Related papers: Markov Chains Approximate Message Passing
Approximate message passing (AMP) is a class of low-complexity, scalable algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal from noisy, linear measurements. AMP is an iterative…
Motivated by multimodal estimation, we study a multi-view spiked Wigner model in which several noisy matrix observations contain correlated latent spikes. We derive a spectral estimator for the latent spikes by linearizing approximate…
We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…
Stochastic Gradient (SG) Markov Chain Monte Carlo algorithms (MCMC) are popular algorithms for Bayesian sampling in the presence of large datasets. However, they come with little theoretical guarantees and assessing their empirical…
Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in…
This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations. While computing the Bayes-optimal estimator seems intractable in general due to its nonconvex…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov…
Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…
Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model $\boldsymbol{Y}=\sum_{k=1}^K b_k \boldsymbol{A}_k \boldsymbol{C} +\boldsymbol{W} $, where $\{b_k\}$ and…
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 study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
Retraining a model using its own predictions together with the original, potentially noisy labels is a well-known strategy for improving the model performance. While prior works have demonstrated the benefits of specific heuristic…
We consider tensor factorizations using a generative model and a Bayesian approach. We compute rigorously the mutual information, the Minimal Mean Squared Error (MMSE), and unveil information-theoretic phase transitions. In addition, we…
Markov chain Monte Carlo algorithms have important applications in counting problems and in machine learning problems, settings that involve estimating quantities that are difficult to compute exactly. How much can quantum computers speed…
In this paper, we address the problem of recovering complex-valued signals from a set of complex-valued linear measurements. Approximate message passing (AMP) is one state-of-the-art algorithm to recover real-valued sparse signals. However,…
Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical…
The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…
Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work we perform an analytic study of the performances of one of them, the Langevin…
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.…