@conference {93, title = {Speeding up the execution of a large number of statistical tests of independence}, booktitle = {Proceedings of ASAI 2010, Argentinean Symposioum of Artificial Intelligence}, year = {2010}, isbn = {978-950-9474-49-9}, author = {Schl{\"u}ter, Federico and Bromberg, Facundo and P{\'e}rez, Diego S} } @article {211, title = {{B}lankets {J}oint {P}osterior score for learning {M}arkov network structures }, journal = {International Journal of Approximate Reasoning}, volume = {https://doi.org/10.1016/j.ijar.2017.10.018}, year = {2017}, month = {10/2017}, type = {Regular Issu}, abstract = {

Markov networks are extensively used to model\ complex sequential, spatial, and relational interactions\ in a wide range of fields.\ By learning the Markov network independence structure of a domain, more accurate joint probability distributions can be obtained for inference tasks or, more directly, for interpreting the most significant relations among the variables. Recently, several researchers have investigated techniques for automatically learning the structure from data by obtaining the probabilistic maximum-a-posteriori structure given the available data. However, all the approximations proposed decompose the posterior of the whole structure into local sub-problems, by assuming that the posteriors of\ the Markov blankets of all the variables are mutually independent.\ In this work, we propose a scoring function for relaxing such assumption.\ The Blankets Joint Posterior\ score computes the\ joint posterior of structures as a joint distribution of the collection of its Markov blankets. Essentially, the whole posterior is obtained by computing the posterior of the blanket of each variable as a conditional distribution that takes into account information from other blankets in the network.\ We show in our experimental results that the proposed approximation\ can improve the sample complexity of state-of-the-art competitors\ when learning complex networks, where the independence assumption between blanket variables is clearly incorrect.\ 

}, keywords = {blankets posterior, irregular structures, Markov network, scoring function, Structure learning}, author = {Schl{\"u}ter, Federico and Strappa, Yanela and Bromberg, Facundo and Milone, Diego H.} } @article {69, title = {The IBMAP approach for Markov network structure learning}, journal = {Annals of Mathematics and Artificial Intelligence}, volume = {72}, year = {2014}, month = {04/2014}, pages = {197--223}, chapter = {197}, abstract = {

In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum.

}, keywords = {68T05, EDAs, Independence tests, Knowledge discovery, Markov network, Structure learning}, issn = {1012-2443}, doi = {10.1007/s10472-014-9419-5}, url = {http://dx.doi.org/10.1007/s10472-014-9419-5}, author = {Schl{\"u}ter, Federico and Bromberg, Facundo and Edera, Alejandro} } @article {91, title = {Learning Markov networks networks with context-specific independences.}, journal = { International Journal on Artificial Intelligence Tools}, volume = {23}, year = {2014}, month = {12/2014}, chapter = {1460030}, abstract = {

This work focuses on learning the structure of Markov networks from data. Markov networks are parametric models for compactly representing complex probability distributions. These models are composed by: a structure and numerical weights, where the structure describes independences that hold in the distribution. Depending on which is the goal of structure learning, learning algorithms can be divided into: density estimation algorithms, where structure is learned for answering inference queries; and knowledge discovery algorithms, where structure is learned for describing independences qualitatively. The latter algorithms present an important limitation for describing independences because they use a single graph; a coarse grain structure representation which cannot
represent flexible independences. For instance, context-specific independences cannot be described by a single graph. To overcome this limitation, this work proposes a new alternative representation named canonical model as well as the CSPC algorithm; a novel knowledge discovery algorithm for learning canonical models by using context-specific independences as constraints. On an extensive empirical evaluation, CSPC learns more accurate structures than state-of-the-art density estimation and knowledge discovery algorithms. Moreover, for answering inference queries, our approach obtains competitive results against density estimation algorithms, significantly outperforming knowledge discovery algorithms.

}, keywords = {CSI models, Knowledge discovery, Markov networks; structure learning; context-specific independences}, issn = {ISSN: 0218-2130}, doi = {10.1142/S0218213014600306}, url = {http://www.worldscientific.com/doi/abs/10.1142/S0218213014600306}, author = {Edera, Alejandro and Schl{\"u}ter, Federico and Bromberg, Facundo} } @article {87, title = {Markov random fields factorization with context-specific independences}, year = {2013}, institution = {arXiv.org}, abstract = {

Markov random fields provide a compact representation of joint probability distributions by representing its independence properties in an undirected graph. The well-known Hammersley-Clifford theorem uses these conditional independences to factorize a Gibbs distribution into a set of factors. However, an important issue of using a graph to represent independences is that it cannot encode some types of independence relations, such as the context-specific independences (CSIs). They are a particular case of conditional independences that is true only for a certain assignment of its conditioning set; in contrast to conditional independences that must hold for all its assignments. This work presents a method for factorizing a Markov random field according to CSIs present in a distribution, and formally guarantees that this factorization is correct. This is presented in our main contribution, the context-specific Hammersley-Clifford theorem, a generalization to CSIs of the Hammersley-Clifford theorem that applies for conditional independences.

