S-AMP for Non-linear Observation Models

Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP) algorithm as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation propagation (EP) like algorithms from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.Comment: 6 page

A Productivity Management Application of the Solow Development Model by the Asian Largest Economies

In application of the Solow development model, other Asian or non-Asian smaller economies may learn from the productivity management model design emulated by the economic development patterns of the largest Asian economies; China, India, Japan, Indonesia, and South Korea. The objective of the study was fundamentally formulated to explore the application of the economic design thinking of the Solow development model on the five Asian largest economies. Using the data envelopment analysis or DEA, the study sought to evaluate the two Solow development models, y/L = f (K/L, L/pop, s/y) or y/Lt = K/Lt (R&Dt)1-depr without using technology, and y/L = f (K/L, L/pop, s/y, R&D/y) or y/Lt = K/Lt (R&Dt Lt)1-depr with technology. The DEA observation specifically applied the Malmquist Productivity Index and Linear Programming model to evaluate the y/L objective function in order to answer the study’s four research questions. It was concluded that the Solow development design thinking models, the ones with and without R&D for innovation, didn’t show any difference in utilities of both. Any economies for the productivity management models seemed to be relevantly indifferent. Keywords: Data Envelopment Analysis or DEA, Malmquist Productivity Index or MPI, change in total factor productivity or Δ TFP index, decision-making unit or DMU, linear programming or LP, human development index or HDI

A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations

The paper deals with the development, parametrization and validation of a phenology model of the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) populations in northern latitudes. The model is built on diapause and poikilothermic population development theories and represents the phenological events of entries into and emergence from pre-diapause, diapause and post-diapause phases. The rate sum models for pre-diapause and post-diapause development are based on published non-linear temperature dependent rate functions. The rate sum model for diapause, however, is negatively affected by the photoperiod during diapause and positively influenced by the photoperiod at the time of diapause entry. The diapause model is parametrized with 3-year data from 25 locations in Europe and Cyprus, and validated with 1-3 year observations from 18 locations in Europe and California. Despite restrictive assumptions and limitations imposed by weather data recorded at variable distances from the observation sites, and the variable qualities of observation data, the model’s predictive and explanatory capabilities are useful for adaptive pest management and assessments of the invasive potential. The need for controlled experiments is recognized and suggestions are made for improving the model

Dynamical Functional Theory for Compressed Sensing

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix ensemble. By design, the fixed points of the algorithm obey the Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way that the resulting fields become Gaussian random variables allowing for an explicit analysis. The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem.Comment: 5 pages, accepted for ISIT 201

Approximate Message Passing with Restricted Boltzmann Machine Priors

Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance

Generalized Approximate Survey Propagation for High-Dimensional Estimation

In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized Approximate Message Passing (GAMP) is known to achieve optimal performance for GLE. However, its performance can significantly degrade whenever there is a mismatch between the assumed and the true generative model, a situation frequently encountered in practice. In this paper, we propose a new algorithm, named Generalized Approximate Survey Propagation (GASP), for solving GLE in the presence of prior or model mis-specifications. As a prototypical example, we consider the phase retrieval problem, where we show that GASP outperforms the corresponding GAMP, reducing the reconstruction threshold and, for certain choices of its parameters, approaching Bayesian optimal performance. Furthermore, we present a set of State Evolution equations that exactly characterize the dynamics of GASP in the high-dimensional limit