An MDL framework for sparse coding and dictionary learning

The power of sparse signal modeling with learned over-complete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these models, such as under-fitting or over-fitting given sets of data, are still not well characterized in the literature. As a result, the success of sparse modeling depends on hand-tuning critical parameters for each data and application. This work aims at addressing this by providing a practical and objective characterization of sparse models by means of the Minimum Description Length (MDL) principle -- a well established information-theoretic approach to model selection in statistical inference. The resulting framework derives a family of efficient sparse coding and dictionary learning algorithms which, by virtue of the MDL principle, are completely parameter free. Furthermore, such framework allows to incorporate additional prior information to existing models, such as Markovian dependencies, or to define completely new problem formulations, including in the matrix analysis area, in a natural way. These virtues will be demonstrated with parameter-free algorithms for the classic image denoising and classification problems, and for low-rank matrix recovery in video applications

Matroid toric ideals: complete intersection, minors and minimal systems of generators

In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids $\mathcal M$ such that its corresponding toric ideal $I_{\mathcal M}$ is a complete intersection. Secondly, we handle with the problem of detecting minors of a matroid $\mathcal M$ from a minimal set of binomial generators of $I_{\mathcal M}$. In particular, given a minimal set of binomial generators of $I_{\mathcal M}$ we provide a necessary condition for $\mathcal M$ to have a minor isomorphic to $\mathcal U_{d,2d}$ for $d \geq 2$. This condition is proved to be sufficient for $d = 2$ (leading to a criterion for determining whether $\mathcal M$ is binary) and for $d = 3$. Finally, we characterize all matroids $\mathcal M$ such that $I_{\mathcal M}$ has a unique minimal set of binomial generators.Comment: 9 page

C-HiLasso: A Collaborative Hierarchical Sparse Modeling Framework

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso model at the individual feature level, with the block-sparsity property of the Group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the Hierarchical Lasso (HiLasso), which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level, but not necessarily at the lower (inside the group) level, obtaining the collaborative HiLasso model (C-HiLasso). Such signals then share the same active groups, or classes, but not necessarily the same active set. This model is very well suited for applications such as source identification and separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the new framework and optimization approach is complemented with experimental examples and theoretical results regarding recovery guarantees for the proposed models

Image inpainting using patch consensus and DCT priors.

We present an implementation of the PACO-DCT inpainting algorithm. This method is based on maximizing the likelihood of image patches in terms of their DCT coefficients, while requiring consensus on the overlapping patches. The resulting problem is solved as an instance of the PACO framework

¿La prueba de referencia está desnaturalizando la estructura del sistema acusatorio?

El trabajo está encaminado a hacer un estudio crítico al sistema Acusatorio implementando en Colombia, con la admisión de la prueba de referencia entendida como tal, toda declaración realizada por fuera del juicio oral, autorizada para las personas que no comparecen a la audiencia de juicio oral, siempre y cuando se cumplan con los presupuestos del art. 438 del Código adjetivo. La aprobación de la prueba de referencia por parte del operador judicial, en algunos eventos, está desnaturalizando el sistema acusatorio, toda vez que viene siendo utilizada en situaciones no previstas por el legislador, como es del literal b) “evento similar” del artículo 438 del C. P. P., equiparándola a la imposibilidad de localizar al declarante. En ningún momento las situaciones jurídicas de secuestro y desaparición forzada, tienen similitud con la imposibilidad de ubicar al declarante. La admisión de prueba de referencia, tal como está concebida si bien se ajusta a la Constitución y la ley, pero al momento de su aplicación se está desbordando el querer del legislador, aceptando su práctica a eventos no autorizado por la norma (imposibilidad de localización del testigo), debiendo por tanto, el legislador hacer el ajuste pertinente, con miras a sostener la ideología del sistema acusatorio (Ley 906 de 2004), que la misma debe practicarse en la audiencia de juicio oral, ante la presencia del juez de conocimiento, sujetas a la confrontación y contradicción de las partes, en cumplimiento de los principios de publicidad, contradicción y mediación

