Related papers: Testing exchangeability by pairwise betting
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
In software testing, the large size of the input domain makes exhaustively testing the inputs a daunting and often impossible task. Pair-wise testing is a popular approach to combinatorial testing problems. This paper reviews Pair-wise…
We propose a novel nonparametric sequential test for composite hypotheses for means of multiple data streams. Our proposed method, \emph{peeking with expectation-based averaged capital} (PEAK), builds upon the testing-by-betting framework…
We study the problem of active nonparametric sequential two-sample testing over multiple heterogeneous data sources. In each time slot, a decision-maker adaptively selects one of $K$ data sources and receives a paired sample generated from…
In the theory of algorithmic randomness, one of the central notions is that of computable randomness. An infinite binary sequence X is computably random if no recursive martingale (strategy) can win an infinite amount of money by betting on…
When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…
We provide practical, efficient, and nonparametric methods for auditing the fairness of deployed classification and regression models. Whereas previous work relies on a fixed-sample size, our methods are sequential and allow for the…
A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and…
We study testable implications of multiple equilibria in discrete games with incomplete information. Unlike de Paula and Tang (2012), we allow the players' private signals to be correlated. In static games, we leverage independence of…
We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously;…
Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…
In some applications, an experimental unit is composed of two distinct but related subunits. The response from such a unit is $(X_{1}, X_{2})$ but we observe only $Y_1 = \min\{X_{1},X_{2}\}$ and $Y_2 = \max\{X_{1},X_{2}\}$, i.e., the…
A randomized trial and an analysis of observational data designed to emulate the trial sample observations separately, but have the same eligibility criteria, collect information on some shared baseline covariates, and compare the effects…
The technique of ``testing by betting" frames nonparametric sequential hypothesis testing as a multiple-round game, where a player bets on future observations that arrive in a streaming fashion, accumulates wealth that quantifies evidence…
Feature-based SPL analysis and family-based model checking have seen rapid development. Many model checking problems can be reduced to two-player games on finite graphs. A prominent example is mu-calculus model checking, which is generally…
We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…
We study discounted infinitely repeated games in which players agree on a cooperative mixed action profile but, at each step, observe only the realized pure actions. This form of imperfect monitoring breaks classical trigger strategies,…
Self-testing allows us to determine, through classical interaction only, whether some players in a non-local game share particular quantum states. Most work on self-testing has concentrated on developing tests for small states like one pair…
This note continues study of exchangeability martingales, i.e., processes that are martingales under any exchangeable distribution for the observations. Such processes can be used for detecting violations of the IID assumption, which is…
In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…