相关论文: Testing Mixtures of Discrete Distributions

We show a hardness result for random smoothing to achieve certified adversarial robustness against attacks in the $\ell_p$ ball of radius $\epsilon$ when $p>2$. Although random smoothing has been well understood for the $\ell_2$ case using…

We study distribution testing in the standard access model and the conditional access model when the memory available to the testing algorithm is bounded. In both scenarios, the samples appear in an online fashion and the goal is to test…

We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to $b$ bits. We investigate both the $d$- and infinite-dimensional signal…

Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models…

We introduce a method for testing quantum correlations in terms of quasiprobability functions in the presence of noise. We analyze the effects of measurement imperfection and thermal environment on quantum correlations and show that their…

Sampling from the output distribution of chaotic quantum evolutions, and of pseudo-random universal quantum circuits in particular, has been proposed as a prominent milestone for near-term quantum supremacy. The same paper notes that…

We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to…

A natural problem in high-dimensional inference is to decide if a classifier $f:\mathbb{R}^n \rightarrow \{-1,1\}$ depends on a small number of linear directions of its input data. Call a function $g: \mathbb{R}^n \rightarrow \{-1,1\}$, a…

Understanding the power and limitations of classical and quantum information and how they differ is a fundamental endeavor. In property testing of distributions, a tester is given samples over a typically large domain $\{0,1\}^n$. An…

Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…

Estimation of the mixing distribution under a general mixture model is a very difficult problem, especially when the mixing distribution is assumed to have a density. Predictive recursion (PR) is a fast, recursive algorithm for…

Results on the hardness of approximate sampling are seen as important stepping stones towards a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include…

The objective of goodness-of-fit testing is to assess whether a dataset of observations is likely to have been drawn from a candidate probability distribution. This paper presents a rank-based family of goodness-of-fit tests that is…

We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution…

Previous studies in quantum information have recognized that specific types of noise can encode information in certain applications. However, the role of noise in Quantum Hypothesis Testing (QHT), traditionally assumed to undermine…

We study a class of hypothesis testing problems in which, upon observing the realization of an $n$-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether…

Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…

Learning deep neural network (DNN) classifier with noisy labels is a challenging task because the DNN can easily over-fit on these noisy labels due to its high capability. In this paper, we present a very simple but effective training…

Deep neural networks tend to memorize noisy labels, severely degrading their generalization performance. Although Mixup has demonstrated effectiveness in improving generalization and robustness, existing Mixup-based methods typically…

This work is concerned with the detection of a mixture distribution from a $\mathbb{R}$-valued sample. Given a sample $X_1,\dots,X_n$ and an even density $\phi$, our aim is to detect whether the sample distribution is $\phi(\cdot-\mu)$ for…