相关论文: Perfect simulation from the Quicksort limit distri…

We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this…

In this work we consider the problem of fitting Random Utility Models (RUMs) to user choices. Given the winner distributions of the subsets of size $k$ of a universe, we obtain a polynomial-time algorithm that finds the RUM that best…

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…

We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…

We study the distribution of dynamical quantities in various one-dimensional, disordered models the critical behavior of which is described by an infinite randomness fixed point. In the {\it disordered contact process}, the quenched…

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of…

We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to…

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss networks. We use a variation of Dominated Coupling From The Past for which we simulate a…

It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing…

We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…

We present a general approach to constructing permutation tests that are both exact for the null hypothesis of equality of distributions and asymptotically correct for testing equality of parameters of distributions while allowing the…

A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the…

This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…

Let $\a$ be a real-valued random variable of mean zero and variance 1. Let $M_n(\a)$ denote the $n \times n$ random matrix whose entries are iid copies of $\a$ and $\sigma_n(M_n(\a))$ denote the least singular value of $M_n(\a)$.…

We revisit the method of Kirschenhofer, Prodinger and Tichy to calculate the moments of comparisons used by the quick sort algorithm. We reemphasize that this approach helps in calculating these quantities with less computation. We also…

We consider several problems in the field of distributed optimization and hypothesis testing. We show how to obtain convergence times for these problems that scale linearly with the total number of nodes in the network by using a recent…

Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to…

Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…