Related papers: Near-Optimal and Tractable Estimation under Shift-…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…

We study the complexity of high-dimensional approximation in the $L_2$-norm when different classes of information are available; we compare the power of function evaluations with the power of arbitrary continuous linear measurements. Here,…

Given an $n \times d$ dimensional dataset $A$, a projection query specifies a subset $C \subseteq [d]$ of columns which yields a new $n \times |C|$ array. We study the space complexity of computing data analysis functions over such…

This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…

We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibility induced by smoothness, we obtain explicit, deterministic…

Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical…

The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered.…

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…

We show that for every $k\in\mathbb{N}$ and $\varepsilon>0$, for large enough alphabet $R$, given a $k$-CSP with alphabet size $R$, it is NP-hard to distinguish between the case that there is an assignment satisfying at least…

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$,…

The paper presents analytic expressions of minimax (worst-case) estimates for solutions of linear abstract Neumann problems in Hilbert space with uncertain (not necessarily bounded!) inputs and boundary conditions given incomplete…

Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected…

This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…

A typical desideratum for quantifying the uncertainty from a classification model as a prediction set is class-conditional singleton set calibration. That is, such sets should map to the output of well-calibrated selective classifiers,…

We consider the problem of constructing confidence intervals (CIs) for the population mean of $N$ values $\{x_1, \ldots, x_N\} \subset \Sigma^N$ based on a random sample of size $n$, denoted by $X^n \equiv (X_1, \ldots, X_n)$, drawn…

With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources…

Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…

This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algorithms with Markovian noise. As a corollary, we also obtain…