@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} }