Related papers: Pseudorandomness, symmetry, smoothing: I
We provide the first proof of convergence for normalized error feedback algorithms across a wide range of machine learning problems. Despite their popularity and efficiency in training deep neural networks, traditional analyses of error…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
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…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example,…
We identify a new notion of pseudorandomness for randomness sources, which we call the average bias. Given a distribution $Z$ over $\{0,1\}^n$, its average bias is: $b_{\text{av}}(Z) =2^{-n} \sum_{c \in \{0,1\}^n} |\mathbb{E}_{z \sim…
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 the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
The remarkable results for denoising in computer vision using diffusion models given in \cite{SDWMG,HJA,HHG} yield a robust mathematical justification for algorithms based on crucial properties of a sequence of Gaussian independent $N(0,1)$…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
Under the assumption that the distribution of a nonnegative random variable $X$ admits a bounded coupling with its size biased version, we prove simple and strong concentration bounds. In particular the upper tail probability is shown to…
Power-law probability distributions arise often in the social and natural sciences. Statistics have been developed for estimating the exponent parameter as well as gauging goodness-of-fit to a power law. Yet paradoxically, many famous power…
Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning combating distributional uncertainty, e.g., the uncertainty of an empirical distribution compared…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…
The celebrated minimax principle of Yao (1977) says that for any Boolean-valued function $f$ with finite domain, there is a distribution $\mu$ over the domain of $f$ such that computing $f$ to error $\epsilon$ against inputs from $\mu$ is…
This article demonstrates how recent developments in the theory of empirical processes allow us to construct a new family of asymptotically distribution-free smooth tests. Their distribution-free property is preserved even when the…
Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding's inequality that use…
A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently…