Related papers: Boolean Compressed Sensing and Noisy Group Testing

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an at- tractive method for…

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

Machine learning in the context of noise is a challenging but practical setting to plenty of real-world applications. Most of the previous approaches in this area focus on the pairwise relation (casual or correlational relationship) with…

Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…

In query learning, the goal is to identify an unknown object while minimizing the number of "yes or no" questions (queries) posed about that object. We consider three extensions of this fundamental problem that are motivated by practical…

Label noise is a common problem in real-world datasets, affecting both model training and validation. Clean data are essential for achieving strong performance and ensuring reliable evaluation. While various techniques have been proposed to…

We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…

The Quantitative Group Testing (QGT) is about learning a (hidden) subset $K$ of some large domain $N$ using a sequence of queries, where a result of a query provides information about the size of the intersection of the query with the…

We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We…

The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…

In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…

Sorting is the task of ordering $n$ elements using pairwise comparisons. It is well known that $m=\Theta(n\log n)$ comparisons are both necessary and sufficient when the outcomes of the comparisons are observed with no noise. In this paper,…

We consider nonadaptive group testing where each item is placed in a constant number of tests. The tests are chosen uniformly at random with replacement, so the testing matrix has (almost) constant column weights. We show that performance…

Standard compressive sensing results state that to exactly recover an s sparse signal in R^p, one requires O(s. log(p)) measurements. While this bound is extremely useful in practice, often real world signals are not only sparse, but also…

This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible…

We formulate and study a statistical version of Katona's two-round search problem of finding at least one excellent element in a set. A population of $n$ elements is considered, where each element is independently excellent with probability…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

We consider the quantum decoding problem. It consists in recovering a codeword given a superposition of noisy versions of this codeword. By measuring the superposition, we get back to the classical decoding problem. It appears for the first…

Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…

The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…