Probabilistic Matching of Planar Regions

We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes $A$ and $B$, the algorithm computes a transformation $t$ such that with high probability the area of overlap of $t(A)$ and $B$ is close to maximal. In the case of polygons, we give a time bound that does not depend significantly on the number of vertices

Probabilistic Matching: Causal Inference under Measurement Errors

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal inference studies may require unobserved high-level information which needs to be inferred from other observed attributes. In such cases, inaccuracies of the applied inference methods will result in noisy outputs. In this study, we propose a novel approach for causal inference when one or more key variables are noisy. Our method utilizes the knowledge about the uncertainty of the real values of key variables in order to reduce the bias induced by noisy measurements. We evaluate our approach in comparison with existing methods both on simulated and real scenarios and we demonstrate that our method reduces the bias and avoids false causal inference conclusions in most cases.Comment: In Proceedings of International Joint Conference Of Neural Networks (IJCNN) 201

Probabilistic matching pursuit with Gabor dictionaries

We propose a probabilistic extension of the matching pursuit adaptive signal processing algorithm introduced by Mallat and others. In adaptive signal processing, signals are expanded in terms of a large linearly dependent `dictionary' of functions rather than in terms of an orthonormal basis. Matching pursuit is a simple greedy algorithm for generating an expansion of a given signal. In probabilistic matching pursuit multiple random expansions are obtained as estimates for a given signal. The new algorithm is illustrated in the context of signal denoising. Although most of the random expansions generated by probabilistic matching pursuit are poorer estimates for the signal than those obtained by matching pursuit, our final estimate, obtained as an expected value computed by means of an ergodic average, can improve the result obtained by MP in some denoising situations. One of the major underlying ideas is a novel notion of coherence between a signal and the dictionary. Several simulated examples are presented.Fil: Ferrando, Sebastian Esteban. Ryerson Polytechnic University; CanadáFil: Doolittle, E.J.. University of Toronto; CanadáFil: Bernal, A. J.. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Bernal, Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin

Detection of Biochemical Pathways by Probabilistic Matching of Phyletic Vectors

A phyletic vector, also known as a phyletic (or phylogenetic) pattern, is a binary representation of the presences and absences of orthologous genes in different genomes. Joint occurrence of two or more genes in many genomes results in closely similar binary vectors representing these genes, and this similarity between gene vectors may be used as a measure of functional association between genes. Better understanding of quantitative properties of gene co-occurrences is needed for systematic studies of gene function and evolution. We used the probabilistic iterative algorithm Psi-square to find groups of similar phyletic vectors. An extended Psi-square algorithm, in which pseudocounts are implemented, shows better sensitivity in identifying proteins with known functional links than our earlier hierarchical clustering approach. At the same time, the specificity of inferring functional associations between genes in prokaryotic genomes is strongly dependent on the pathway: phyletic vectors of the genes involved in energy metabolism and in de novo biosynthesis of the essential precursors tend to be lumped together, whereas cellular modules involved in secretion, motility, assembly of cell surfaces, biosynthesis of some coenzymes, and utilization of secondary carbon sources tend to be identified with much greater specificity. It appears that the network of gene coinheritance in prokaryotes contains a giant connected component that encompasses most biosynthetic subsystems, along with a series of more independent modules involved in cell interaction with the environment

Reorganization

One of the productive activities engaging the work force is reorganizing. When factors of production are better matched, productivity is higher. The probabilistic matching model of Diamond, Mortensen, and others provides a way to make the idea of reorganization precise. Because the flow of organizational effort generates benefits lasting well into the future, it is appropriate to think of organizational capital. Unemployment-job seeking-is one of the inputs to organization. The flow of organizational effort represented by unemployment is analogous to the flow of physical investment. When an adverse technology shock causes job destruction, the economy substitutes the formation of new organizational capital for the flow of output. An increase in the interest rate can cause intertemporal substitution toward lower job destruction and less reorganization, but this effect may not come into play for a brief unexpected increase, and may be overwhelmed by intertemporal substitution in physical capital.

Procedurally Fair and Stable Matching

We motivate procedural fairness for matching mechanisms and study two procedurally fair and stable mechanisms: employment by lotto (Aldershof et al., 1999) and the random order mechanism (Roth and Vande Vate, 1990, Ma, 1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and the random order mechanism. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism, that combines aspects of procedural and "endstate'' fairness. Aldershof et al. (1999) and Ma (1996) that exist on the probability distribution induced by both mechanisms. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism.procedural fairness, random mechanism, stability, two-sided matching