horizontal line segments of the same length in…
This paper introduces a new type of regression methodology named as Convex-Area-Wise Linear Regression(CALR), which separates given datasets by disjoint convex areas and fits different linear regression models for different areas. This…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
This paper introduces the use of tailored variational forms for variational quantum eigensolver that have properties of representing certain constraints on the search domain of a linear constrained quadratic binary optimization problem…
We present algorithms that run in linear time on pointer machines for a collection of problems, each of which either directly or indirectly requires the evaluation of a function defined on paths in a tree. These problems previously had…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
Solving linear systems and quadratic programming (QP) problems are both ubiquitous tasks in the engineering and computing fields. Direct methods for solving systems, such as Cholesky, LU, and QR factorizations, exhibit data-independent time…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…