Approximate algorithms for credal networks with binary variables

This paper presents a family of algorithms for approximate inference in credal networks (that is, models based on directed acyclic graphs and set-valued probabilities) that contain only binary variables. Such networks can represent incomplete or vague beliefs, lack of data, and disagreements among experts; they can also encode models based on belief functions and possibilistic measures. All algorithms for approximate inference in this paper rely on exact inferences in credal networks based on polytrees with binary variables, as these inferences have polynomial complexity. We are inspired by approximate algorithms for Bayesian networks; thus the Loopy 2U algorithm resembles Loopy Belief Propagation, while the Iterated Partial Evaluation and Structured Variational 2U algorithms are, respectively, based on Localized Partial Evaluation and variational techniques. (C) 2007 Elsevier Inc. All rights reserved.

A incorporação dos negros no mercado de trabalho: um estudo de 1930 a 1945

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Given a reproducing kernel Hilbert space (H,〈.,.〉)(H,〈.,.〉) of real-valued functions and a suitable measure μμ over the source space D⊂RD⊂R, we decompose HH as the sum of a subspace of centered functions for μμ and its orthogonal in HH. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Set of Matlab function to study geometrical parameters or channels

This set of functions allows one to compute the radius of curvature of a river in planform for the purpose of making correlations with other geometric parameters of a channel. The code may also be used to compute the width of a channel.

Inteligencia artificial para la predicción y control del acabado superficial en procesos de fresado a alta velocidad

El objetivo principal de esta tesis doctoral es profundizar en el análisis y diseño de un sistema inteligente para la predicción y control del acabado superficial en un proceso de fresado a alta velocidad, basado fundamentalmente en clasificadores Bayesianos, con el prop´osito de desarrollar una metodolog´ıa que facilite el diseño de este tipo de sistemas. El sistema, cuyo propósito es posibilitar la predicción y control de la rugosidad superficial, se compone de un modelo aprendido a partir de datos experimentales con redes Bayesianas, que ayudar´a a comprender los procesos dinámicos involucrados en el mecanizado y las interacciones entre las variables relevantes. Dado que las redes neuronales artificiales son modelos ampliamente utilizados en procesos de corte de materiales, también se incluye un modelo para fresado usándolas, donde se introdujo la geometría y la dureza del material como variables novedosas hasta ahora no estudiadas en este contexto. Por lo tanto, una importante contribución en esta tesis son estos dos modelos para la predicción de la rugosidad superficial, que se comparan con respecto a diferentes aspectos: la influencia de las nuevas variables, los indicadores de evaluación del desempeño, interpretabilidad. Uno de los principales problemas en la modelización con clasificadores Bayesianos es la comprensión de las enormes tablas de probabilidad a posteriori producidas. Introducimos un m´etodo de explicación que genera un conjunto de reglas obtenidas de árboles de decisión. Estos árboles son inducidos a partir de un conjunto de datos simulados generados de las probabilidades a posteriori de la variable clase, calculadas con la red Bayesiana aprendida a partir de un conjunto de datos de entrenamiento. Por último, contribuimos en el campo multiobjetivo en el caso de que algunos de los objetivos no se puedan cuantificar en números reales, sino como funciones en intervalo de valores. Esto ocurre a menudo en aplicaciones de aprendizaje automático, especialmente las basadas en clasificación supervisada. En concreto, se extienden las ideas de dominancia y frontera de Pareto a esta situación. Su aplicación a los estudios de predicción de la rugosidad superficial en el caso de maximizar al mismo tiempo la sensibilidad y la especificidad del clasificador inducido de la red Bayesiana, y no solo maximizar la tasa de clasificación correcta. Los intervalos de estos dos objetivos provienen de un m´etodo de estimación honesta de ambos objetivos, como e.g. validación cruzada en k rodajas o bootstrap.---ABSTRACT---The main objective of this PhD Thesis is to go more deeply into the analysis and design of an intelligent system for surface roughness prediction and control in the end-milling machining process, based fundamentally on Bayesian network classifiers, with the aim of developing a methodology that makes easier the design of this type of systems. The system, whose purpose is to make possible the surface roughness prediction and control, consists of a model learnt from experimental data with the aid of Bayesian networks, that will help to understand the dynamic processes involved in the machining and the interactions among the relevant variables. Since artificial neural networks are models widely used in material cutting proceses, we include also an end-milling model using them, where the geometry and hardness of the piecework are introduced as novel variables not studied so far within this context. Thus, an important contribution in this thesis is these two models for surface roughness prediction, that are then compared with respecto to different aspects: influence of the new variables, performance evaluation metrics, interpretability. One of the main problems with Bayesian classifier-based modelling is the understanding of the enormous posterior probabilitiy tables produced. We introduce an explanation method that generates a set of rules obtained from decision trees. Such trees are induced from a simulated data set generated from the posterior probabilities of the class variable, calculated with the Bayesian network learned from a training data set. Finally, we contribute in the multi-objective field in the case that some of the objectives cannot be quantified as real numbers but as interval-valued functions. This often occurs in machine learning applications, especially those based on supervised classification. Specifically, the dominance and Pareto front ideas are extended to this setting. Its application to the surface roughness prediction studies the case of maximizing simultaneously the sensitivity and specificity of the induced Bayesian network classifier, rather than only maximizing the correct classification rate. Intervals in these two objectives come from a honest estimation method of both objectives, like e.g. k-fold cross-validation or bootstrap.

On the uniform approximation of Cauchy continuous functions

In the context of real-valued functions defined on metric spaces, it is known that the locally Lipschitz functions are uniformly dense in the continuous functions and that the Lipschitz in the small functions - the locally Lipschitz functions where both the local Lipschitz constant and the size of the neighborhood can be chosen independent of the point - are uniformly dense in the uniformly continuous functions. Between these two basic classes of continuous functions lies the class of Cauchy continuous functions, i.e., the functions that map Cauchy sequences in the domain to Cauchy sequences in the target space. Here, we exhibit an intermediate class of Cauchy continuous locally Lipschitz functions that is uniformly dense in the real-valued Cauchy continuous functions. In fact, our result is valid when our target space is an arbitrary Banach space.

Lower semicontinuity of the feasible set mapping of linear systems relative to their domains

This paper deals with stability properties of the feasible set of linear inequality systems having a finite number of variables and an arbitrary number of constraints. Several types of perturbations preserving consistency are considered, affecting respectively, all of the data, the left-hand side data, or the right-hand side coefficients.

The Use of the Relative Interior in Integration with Nonconvex Data

Introducing an appropriate inclusion between approximate minima associated with two nonconvex functions, we derive explicit relations between the closed convex hulls of these functions. The formula we obtain goes beyond the so-called epi-pointed property of functions which is usually concerned with such a topic.

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Stability in Linear Optimization Under Perturbations of the Left-Hand Side Coefficients

This paper studies stability properties of linear optimization problems with finitely many variables and an arbitrary number of constraints, when only left hand side coefficients can be perturbed. The coefficients of the constraints are assumed to be continuous functions with respect to an index which ranges on certain compact Hausdorff topological space, and these properties are preserved by the admissible perturbations. More in detail, the paper analyzes the continuity properties of the feasible set, the optimal set and the optimal value, as well as the preservation of desirable properties (boundedness, uniqueness) of the feasible and of the optimal sets, under sufficiently small perturbations.

Introduction to the Maple Power Tool Intpakx

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

2000 Mathematics Subject Classification: 35J05, 35C15, 44P05

Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space

2000 Mathematics Subject Classification: Primary 43A22, 43A25.