We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP) algorithm for …

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of m points in n dimensions, n,m → ∞ and α = m/n stays finite. Using exact but non-rigorous methods from statistical physics, we determine …

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has been a number …

We consider the problem of partially recovering hidden binary variables from the observation of (few) censored edge weights, a problem with applications in community detection, correlation clustering and synchronization. We describe two spectral …

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