Related papers: Testability of relations between permutations
This paper is a journal counterpart to our FOCS 2021 paper, in which we initiate the study of property testing problems concerning a finite system of relations $E$ between permutations, generalizing the study of stability in permutations.…
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…
Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…
An action trace is a function naturally associated to a probability measure preserving action of a group on a standard probability space. For countable amenable groups, we characterise stability in permutations using action traces. We…
We formulate and analyze a novel hypothesis testing problem for inferring the edge structure of an infection graph. In our model, a disease spreads over a network via contagion or random infection, where the random variables governing the…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we…
Neural networks are powerful predictive models, but they provide little insight into the nature of relationships between predictors and outcomes. Although numerous methods have been proposed to quantify the relative contributions of input…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
We propose using a permutation test to detect discontinuities in an underlying economic model at a known cutoff point. Relative to the existing literature, we show that this test is well suited for event studies based on time-series data.…
The main problem in the area of graph property testing is to understand which graph properties are \emph{testable}, which means that with constantly many queries to any input graph $G$, a tester can decide with good probability whether $G$…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
This paper develops a method to use singles' data in a non-parametric revealed preference setting of collective household choice. We use it to test the controversial assumption of preference stability between singles and couples, without…
The statistical literature is known to be inconsistent in the use of the terms "permutation test" and "randomization test". Several authors succesfully argue that these terms should be used to refer to two distinct classes of tests and that…
We introduce a notion of \emph{efficient stability} for finite presentations of groups. Informally, a finite presentation using generators $S$ and relations $R$ is \emph{stable} if any map from $S$ to unitaries that approximately satisfies…
Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary…
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…