Related papers: Bitwise MAP Algorithm for Group Testing based on H…
In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main…
Group testing concerns itself with the accurate recovery of a set of "defective" items from a larger population via a series of tests. While most works in this area have considered the classical group testing model, where tests are binary…
We have a large number of samples and we want to find the infected ones using as few number of tests as possible. We can use group testing which tells about a small group of people whether at least one of them is infected. Group testing is…
The importance of aggregated count data, which is calculated from the data of multiple individuals, continues to increase. Collective Graphical Model (CGM) is a probabilistic approach to the analysis of aggregated data. One of the most…
A combinatorial analysis of the false alarm (FA) and misdetection (MD) probabilities of non-adaptive group testing with sparse pooling graphs is developed. The analysis targets the combinatorial orthogonal matching pursuit and definite…
The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…
Recent papers initiated the study of a generalization of group testing where the potentially contaminated sets are the members of a given hypergraph F=(V,E). This generalization finds application in contexts where contaminations can be…
Group testing is a method of identifying infected patients by performing tests on a pool of specimens collected from patients. For the case in which the test returns a false result with finite probability, we propose Bayesian inference and…
Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open…
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…
In this paper, we disclose the statistical behavior of the max-product algorithm configured to solve a maximum a posteriori (MAP) estimation problem in a network of distributed agents. Specifically, we first build a distributed hypothesis…
Group testing is a well known search problem that consists in detecting up to $s$ defective elements of the set $[t]=\{1,\ldots,t\}$ by carrying out tests on properly chosen subsets of $[t]$. In classical group testing the goal is to find…
We propose AD3, a new algorithm for approximate maximum a posteriori (MAP) inference on factor graphs based on the alternating directions method of multipliers. Like dual decomposition algorithms, AD3 uses worker nodes to iteratively solve…
We consider joint detection of co-channel signals---specifically, signals which do not possess a natural separability due to, for example, the multiple access technique or the use of multiple antennas. Iterative joint detection and decoding…
Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus…
We consider the problem of maximum a posteriori (MAP) inference in discrete graphical models. We present a parallel MAP inference algorithm called Bethe-ADMM based on two ideas: tree-decomposition of the graph and the alternating direction…
We propose a new mapping tool for supervised and unsupervised analysis of multivariate binary data with multiple items, questions, or response variables. The mapping assumes an underlying proximity response function, where participants can…
We present a variation of a quantum algorithm for the machine learning task of classification with graph-structured data. The algorithm implements a feature extraction strategy that is based on Gaussian boson sampling (GBS) a near term…
We study the inference problem in the group testing to identify defective items from the perspective of the decision theory. We introduce Bayesian inference and consider the Bayesian optimal setting in which the true generative process of…
Consider a finite population of $N$ items, where item $i$ has a probability $p_i$ to be defective. The goal is to identify all items by means of group testing. This is the generalized group testing problem (hereafter GGTP). In the case of…