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We investigate the scheduling of $n$ jobs divided into $c$ classes on $m$ identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class.…

Data Structures and Algorithms · Computer Science 2019-05-02 Max A. Deppert , Klaus Jansen

Simulated annealing is an effective and general means of optimization. It is in fact inspired by metallurgy, where the temperature of a material determines its behavior in thermodynamics. Likewise, in simulated annealing, the actions that…

Machine Learning · Computer Science 2020-07-01 Avrim Blum , Chen Dan , Saeed Seddighin

We design fast algorithms for repeatedly sampling from strongly Rayleigh distributions, which include random spanning tree distributions and determinantal point processes. For a graph $G=(V, E)$, we show how to approximately sample…

Data Structures and Algorithms · Computer Science 2022-09-20 Nima Anari , Yang P. Liu , Thuy-Duong Vuong

Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…

Probability · Mathematics 2023-01-09 Samuel Herrmann , Nicolas Massin

One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…

Machine Learning · Statistics 2015-11-10 Ahmed El Alaoui , Michael W. Mahoney

The quantum stochastic drift protocol, also known as qDRIFT, has become a popular algorithm for implementing time-evolution of quantum systems using randomised compiling. In this work we develop qFLO, a higher order randomised algorithm for…

Quantum Physics · Physics 2025-01-28 James D. Watson

We study a new framework for property testing of probability distributions, by considering distribution testing algorithms that have access to a conditional sampling oracle.* This is an oracle that takes as input a subset $S \subseteq [N]$…

Data Structures and Algorithms · Computer Science 2015-01-19 Clement Canonne , Dana Ron , Rocco A. Servedio

We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…

Optimization and Control · Mathematics 2020-08-24 Andrzej Ruszczynski , Jianing Yao

Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…

Quantum Physics · Physics 2026-02-02 Marcello Benedetti , Harry Buhrman , Jordi Weggemans

We review the derivation of the Kac master equation model for random collisions of particles, its relationship to the Poisson process, and existing algorithms for simulating values from the marginal distribution of velocity for a single…

Computation · Statistics 2016-03-07 Jem Corcoran , Dale Jennings , Paul VaughanMiller

Finding a small spectral approximation for a tall $n \times d$ matrix $A$ is a fundamental numerical primitive. For a number of reasons, one often seeks an approximation whose rows are sampled from those of $A$. Row sampling improves…

Data Structures and Algorithms · Computer Science 2016-04-20 Michael B. Cohen , Cameron Musco , Jakub Pachocki

In 2016, Karney proposed an exact sampling algorithm for the standard normal distribution. In this paper, we study the computational complexity of this algorithm under the random deviate model. Specifically, Karney's algorithm requires the…

Data Structures and Algorithms · Computer Science 2020-08-11 Yusong Du , Baoying Fan , Baodian Wei

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…

Numerical Analysis · Mathematics 2017-01-04 Bogdan Opanchuk , Simon Kiesewetter , Peter D. Drummond

A major bottleneck of standard auto-regressive large language models is that their inference process is inherently sequential, resulting in very long and costly inference times. To circumvent this, practitioners proposed a class of language…

Machine Learning · Computer Science 2025-11-11 Sitan Chen , Kevin Cong , Jerry Li

Given a quadratic map Q : K^n -> K^k defined over a computable subring D of a real closed field K, and a polynomial p(Y_1,...,Y_k) of degree d, we consider the zero set Z=Z(p(Q(X)),K^n) of the polynomial p(Q(X_1,...,X_n)). We present a…

Symbolic Computation · Computer Science 2007-05-23 Dima Grigoriev , Dmitrii V. Pasechnik

The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…

Machine Learning · Statistics 2022-05-17 Yuxin Dong , Tieliang Gong , Shujian Yu , Chen Li

Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust…

Machine Learning · Computer Science 2024-04-04 Nika Haghtalab , Michael I. Jordan , Eric Zhao

This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach…

Optimization and Control · Mathematics 2020-11-11 Kai Du , Qingxin Meng , Fu Zhang

We investigate distribution testing with access to non-adaptive conditional samples. In the conditional sampling model, the algorithm is given the following access to a distribution: it submits a query set $S$ to an oracle, which returns a…

Data Structures and Algorithms · Computer Science 2018-11-06 Gautam Kamath , Christos Tzamos

In this paper, we consider distributed algorithms for solving the empirical risk minimization problem under the master/worker communication model. We develop a distributed asynchronous quasi-Newton algorithm that can achieve superlinear…

Optimization and Control · Mathematics 2019-06-11 Saeed Soori , Konstantin Mischenko , Aryan Mokhtari , Maryam Mehri Dehnavi , Mert Gurbuzbalaban
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