Ego-centred models of social networks: the social atom

Mención Internacional en el título de doctorThis thesis set out to contribute to the realm of social physics, with a particular focus on human social networks. Our approach, however, is somewhat di erent from what is typical in disciplines such as complex systems or statistical physics. Rather than simplifying the features of the constituents of our system (people), and stressing their rules of interaction, we focus on better understanding those very same constituents, modelling them as social atoms. Our rationale is that a better understanding of such an atom may shed light on how (and why) it interacts with other atoms to form social collectives. Given its robustness and the evolutionary roots of its premises, we use the Social Brain Hypothesis as our departure point. This theory states that the evolutionary drive behind the development of large brains in humans was the need to process social information and that the limited capacity of our brains imposes a limit to the number of relationships we can manage— the so-called “Dunbar’s number”, roughly 150. Moreover, evidence keeps revealing that these relationships are further organised in a series of hierarchically inclusive layers with decreasing emotional intensity, whose sizes exhibit a more or less constant scaling. Notwithstanding the empirical evidence, neither the presence of scaling in the organisation of personal networks nor its connection with limited cognitive skills had been explained so far. In Chapter 2 we present a mathematical model that solves this puzzle. The assumptions of the model are quite simple, and well founded on empirical evidence. Firstly, the number of relationships we maintain tends to be stable on average. Secondly, these relationships are costly, and our resources are limited. With these two premises, our results show that the hierarchical organisation emerges naturally from the principle of maximum entropy. Not only that, but we also predict a hitherto unnoticed regime of organisation whose existence we prove using several datasets from communities of immigrants. The former model considers that relationships can only belong to a discrete set of categories (layers). In Chapter 3 we extend it so that relationships are classified in a continuum. This modification allows us to test the model with data from very di erent sources such as online communications, face-to-face contacts, and phone calls. Our results show that the two regimes of organisation found in the previous model persist in this variant, and reveal the underlying existence of a (universal) scaling parameter which does not depend on any particular number of layers. To incorporate these ideas into socio-centric models, we build on the so-called Structural Balance Theory. This theory, underpinned by psychological motivations, posits that the structure of social networks of positive and negative relationships are highly interdependent. However, the theory has received little empirical validation, and negative social relationships are poorly understood—both from an ego-centric and a socio-centric perspective. For that reason, we turn to developing an experimental software in order to gather data within a school. In Chapters 4 and 5 we present results from these experiments. In Chapter 4 we analyse the socio-centric networks using machine learning techniques and find that the structure of positive and negative networks is indeed very much connected. Besides, we study the two types of networks separately, showing that they exhibit quite distinct features and that gender e ects in negative social networks are weak and asymmetrical for boys and girls. In Chapter 5, on the other hand, we focus on the structure of negative personal networks. Remarkably, using data from two di erent experimental settings, we show that the structure of personal networks of negative relationships mirrors that of the positive ones and exhibits a similar scaling—albeit their size is significantly smaller. Chapter 6 summarises our results and presents future (and current) lines of investigation. Among them, we outline a model of a social fluid that uses the insights gained with this thesis to build a model of social collectives as ensembles of personal networks. This model is compatible, at the micro-level, with the observations of the social brain hypothesis, and, at the macro-level, with the premises of the structural balance theory.This thesis would not have been possible without the support of Fundación BBVA through its 2016 call project ”Los números de Dunbar y la estructura de las sociedades digitales: modelización y simulación (DUNDIG)”, and we are very thankful for it. Support for early stages of this work through projects IBSEN (European Commission, H2020 FET Open RIA 662725) and VARIANCE (Ministerio de Economía y Competitividad/FEDER, project no. FIS2015-64349-P) is also acknowledgedPrograma Oficial de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Javier Martín Buldú.- Secretario: José Luis Molina González.- Vocal: Roberta Sinatr

Evaluación del comportamiento de un grupo bajo cautiverio de Lagothrix lagotricha en el Zoológico de Guallabamba

Lagothrix lagotricha commonly known as woolly monkey is an endemic species from the Amazon basin. This species inhabits the Amazon Rain Forest of Ecuador, Peru, Colombia Bolivia and Brazil. L lagotrichia is a very social species that can live in groups up to 40 individuals, within an area of 1100 hectares, were it uses the middle and high canopy area. The temperament of this animal is shy, sociable and non territorial, nevertheless; this specie has a complex social structure with hierarchy between individuals.Lagothrix lagotricha o comúnmente conocido como mono lanudo o chorongo, es un especie endémica de la parte Amazónica de Ecuador, Perú, Colombia, Bolivia y Brasil. El chorongo es una especie sumamente social y se conoce que puede vivir en grupos de hasta 40 individuos. Los grupos tienen un área de vida de 1100 hectáreas, de las cuales utilizan el estrato medio y alto del bosque tropical. El carácter de este animal es tranquilo, sociable y no territorial, sin embargo posee una compleja estructura social donde existe una clara jerarquía entre los individuos

¿Las zonas francas, son una opción para America Latina?

En ensayo se hará el análisis del comportamiento de algunas Zonas francas específicas en países de Latino América como Colombia, Costa Rica, Republica Dominicana, Brasil y México lograremos entender el verdadero impacto y si realmente son motor de desarrollo. Por otro lado se observan grandes casos de Zonas Francas de Países como el caso en Malasia donde ha logrado compaginar toda una región completa para el desarrollo de una Zona Franca y el caso de China. Esto con el fin de llegar a evaluar si realmente es el camino a seguir por los países en vía de desarrollo o si es otra estrategia de las grandes multinacionales para disminuir sus costos y arrasar con cuanto encuentren en su camin