Expectation-Maximization Gaussian-Mixture Approximate Message Passing

When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE). If this distribution was apriori known, then one could use computationally efficient approximate message passing (AMP) techniques for nearly minimum MSE (MMSE) recovery. In practice, though, the distribution is unknown, motivating the use of robust algorithms like LASSO---which is nearly minimax optimal---at the cost of significantly larger MSE for non-least-favorable distributions. As an alternative, we propose an empirical-Bayesian technique that simultaneously learns the signal distribution while MMSE-recovering the signal---according to the learned distribution---using AMP. In particular, we model the non-zero distribution as a Gaussian mixture, and learn its parameters through expectation maximization, using AMP to implement the expectation step. Numerical experiments on a wide range of signal classes confirm the state-of-the-art performance of our approach, in both reconstruction error and runtime, in the high-dimensional regime, for most (but not all) sensing operators

Bilinear Generalized Approximate Message Passing—Part II: Applications

In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case. In Part I of this two-part paper, we derived our Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, and proposed an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assumed priors, and two rank-selection strategies. Here, in Part II, we discuss the specializations of BiG-AMP to the problems of matrix completion, robust PCA, and dictionary learning, and present the results of an extensive empirical study comparing BiG-AMP to state-of-the-art algorithms on each problem. Our numerical results, using both synthetic and real-world datasets, demonstrate that EM-BiG-AMP yields excellent reconstruction accuracy (often best in class) while maintaining competitive runtimes

Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices

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 protocols in a wide range of applications. Using an interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a strategy that allows compressed sensing to be performed at acquisition rates approaching to the theoretical optimal limits. In this paper, we give a more thorough presentation of our approach, and introduce many new results. We present the probabilistic approach to reconstruction and discuss its optimality and robustness. We detail the derivation of the message passing algorithm for reconstruction and expectation max- imization learning of signal-model parameters. We further develop the asymptotic analysis of the corresponding phase diagrams with and without measurement noise, for different distribution of signals, and discuss the best possible reconstruction performances regardless of the algorithm. We also present new efficient seeding matrices, test them on synthetic data and analyze their performance asymptotically.Comment: 42 pages, 37 figures, 3 appendixe

Conflicted Emotions Following Trust-based Interaction

We investigated whether 20 emotional states, reported by 170 participants after participating in a Trust game, were experienced in a patterned way predicted by the “Recalibrational Model” or Valence Models. According to the Recalibrational Model, new information about trust-based interaction outcomes triggers specific sets of emotions. Unlike Valence Models that predict reports of large sets of either positive or negative emotional states, the Recalibrational Model predicts the possibility of conflicted (concurrent positive and negative) emotional states. Consistent with the Recalibrational Model, we observed reports of conflicted emotional states activated after interactions where trust was demonstrated but trustworthiness was not. We discuss the implications of having conflicted goals and conflicted emotional states for both scientific and well-being pursuits

Factor graph based detection approach for high-mobility OFDM systems with large FFT modes

In this article, a novel detector design is proposed for orthogonal frequency division multiplexing (OFDM) systems over frequency selective and time varying channels. Namely, we focus on systems with large OFDM symbol lengths where design and complexity constraints have to be taken into account and many of the existing ICI reduction techniques can not be applied. We propose a factor graph (FG) based approach for maximum a posteriori (MAP) symbol detection which exploits the frequency diversity introduced by the ICI in the OFDM symbol. The proposed algorithm provides high diversity orders allowing to outperform the free-ICI performance in high-mobility scenarios with an inherent parallel structure suitable for large OFDM block sizes. The performance of the mentioned near-optimal detection strategy is analyzed over a general bit-interleaved coded modulation (BICM) system applying low-density parity-check (LDPC) codes. The inclusion of pilot symbols is also considered in order to analyze how they assist the detection process