Related papers: Sorting by Swaps with Noisy Comparisons

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…

This paper introduces a new comparison base stable sorting algorithm, named RS sort. RS Sort involves only the comparison of pair of elements in an array which ultimately sorts the array and does not involve the comparison of each element…

The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…

Suppose we observe a trajectory of length $n$ from an exponentially $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary…

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…

Particles labelled $1,...,n$ are initially arranged in increasing order. Subsequently, each pair of neighboring particles that is currently in increasing order swaps according to a Poisson process of rate 1. We analyze the asymptotic…

In interactive systems, feedback is often provided in the form of preference between queried options rather than precise scores, which motivates optimization methods to learn from such comparisons. In this work, we propose a…

A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…

A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

This paper studies one-sided hypothesis testing under random sampling without replacement. That is, when $n+1$ binary random variables $X_1,\ldots, X_{n+1}$ are subject to a permutation invariant distribution and $n$ binary random variables…

In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…

We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a null…

Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach…

We characterize the minimum-length sequences of independent lazy simple transpositions whose composition is a uniformly random permutation. For every reduced word of the reverse permutation there is exactly one valid way to assign…

We consider the problem of ranking a set of objects based on their performance when the measurement of said performance is subject to noise. In this scenario, the performance is measured repeatedly, resulting in a range of measurements for…

In a typical optimization problem, the task is to pick one of a number of options with the lowest cost or the highest value. In practice, these cost/value quantities often come through processes such as measurement or machine learning,…

Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large.…

Consider a target moving at a constant velocity on a unit-circumference circle, starting at an arbitrary location. To acquire the target, any region of the circle can be probed to obtain a noisy measurement of the target's presence, where…

Randomized smoothing is a popular certified defense against adversarial attacks. In its essence, we need to solve a problem of statistical estimation which is usually very time-consuming since we need to perform numerous (usually $10^5$)…