Related papers: Pointwise Bounds for Distribution Estimation under…
We analyze convergence rates of norm-minimization-based outer approximation algorithms for convex vector optimization when the scalarization uses an $\ell_p$ norm with $p \in (1,\infty)$. While the Euclidean case ($p=2$) achieves the…
We present a communication-efficient distributed protocol for computing the Babai point, an approximate nearest point for a random vector ${\bf X}\in\mathbb{R}^n$ in a given lattice. We show that the protocol is optimal in the sense that it…
Estimation of Distribution Algorithms (EDAs) are one branch of Evolutionary Algorithms (EAs) in the broad sense that they evolve a probabilistic model instead of a population. Many existing algorithms fall into this category. Analogous to…
Most of the literature on differential privacy considers the item-level case where each user has a single observation, but a growing field of interest is that of user-level privacy where each of the $n$ users holds $T$ observations and…
Consider a distributed detection problem in which the underlying distributions of the observations are unknown; instead of these distributions, noisy versions of empirically observed statistics are available to the fusion center. These…
We study active sampling algorithms for linear regression, which aim to query only a few entries of a target vector $b\in\mathbb R^n$ and output a near minimizer to $\min_{x\in\mathbb R^d} \|Ax-b\|$, for a design matrix $A\in\mathbb R^{n…
Consider the standard linear regression model $\y = \Xmat \betastar + w$, where $\y \in \real^\numobs$ is an observation vector, $\Xmat \in \real^{\numobs \times \pdim}$ is a design matrix, $\betastar \in \real^\pdim$ is the unknown…
In modern machine learning, users often have to collaborate to learn the distribution of the data. Communication can be a significant bottleneck. Prior work has studied homogeneous users -- i.e., whose data follow the same discrete…
In this paper, we study communication efficient distributed algorithms for distributionally robust federated learning via periodic averaging with adaptive sampling. In contrast to standard empirical risk minimization, due to the minimax…
In this paper, we consider the adaptive Eulerian--Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a…
We present an algorithm that releases a pure differentially private (under the replacement neighboring relation) sparse histogram for $n$ participants over a domain of size $d \gg n$. Our method achieves the optimal $\ell_\infty$-estimation…
We study recovery of piecewise-constant signals on graphs by the estimator minimizing an $l_0$-edge-penalized objective. Although exact minimization of this objective may be computationally intractable, we show that the same statistical…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
We study schemes and lower bounds for distributed minimax statistical estimation over a Gaussian multiple-access channel (MAC) under squared error loss, in a framework combining statistical estimation and wireless communication. First, we…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…