}, issn = {arXiv:1306.2295}, author = {Edera, Alejandro and Bromberg, Facundo and Schl{\"u}ter, Federico} } @mastersthesis {161, title = {El enfoque IBMAP para aprendizaje de estructuras de redes de Markov}, volume = {Doctorado en Ciencias de la Computaci{\'o}n (PhD in Computer Science)}, year = {2014}, month = {11/2014}, pages = {138}, type = {Doctorado}, abstract = {

Las redes de Markov\ son modelos probabil{\'\i}sticos gr{\'a}ficos,\ una herramienta computacional para el modelado eficiente de distribuciones de probabilidad\ que utiliza grafos para facilitar la representaci{\'o}n de problemas complejos.\ Estos modelos han sido dise{\~n}ados para ser manipulados por sistemas expertos,\ utilizando la teor{\'\i}a de la probabilidad para razonar eficientemente bajo condiciones de incertidumbre.\ Sin embargo, una limitaci{\'o}n importante para el uso de estos modelos es que en la pr{\'a}ctica\ resulta complejo dise{\~n}arlos manualmente, ya que el conocimiento de expertos no siempre es suficiente,\ sumado al hecho de que muchos dominios reales poseen una gran dimensionalidad.\ Por esto, el aprendizaje\ de estos modelos a partir de datos\ es un t{\'o}pico que ha tomado gran relevancia, ya que la disponibilidad de datos digitales es cada vez mayor,\ resultando adem{\'a}s en un mecanismo interesante para descubrir nuevo conocimiento a partir de datos digitales.

En este trabajo, la investigaci{\'o}n se centra en un enfoque espec{\'\i}fico de\ aprendizaje de redes de Markov:\ los algoritmos basados en independencia.\ Estos algoritmos est{\'a}n dise{\~n}ados para aprender la estructura de independencias del modelo,\ que es la componente que codifica de un modo compacto el conocimiento sobre la distribuci{\'o}n.\ Los algoritmos basados en independencia han sido dise{\~n}ados bajo lineamientos te{\'o}ricos\ que permiten aprender la estructura de un modo eficiente y robusto, a partir de\ la ejecuci{\'o}n de un conjunto de tests estad{\'\i}sticos de independencia\ sobre los datos.\ Com{\'u}nmente, los resultados de dichos tests son utilizados como restricciones\ que gu{\'\i}an una b{\'u}squeda en el espacio de las estructuras de independencia posibles,\ convergiendo a una estructura que satisface los resultados de todos los tests.\ Estos algoritmos garantizan que la estructura aprendida es correcta\ bajo la suposici{\'o}n de que los tests estad{\'\i}sticos son confiables.\ No obstante, un hecho muy com{\'u}n en la pr{\'a}ctica suele ser que los datos disponibles no son suficientes para obtener resultados correctos desde los tests estad{\'\i}sticos.\ Cuando esto sucede, los algoritmos basados en independencia\ acumulan y propagan suposiciones de\ independencia incorrectas,\ resultando en un aprendizaje con gran cantidad de errores estructurales.\ Este hecho, que resulta en una limitaci{\'o}n de real importancia\ a la hora de aplicar esta tecnolog{\'\i}a,\ es la motivaci{\'o}n de la presente tesis.

En este trabajo se presenta el enfoque de m{\'a}ximo a posteriori basado en independencias\ para aprendizaje de estructuras de redes de Markov (IBMAP, del ingl{\'e}s independence-based maximum-a-posteriori).\ Dado que los algoritmos tradicionales descartan la estructura correcta cada vez que ejecutan\ un test err{\'o}neo, se propone un enfoque que asigna probabilidades a las distintas estructuras,\ sin descartar ninguna. Para esto, se propone una funci{\'o}n de puntaje de estructuras basada en tests estad{\'\i}sticos denominada IB-score\ (puntaje basado en independencias).\ Esta funci{\'o}n permite computar de un modo aproximado la probabilidad a posteriori\ de una estructura dados los datos Pr(G|D), combinando los resultados de un conjunto de tests estad{\'\i}sticos.\ De este modo, las diferentes estructuras poseen un puntaje m{\'a}s alto o m{\'a}s bajo seg{\'u}n\ las probabilidades de las independencias que codifican.\ En resumen, el enfoque propuesto consiste en la maximizaci{\'o}n de la funci{\'o}n IB-score sobre el espacio de todas las estructuras posibles.\ A modo de instanciaci{\'o}n de este enfoque se presenta una srie de algoritmos que maximizan dicha funci{\'o}n\ con diversos mecanismos de optimizaci{\'o}n.\ 

Para validar el enfoque se evalu{\'o} el desempe{\~n}o de las distintas instanciaciones de la b{\'u}squeda,\ evaluando la calidad de las estructuras aprendidas con respecto\ a algoritmos basados en independencia que pertenecen al estado del arte.\ Se presentan resultados sistem{\'a}ticos sobre una gran variedad de dimensiones del problema,\ demostrando que este enfoque permite mejorar significativamente la calidad de las estructuras aprendidas.\ Se demuestra tambi{\'e}n que dichas mejoras pueden obtenerse a un costo computacional\ competitivo respecto de los algoritmos del estado del arte.\ Dicha experimentaci{\'o}n fue llevada a cabo sobre datos sint{\'e}ticos y datos del mundo real, y en una aplicaci{\'o}n de aprendizaje de estructuras para algoritmos evolutivos.

}, author = {Schl{\"u}ter, Federico and Bromberg, Facundo} }