Efficient Algorithms for Bayesian Network Parameter Learning from Incomplete Data

We propose an efficient family of algorithms to learn the parameters of a Bayesian network from incomplete data. In contrast to textbook approaches such as EM and the gradient method, our approach is non-iterative, yields closed form parameter estimates, and eliminates the need for inference in a Bayesian network. Our approach provides consistent parameter estimates for missing data problems that are MCAR, MAR, and in some cases, MNAR. Empirically, our approach is orders of magnitude faster than EM (as our approach requires no inference). Given sufficient data, we learn parameters that can be orders of magnitude more accurate

Model Creation and Equivalence Proofs of Cellular Automata and Artificial Neural Networks

Computational methods and mathematical models have invaded arguably every scientific discipline forming its own field of research called computational science. Mathematical models are the theoretical foundation of computational science. Since Newton's time, differential equations in mathematical models have been widely and successfully used to describe the macroscopic or global behaviour of systems. With spatially inhomogeneous, time-varying, local element-specific, and often non-linear interactions, the dynamics of complex systems is in contrast more efficiently described by local rules and thus in an algorithmic and local or microscopic manner. The theory of mathematical modelling taking into account these characteristics of complex systems has to be established still. We recently presented a so-called allagmatic method including a system metamodel to provide a framework for describing, modelling, simulating, and interpreting complex systems. Implementations of cellular automata and artificial neural networks were described and created with that method. Guidance from philosophy were helpful in these first studies focusing on programming and feasibility. A rigorous mathematical formalism, however, is still missing. This would not only more precisely describe and define the system metamodel, it would also further generalise it and with that extend its reach to formal treatment in applied mathematics and theoretical aspects of computational science as well as extend its applicability to other mathematical and computational models such as agent-based models. Here, a mathematical definition of the system metamodel is provided. Based on the presented formalism, model creation and equivalence of cellular automata and artificial neural networks are proved. It thus provides a formal approach for studying the creation of mathematical models as well as their structural and operational comparison.Comment: 13 pages, 1 tabl

Fuzzy heterogeneous neural networks for signal forecasting

Fuzzy heterogeneous neural networks are recently introduced models based on neurons accepting heterogeneous inputs (i.e. mixtures of numerical and non-numerical information possibly with missing data) with either crisp or imprecise character, which can be coupled with classical neurons. This paper compares the effectiveness of this kind of networks with time-delay and recurrent architectures that use classical neuron models and training algorithms in a signal forecasting problem, in the context of finding models of the central nervous system controllers.Peer ReviewedPostprint (author's final draft

Improving Data Quality by Leveraging Statistical Relational Learning

Digitally collected data su ↵ ers from many data quality issues, such as duplicate, incorrect, or incomplete data. A common approach for counteracting these issues is to formulate a set of data cleaning rules to identify and repair incorrect, duplicate and missing data. Data cleaning systems must be able to treat data quality rules holistically, to incorporate heterogeneous constraints within a single routine, and to automate data curation. We propose an approach to data cleaning based on statistical relational learning (SRL). We argue that a formalism - Markov logic - is a natural fit for modeling data quality rules. Our approach allows for the usage of probabilistic joint inference over interleaved data cleaning rules to improve data quality. Furthermore, it obliterates the need to specify the order of rule execution. We describe how data quality rules expressed as formulas in first-order logic directly translate into the predictive model in our SRL framework