Related papers: Interactive Proofs For Distribution Testing With C…
We characterize the communication complexity of the following distributed estimation problem. Alice and Bob observe infinitely many iid copies of $\rho$-correlated unit-variance (Gaussian or $\pm1$ binary) random variables, with unknown…
Interactive proofs are often considered as costs of formal modelling activity. In an incremental development environment such as the Rodin platform for Event-B, information from proof attempts is important input for adapting the model. This…
Multi Prover Interactive Proof systems (MIPs)were first presented in a cryptographic context, but ever since they were used in various fields. Understanding the power of MIPs in the quantum context raises many open problems, as there are…
This paper develops novel conformal methods to test whether a new observation was sampled from the same distribution as a reference set. Blending inductive and transductive conformal inference in an innovative way, the described methods can…
Distributed frameworks are widely used to handle massive data, where sample size $n$ is very large, and data are often stored in $k$ different machines. For a random vector $X\in \mathbb{R}^p$ with expectation $\mu$, testing the mean vector…
Using the measurement-based quantum computation model, we construct interactive proofs with non-communicating quantum provers and a classical verifier. Our construction gives interactive proofs for all languages in BQP with a polynomial…
Probabilistic programming provides a high-level framework for specifying statistical models as executable programs with built-in randomness and conditioning. Existing inference techniques, however, typically compute posterior distributions…
In many-to-many matching models, substitutable preferences constitute the largest domain for which a pairwise stable matching is guaranteed to exist. In this note, we extend the recently proposed algorithm of Hatfield et al. [3] to test…
We study the problem of discrete distribution testing in the two-party setting. For example, in the standard closeness testing problem, Alice and Bob each have $t$ samples from, respectively, distributions $a$ and $b$ over $[n]$, and they…
This paper introduces a novel goodness-of-fit test technique for parametric conditional distributions. The proposed tests are based on a residual marked empirical process, for which we develop a conditional Principal Component Analysis. The…
Linearity testing has been a focal problem in property testing of functions. We combine different known techniques and observations about linearity testing in order to resolve two recent versions of this task. First, we focus on the online…
We study property testing in the subcube conditional model introduced by Bhattacharyya and Chakraborty (2017). We obtain the first equivalence test for $n$-dimensional distributions that is quasi-linear in $n$, improving the previously…
We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…
We study prepare-and-measure experiments where the sender (Alice) receives trusted quantum inputs but has an untrusted state-preparation device and the receiver (Bob) has a fully-untrusted measurement device. A distributed-sampling task…
Conditional identity in distribution (Berti et al. (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper, a class of random sequences, called Generalized Species…
This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction…
We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and…
The division of goods in the online realm poses opportunities and challenges. While innovative mechanisms can be developed, uncertainty about the future may hinder effective solutions. This project aims to explore fair distribution models…
We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…
In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…