Related papers: Approximate Message Passing with Restricted Boltzm…

Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…

Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training,…

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

Approximate Message Passing (AMP) type algorithms are widely used for signal recovery in high-dimensional noisy linear systems. Recently, a principle called Memory AMP (MAMP) was proposed. Leveraging this principle, the gradient descent…

Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study…

Restricted Boltzmann Machine (RBM) is a bipartite graphical model that is used as the building block in energy-based deep generative models. Due to numerical stability and quantifiability of the likelihood, RBM is commonly used with…

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…

Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…

Approximate Message Passing (AMP), originally designed to solve high-dimensional linear inverse problems, has found broad applications in signal processing and statistical inference. Among its key variants, Vector Approximate Message…

Approximate message passing (AMP) has emerged both as a popular class of iterative algorithms and as a powerful analytic tool in a wide range of statistical estimation problems and statistical physics models. A well established line of AMP…

We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…

Vector perturbation (VP) precoding is a promising technique for multiuser communication systems operating in the downlink. In this work, we introduce a hybrid framework to improve the performance of lattice reduction (LR) aided precoding in…

Probabilistic variants of Model Order Reduction (MOR) methods have recently emerged for improving stability and computational performance of classical approaches. In this paper, we propose a probabilistic Reduced Basis Method (RBM) for the…

Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…

Approximate-message passing (AMP) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations. This is demonstrated…

A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica…

Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is…

Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an…

Restricted Boltzmann Machines (RBMs) are generative models which can learn useful representations from samples of a dataset in an unsupervised fashion. They have been widely employed as an unsupervised pre-training method in machine…

Restricted Boltzmann machines are undirected neural networks which have been shown to be effective in many applications, including serving as initializations for training deep multi-layer neural networks. One of the main reasons for their…