Related papers: Sample complexity of population recovery
The increasing interest in subpopulation analysis has led to the development of various new trial designs and analysis methods in the fields of personalized medicine and targeted therapies. In this paper, subpopulations are defined in terms…
Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give…
In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing…
We consider the problem of approximating a function in general nonlinear subsets of $L^2$ when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…
We consider the problem of learning an $\varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Given access to a generative model, we achieve rate-optimal sample…
In noisy evolutionary optimization, sampling is a common strategy to deal with noise. By the sampling strategy, the fitness of a solution is evaluated multiple times (called \emph{sample size}) independently, and its true fitness is then…
We study the problem of recovering the common $k$-sized support of a set of $n$ samples of dimension $d$, using $m$ noisy linear measurements per sample. Most prior work has focused on the case when $m$ exceeds $k$, in which case $n$ of the…
We consider the following signal recovery problem: given a measurement matrix $\Phi\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = \Phi\theta^* + \epsilon$ where $\epsilon\in…
The compact genetic algorithm is an Estimation of Distribution Algorithm for binary optimisation problems. Unlike the standard Genetic Algorithm, no cross-over or mutation is involved. Instead, the compact Genetic Algorithm uses a virtual…
The problem of estimating the delays and amplitudes of a positive stream of pulses appears in many applications, such as single-molecule microscopy. This paper suggests estimating the delays and amplitudes using a convex program, which is…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
The population recovery problem asks one to recover an unknown distribution over $n$-bit strings given access to independent noisy samples of strings drawn from the distribution. Recently, Ban et al. [BCF+19] studied the problem where the…
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 introduce the problem of hidden Hamiltonian cycle recovery, where there is an unknown Hamiltonian cycle in an $n$-vertex complete graph that needs to be inferred from noisy edge measurements. The measurements are independent and…
We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured…
Latent class models are widely used for identifying unobserved subgroups from multivariate categorical data in social sciences, with binary data as a particularly popular example. However, accurately recovering individual latent class…
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
In this paper, we study the phase retrieval problem in the situation where the vector to be recovered has an a priori structure that can encoded into a regularization term. This regularizer is intended to promote solutions conforming to…
Consider the following estimation problem: there are $n$ entities, each with an unknown parameter $p_i \in [0,1]$, and we observe $n$ independent random variables, $X_1,\ldots,X_n$, with $X_i \sim $ Binomial$(t, p_i)$. How accurately can…