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Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of…
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…
We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and…
In this work, a Bayesian approximate message passing algorithm is proposed for solving the multiple measurement vector (MMV) problem in compressive sensing, in which a collection of sparse signal vectors that share a common support are…
Consider the task of estimating a 3-order $n \times n \times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. We introduce a similarity based collaborative filtering algorithm for estimating a tensor from…
Matrix denoising is central to signal processing and machine learning. Its statistical analysis when the matrix to infer has a factorised structure with a rank growing proportionally to its dimension remains a challenge, except when it is…
Purpose: For quantitative susceptibility mapping (QSM), the lack of ground-truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with…
Markov chain Monte Carlo algorithms have long been observed to obtain near-optimal performance in various Bayesian inference settings. However, developing a supporting theory that makes these studies rigorous has proved challenging. In this…
Compressed sensing (CS) deals with the problem of reconstructing a sparse vector from an under-determined set of observations. Approximate message passing (AMP) is a technique used in CS based on iterative thresholding and inspired by…
Approximate message passing (AMP) is a class of efficient algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal \beta_0 from noisy, linear measurements y = A \beta_0 + w. When applying…
Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean square error (MMSE)…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
We introduce Tree-AMP, standing for Tree Approximate Message Passing, a python package for compositional inference in high-dimensional tree-structured models. The package provides a unifying framework to study several approximate message…
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding…
This letter proposes a novel message-passing algorithm for signal recovery in compressed sensing. The proposed algorithm solves the disadvantages of approximate message-passing (AMP) and orthogonal/vector AMP, and realizes their advantages.…
Approximate message passing (AMP) is an effective iterative sparse recovery algorithm for linear system models. Its performance is characterized by the state evolution (SE) which is a simple scalar recursion. However, depending on a…
Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix…