A Semantic Similarity Measure for Expressive Description Logics

A totally semantic measure is presented which is able to calculate a similarity value between concept descriptions and also between concept description and individual or between individuals expressed in an expressive description logic. It is applicable on symbolic descriptions although it uses a numeric approach for the calculus. Considering that Description Logics stand as the theoretic framework for the ontological knowledge representation and reasoning, the proposed measure can be effectively used for agglomerative and divisional clustering task applied to the semantic web domain.Comment: 13 pages, Appeared at CILC 2005, Convegno Italiano di Logica Computazionale also available at http://www.disp.uniroma2.it/CILC2005/downloads/papers/15.dAmato_CILC05.pd

Visualizing and Understanding Sum-Product Networks

Sum-Product Networks (SPNs) are recently introduced deep tractable probabilistic models by which several kinds of inference queries can be answered exactly and in a tractable time. Up to now, they have been largely used as black box density estimators, assessed only by comparing their likelihood scores only. In this paper we explore and exploit the inner representations learned by SPNs. We do this with a threefold aim: first we want to get a better understanding of the inner workings of SPNs; secondly, we seek additional ways to evaluate one SPN model and compare it against other probabilistic models, providing diagnostic tools to practitioners; lastly, we want to empirically evaluate how good and meaningful the extracted representations are, as in a classic Representation Learning framework. In order to do so we revise their interpretation as deep neural networks and we propose to exploit several visualization techniques on their node activations and network outputs under different types of inference queries. To investigate these models as feature extractors, we plug some SPNs, learned in a greedy unsupervised fashion on image datasets, in supervised classification learning tasks. We extract several embedding types from node activations by filtering nodes by their type, by their associated feature abstraction level and by their scope. In a thorough empirical comparison we prove them to be competitive against those generated from popular feature extractors as Restricted Boltzmann Machines. Finally, we investigate embeddings generated from random probabilistic marginal queries as means to compare other tractable probabilistic models on a common ground, extending our experiments to Mixtures of Trees.Comment: Machine Learning Journal paper (First Online), 24 page

Modelling and Searching of Combinatorial Spaces Based on Markov Logic Networks

Markov Logic Networks (MLNs) combine Markov networks (MNs) and first-order logic by attaching weights to first-order formulas and using these as templates for features of MNs. Learning the structure of MLNs is performed by state-of-the-art methods by maximizing the likelihood of a relational database. This leads to suboptimal results for prediction tasks due to the mismatch between the objective function (likelihood) and the task of classification (maximizing conditional likelihood (CL)). In this paper we propose two algorithms for learning the structure of MLNs. The first maximizes the CL of query predicates instead of the joint likelihood of all predicates while the other maximizes the area under the Precision-Recall curve (AUC). Both algorithms set the parameters by maximum likelihood and choose structures by maximizing CL or AUC. For each of these algorithms we develop two different searching strategies. The first is based on Iterated Local Search and the second on Greedy Randomized Adaptive Search Procedure. We compare the performances of these randomized search approaches on real-world datasets and show that on larger datasets, the ILS-based approaches perform better, both in terms of CLL and AUC, while on small datasets, ILS and RBS approaches are competitive and RBS can also lead to better results for AUC