Related papers: Negative association, ordering and convergence of …
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
We study the theoretical convergence properties of random-search methods when optimizing non-convex objective functions without having access to derivatives. We prove that standard random-search methods that do not rely on second-order…
In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…
The reversible jump algorithm is a useful Markov chain Monte Carlo method introduced by Green (1995) that allows switches between subspaces of differing dimensionality, and therefore, model selection. Although this method is now…
We consider reinforcement learning in an environment modeled by an episodic, finite, stage-dependent Markov decision process of horizon $H$ with $S$ states, and $A$ actions. The performance of an agent is measured by the regret after…
It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic (WH) formulations of Einstein's equations. Here we explicitly show that with…
This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or…
Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
We study parallel algorithms for correlation clustering. Each pair among $n$ objects is labeled as either "similar" or "dissimilar". The goal is to partition the objects into arbitrarily many clusters while minimizing the number of…
Sundararajan and Chakraborty (2007) introduced a new sorting algorithm by modifying the fast and popular Quick sort and removing the interchanges. In a subsequent empirical study, Sourabh, Sundararajan and Chakraborty (2007) demonstrated…
We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…
Despite the strong theoretical guarantees that variance-reduced finite-sum optimization algorithms enjoy, their applicability remains limited to cases where the memory overhead they introduce (SAG/SAGA), or the periodic full gradient…
We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…
We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ (and possibly some labels ${\boldsymbol y}\in{\mathbb R}^n$) and would like to estimate a…
Negative sampling schemes enable efficient training given a large number of classes, by offering a means to approximate a computationally expensive loss function that takes all labels into account. In this paper, we present a new connection…
Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming…
System reliability assessment(SRA) is a challenging task due to the limited experimental data and the complex nature of the system structures. Despite a long history dating back to \cite{buehler1957confidence}, exact methods have only been…
Fast convergence and high-quality image recovery are two essential features of algorithms for solving ill-posed imaging inverse problems. Existing methods, such as regularization by denoising (RED), often focus on designing sophisticated…
Weak convergence of various general functionals of partial sums of dependent random variables to stochastic integral now play a major role in the modern statistics theory. In this paper, we obtain the weak convergence of various general…