Regularización Laplaciana en el espacio dual para SVMs

Máster Universitario en en Investigación e Innovación en Inteligencia Computacional y Sistemas InteractivosNowadays, Machine Learning (ML) is a field with a great impact because of its usefulness in solving many types of problems. However, today large amounts of data are handled and therefore traditional learning methods can be severely limited in performance. To address this problem, Regularized Learning (RL) is used, where the objective is to make the model as flexible as possible but preserving the generalization properties, so that overfitting is avoided. There are many models that use regularization in their formulations, such as Lasso, or models that use intrinsic regularization, such as the Support Vector Machine (SVM). In this model, the margin of a separating hyperplane is maximized, resulting in a solution that depends only on a subset of the samples called support vectors. This Master Thesis aims to develop an SVM model with Laplacian regularization in the dual space, under the intuitive idea that close patterns should have similar coefficients. To construct the Laplacian term we will use as basis the Fused Lasso model which penalizes the differences of the consecutive coefficients, but in our case we seek to penalize the differences between every pair of samples, using the elements of the kernel matrix as weights. This thesis presents the different phases carried out in the implementation of the new proposal, starting from the standard SVM, followed by the comparative experiments between the new model and the original method. As a result, we see that Laplacian regularization is very useful, since the new proposal outperforms the standard SVM in most of the datasets used, both in classification and regression. Furthermore, we observe that if we only consider the Laplacian term and we set the parameter C (upper bound for the coefficients) as if it were infinite, we also obtain better performance than the standard SVM metho

Property Crime and Law Enforcement in Italy. A Regional Panel Analysis 1980-95

In this paper a Cobb-Douglas utility function is introduced and solved for a dynamic equation of property crime supply and its determinants, namely deterrents and income. Thereafter, all variables are empirically tested, by means of a simultaneous equations model, for the sign and magnitude of their mutual relationships in a panel of Italy and its two economically and culturally different areas, the North and the South. The period scrutinized is 1980-95 and the results obtained widely differ among the two. When appropriately modeled and instrumented, in fact, property crime is found to react to police and criminal justice deterrence, and also to incomes, with different parameter magnitudes and significance. The same diversity applies to the parameters related to deterrence, flawed in quite a few cases by scarce law enforcement and productivity, and to those related to local incomes, which still reflect for the South a tendency of crime to substitute for legal activities.Models with Panel Data, Illegal Behavior and the Enforcement of Law

Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments

While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, this paper establishes that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. The main identifying assumption is that, conditional on the value of the true regressors, some "measure of location" of the distribution of the measurement error (e.g. its mean, mode or median) is equal to zero. The proposed approach relies on the eigenvalue-eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to order the eigenfunctions so that the decomposition is unique. The authors propose a convenient sieve-based estimator, derive its asymptotic properties and investigate its finite-sample behavior through Monte Carlo simulations. An example of application to the relationship between earnings and divorce rates is also provided.

IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry-property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from geometry to properties. We further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (relative error <5%) and 2) improve the optimized structural performance over the conventional topology-optimized variable-density structure. Specifically, in the minimum compliance example, our IH-GAN generated structure achieves an 84.4% reduction in concentrated stress and an extra 7% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 24.2% and 44.4% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending