Local stability of Belief Propagation algorithm with multiple fixed points

A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such marginals when the underlying graph is a tree. But it has gained its popularity as an efficient way to approximate them in the more general case, even if it can exhibits multiple fixed points and is not guaranteed to converge. In this paper, we express a new sufficient condition for local stability of a belief propagation fixed point in terms of the graph structure and the beliefs values at the fixed point. This gives credence to the usual understanding that Belief Propagation performs better on sparse graphs.Comment: arXiv admin note: substantial text overlap with arXiv:1101.417

The Role of Normalization in the Belief Propagation Algorithm

An important part of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov Random Field. The belief propagation algorithm, which is an exact procedure to compute these marginals when the underlying graph is a tree, has gained its popularity as an efficient way to approximate them in the more general case. In this paper, we focus on an aspect of the algorithm that did not get that much attention in the literature, which is the effect of the normalization of the messages. We show in particular that, for a large class of normalization strategies, it is possible to focus only on belief convergence. Following this, we express the necessary and sufficient conditions for local stability of a fixed point in terms of the graph structure and the beliefs values at the fixed point. We also explicit some connexion between the normalization constants and the underlying Bethe Free Energy

Land tenurial systems and the adoption of Mucuna planted fallow in the derived savannas of West Africa:

In 1987, an improved resource management system that incorporates velvet bean (Mucuna pruriens var. utilis) to address soil fertility and weed (Imperata cylindrica) infestation was introduced to the small-scale farmers in a densely populated area of the derived savannas in Benin Republic (West Africa). Six years later, an adoption study was conducted to assess factors driving the adoption process. Four types of land tenure systems based on mode of access to land were identified: divided inheritance, purchasing, gifts, and sharecropping/renting. The first three provide long-term security over land, and together, they represent about 76 percent of the survey fields. Results from three variants of a probit model indicated that security over land was among the factors that significantly affect the adoption of the technology, with a high marginal effect on the probability of adoption, while gender did not have a significant effect. The most important determinant for adoption is the number of times a field is weeded during a cropping season (a proxy for the amount of labor required to tend a crop for better yields). High weeding requirements favorably affect the adoption of velvet bean only if farmers have full security on the degraded (weedy) land. The predominance of land tenure systems that provide secure property rights, namely the traditional acquisition of land through inheritance or gift mode and the gradual development of a land market, facilitated a quick spread of the Mucuna planted fallows in the study region.Watershed management., Water use India Citizen participation., Irrigation projects India., Gender, Property rights, Agricultural technology, Agricultural growth,

HEALTH COSTS AND EXTERNALITIES OF PESTICIDE USE IN LOCUST AND GRASSHOPPER CONTROL IN THE SAHEL

To evaluate the economic cost of classical chemical control of locusts, externalities of chemical pesticides in the Sahel are estimated through a farmer survey. The costs of human health, losses in domestic animals and of destroying obsolete pesticides are estimated at $4 per treated ha for chemical control.Environmental Economics and Policy, Health Economics and Policy,

Pairwise MRF Calibration by Perturbation of the Bethe Reference Point

We investigate different ways of generating approximate solutions to the pairwise Markov random field (MRF) selection problem. We focus mainly on the inverse Ising problem, but discuss also the somewhat related inverse Gaussian problem because both types of MRF are suitable for inference tasks with the belief propagation algorithm (BP) under certain conditions. Our approach consists in to take a Bethe mean-field solution obtained with a maximum spanning tree (MST) of pairwise mutual information, referred to as the \emph{Bethe reference point}, for further perturbation procedures. We consider three different ways following this idea: in the first one, we select and calibrate iteratively the optimal links to be added starting from the Bethe reference point; the second one is based on the observation that the natural gradient can be computed analytically at the Bethe point; in the third one, assuming no local field and using low temperature expansion we develop a dual loop joint model based on a well chosen fundamental cycle basis. We indeed identify a subclass of planar models, which we refer to as \emph{Bethe-dual graph models}, having possibly many loops, but characterized by a singly connected dual factor graph, for which the partition function and the linear response can be computed exactly in respectively O(N) and $O(N^2)$ operations, thanks to a dual weight propagation (DWP) message passing procedure that we set up. When restricted to this subclass of models, the inverse Ising problem being convex, becomes tractable at any temperature. Experimental tests on various datasets with refined $L_0$ or $L_1$ regularization procedures indicate that these approaches may be competitive and useful alternatives to existing ones.Comment: 54 pages, 8 figure. section 5 and refs added in V

Revue musicale (16 novembre 1891)

Transcript of REVUE MUSICALE by Victorin Joncières, appearing in LA LIBERTÉ, 16 novembre 1891, p. 1

Nonclassical states in strongly correlated bosonic ring ladders

We study the ground state of a bosonic ring ladder under a gauge flux in the vortex phase, corresponding to the case where the single-particle dispersion relation has two degenerate minima. By combining exact diagonalization and an approximate fermionization approach we show that the ground state of the system evolves from a fragmented state of two single-particle states at weak interparticle interactions to a fragmented state of two Fermi seas at large interactions. Fragmentation is inferred from the study of the eigenvalues of the reduced single-particle density matrix as well as from the calculation of the fidelity of the states. We characterize these nonclassical states by the momentum distribution, the chiral currents and the current-current correlations

Du papegau au perroquet : antonomase et parodie: antonomase et parodie

This article intends to study the link between antonomasia and parody based upon the use of two words : « papegau » (popinjay) and « perroquet » (parrot). What does the substitution of one sign with the other actually mean and to what extent does the antonomasia have a parodic potential ? And lastly, is the parrot a preferred parodic figure ?Cette étude est née d’une interrogation : pourquoi le potentiel parodique dont dispose le psittacus n’a-t-il pas été utilisé davantage et plus tôt dans la littérature ? Pour esquisser quelques réponses, nous allons retisser un réseau de textes et de sens pour rendre compte du glissement sémantique ou de la métamorphose qui s’opère en passant du papegau à Parroquet et de Parroquet au perroquet. Pour ce faire, nous envisagerons de manière privilégiée un texte bref, inséré dans Le Chevalier Errant (1394) de Thomas de Saluces, dans lequel apparaît la première occurrence connue du mot « perroquet ». Il nous a semblé intéressant de voir si ce texte fonctionne comme un pivot dans la représentation de l’oiseau du fait du changement de signe et ce qu’un tel changement implique