Convergence analysis of a proximal Gauss-Newton method

An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some applications for solving constrained nonlinear equations are discussed and the numerical performance of the method is assessed on some significant test problems

Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm

We present a novel algorithm to estimate the barycenter of arbitrary probability distributions with respect to the Sinkhorn divergence. Based on a Frank-Wolfe optimization strategy, our approach proceeds by populating the support of the barycenter incrementally, without requiring any pre-allocation. We consider discrete as well as continuous distributions, proving convergence rates of the proposed algorithm in both settings. Key elements of our analysis are a new result showing that the Sinkhorn divergence on compact domains has Lipschitz continuous gradient with respect to the Total Variation and a characterization of the sample complexity of Sinkhorn potentials. Experiments validate the effectiveness of our method in practice.Comment: 46 pages, 8 figure

Food hypersensitivity in dogs

Realizou-se um estudo retro e prospectivo em 117 cães com prontuários suspeitos de apresentarem hipersensibilidade alimentar. Os animais foram distribuídos em dois grupos: os do grupo I (n=86) foram atendidos em 1993 e 1994 e os do grupo II (n=31) em 1995. Os cães de ambos os grupos foram caracterizados quanto aos aspectos epidemiológicos e clínicos. Os do grupo II foram submetidos a exames complementares para a diferenciação diagnóstica do prurido, incluindo: hemograma, micológico e parasitológico cutâneo, coproparasitológico, histológico de pele e sorológicos - RAST (radioimunoensaio) e ELISA (ensaio imunoenzimático) - ambos para determinação de IgE contra antígenos alimentares -, e ao exame da dieta de eliminação seguida pela exposição provocativa. Este último exame foi o mais confiável para o estabelecimento do diagnóstico, ao determinar que 20 cães, provenientes de ambos os grupos, eram alérgicos a alimentos. Pelos RAST e ELISA, não foi possível demonstrar resultados confiáveis quando comparados aos resultados com a dieta de eliminação. Os animais acometidos foram principalmente machos, com raça definida e na faixa etária de um a seis anos. Os principais alimentos incriminados foram a carne bovina, o arroz e a carne de frango.From 1993 to 1995, 117 cases of dogs suspected of food hypersensitivity were reviewed and analyzed. The animals were distributed in two groups: group I included 86 dogs assisted in the first two years of the study; and group II included 31 dogs that were observed in 1995. Dogs from both groups were characterized according to clinical and epidemiological aspects. Animals from group II were also submitted to exams in order to eliminate other similar causes of pruritus and to establish the diagnosis of food hypersensitivity, including complete blood counting, fungal culture, skin scraping, fecal exam, skin histopathology, and RAST and ELISA (both for the detection of serum IgE against food allergens), as well as test of elimination diet followed by provocative exposure. Elimination diet test proved to be the most reliable tool for definitive diagnosis of food allergy, considering 20 dogs from both groups. It was possible to conclude that male pure bred dogs from one to six-year-old were most affected and RAST and ELISA were not reliable tests for the diagnosis. The most incriminated foods were beef, rice, and chicken

A PERTURBATION­BASED APPROACH FOR MULTI­CLASSIFIER SYSTEM DESIGN

Microsoft, Motorola, Siemens, Hitachi, IAPR, NICI, IUF This paper presents a perturbation­based approach useful to select the best combination method for a multi­classifier system. The basic idea is to simulate small variations in the performance of the set of classifiers and to evaluate to what extent they influence the performance of the combined classifier. In the experimental phase, the Behavioural Knowledge Space and the Dempster­Shafer combination methods have been considered. The experimental results, carried out in the field of hand­written numeral recognition, demonstrate the effectiveness of the new approach

ZONING DESIGN FOR HAND­WRITTEN NUMERAL RECOGNITION

Microsoft, Motorola, Siemens, Hitachi, IAPR, NICI, IUF In the field of Optical Character Recognition (OCR), zoning is used to extract topological information from patterns. In this paper zoning is considered as the result of an optimisation problem and a new technique is presented for automatic zoning. More precisely, local analysis of feature distribution based on Shannon's entropy estimation is performed to determine "core" zones of patterns. An iterative region­growing procedure is applied on the "core" zones to determine the final zoning

Convergence Properties of Stochastic Hypergradients

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of the gradient of the upper-level objective (hypergradient). In this work, we study stochastic approximation schemes for the hypergradient, which are important when the lower-level problem is empirical risk minimization on a large dataset. The method that we propose is a stochastic variant of the approximate implicit differentiation approach in (Pedregosa, 2016). We provide bounds for the mean square error of the hypergradient approximation, under the assumption that the lower-level problem is accessible only through a stochastic mapping which is a contraction in expectation. In particular, our main bound is agnostic to the choice of the two stochastic solvers employed by the procedure. We provide numerical experiments to support our theoretical analysis and to show the advantage of using stochastic hypergradients in practice