Efficient learning of decomposable models with a bounded clique size

The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains.

On the optimal usage of labelled examples in semi-supervised multi-class classification problems

In recent years, the performance of semi-supervised learning has been theoretically investigated. However, most of this theoretical development has focussed on binary classification problems. In this paper, we take it a step further by extending the work of Castelli and Cover [1] [2] to the multi-class paradigm. Particularly, we consider the key problem in semi-supervised learning of classifying an unseen instance x into one of K different classes, using a training dataset sampled from a mixture density distribution and composed of l labelled records and u unlabelled examples. Even under the assumption of identifiability of the mixture and having infinite unlabelled examples, labelled records are needed to determine the K decision regions. Therefore, in this paper, we first investigate the minimum number of labelled examples needed to accomplish that task. Then, we propose an optimal multi-class learning algorithm which is a generalisation of the optimal procedure proposed in the literature for binary problems. Finally, we make use of this generalisation to study the probability of error when the binary class constraint is relaxed.

Lengua y derecho a la educación en la Comunidad Autónoma del País Vasco : reflexiones jurídicas sobre el tránsito hacia un nuevo modelo

The article analyzes the legal regime of Euskara in the education system of the Autonomous Community of the Basque Country (capv). In the capv, the legislation recognizes the right to choose the language of study during the educational cycle. The students are separated into different classrooms based on their language preference. This system of separation (of language models) has made it possible to make great strides, although its implementation also suggests aspects which, from the perspective of a pluralistic Basque society on its way towards greater social, political and language integration, call for further reflection The general model for language planning in the capv was fashioned in the eighties as a model characterized by the guarantee of spaces of language freedom, and the educational system was charged with making the learning of the region’s autochthonous language more widespread. At this point, we already have a fair degree of evidence on which to base an analysis of the system of language models and we are in a position to conclude that perhaps the educational system was given too heavy a burden. Official studies on language performance of Basque schoolchildren show (in a way that is now fully verified) that not all the students who finish their mandatory period of schooling achieve the level of knowledge of Euskara required by the regulations. When faced with this reality, it becomes necessary for us to articulate some alternative to the current configuration of the system of language models, one that will make it possible in the future to have a Basque society that is linguistically more integrated, thereby avoiding having the knowledge or lack of knowledge of one of the official languages become a language barrier between two communities. Many sides have urged a reconsideration of the system of language models. The Basque Parliament itself has requested the Department of Education to design a new system. This article analyzes the legal foundations on which the current system is built and explores the potential avenues for legal cooperation that would make it possible to move towards a new system aimed at guaranteeing higher rates of bilingualism. The system would be sufficiently flexible so as to be able to respond to and accommodate the different sociolinguistic realities of the region.

Augmented Peter Pan: un cuento multilingüe con Realidad Aumentada

[SPA] El objetivo de este Trabajo de Fin de Grado ha sido diseñar un cuento multilingüe que incorpora una innovación tecnológica, la Realidad Aumentada, para favorecer el proceso de enseñanza-aprendizaje lingüístico en la escuela. Para ello, hemos analizado algunos cuentos con Realidad Aumentada que se pueden encontrar en el mercado. Al no encontrar ningún cuento que cumpliese nuestras expectativas, hemos creado un cuento multilingüe con Realidad Aumentada adaptando el cuento clásico “Peter Pan”, que cumple los objetivos de fomentar el aprendizaje de diferentes idiomas y el gusto por la lectura, valorar las lenguas inmigrantes en las aulas y promover el uso de las TIC.

Hizkuntza komunikaziorako gaitasuna lantzeko ikuspegi berriak: teoriatik praktikara

[EUS] Gure gaur egungo gizarte globalizatuak, internazionalki komunikatzeko beharra areagotu du, eta horregatik atzerriko hizkuntzak ikastea ezinbestekoa bihurtu da. Eskola errealitatearen isla denez, behar horri aurre egiteko, gero eta gehiago dira irakaskuntza eleaniztuna garatzeko ikuspegi metodologikoak. Ikuspegi metodologiko hauen artean, CLIL/HEBI eta HTB dira garrantzitsuenetarikoak. HEBIk hizkuntzak eta edukiak batera ikasteari egiten dio erreferentzia, eta HTBk curriculumeko hizkuntzen programazio adostuari. Lan honetan metodologia hauen nondik norakoak aztertzen dira, baita hauek ikastetxe batean nolako ibilbidea izan duten eta nola lantzen diren ere. Azken honetan ikastetxearen eta ikasleen aldetik HEBIrekiko dagoen jarrera aztertzen da, galdetegi batzuen bitartez.

Irteerak ikaskuntza baliabide bezala: Armañon Interpretazio Zentroa

[eus] Haur Hezkuntzan zientziaren ikaskuntzarako baliabide aberasgarrienetako bat irteerak dira, hauek beharrezkoak baitira haurraren garapen integralerako. Horretarako, irteerak eskolaren parte izan behar dute eta irakasleek bisitaldiak proposatu behar dituzte. Hainbat toki daude bisitak egiteko HHko haurrekin eta lan honetan Armañongo Interpretazio Zentroaren hezkuntza eskaintza aztertuko da, adin txikiko umeen kasuan bertako baliabideen eragina ikusi ahal izateko. Zentroaren arduradunen iritziak ezagututa eta HHko haurren bisitaldia aztertuta, emaitzak eta ondorioak aterako dira.