Results are presented on the performance of Adaptive Neuro-Fuzzy Inference system (ANFIS) for wind velocity forecasts in the Isthmus of Tehuantepec region in the state of Oaxaca, Mexico. The data bank was provided by the meteorological station located at the University of Isthmus, Tehuantepec campus, and this data bank covers the period from 2008 to 2011. Three data models were constructed to carry out 16, 24 and 48 hours forecasts using the following variables: wind velocity, temperature, barometric pressure, and date. The performance measure for the three models is the mean standard error (MSE). In this work, performance analysis in short-term prediction is presented, because it is essential in order to define an adequate wind speed model for eolian parks, where a right planning provide economic benefits.

In the present paper we use principles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainty. For this, the main stages of the corresponding process are represented as fuzzy subsets of a set of linguistic labels characterizing the system's performance at each stage. We also introduce three alternative measures of a fuzzy system's effectiveness connected to our general model. These measures include the system's total possibilistic uncertainty, the Shannon's entropy properly modified for use in a fuzzy environment and the "centroid" method in which the coordinates of the center of mass of the graph of the membership function involved provide an alternative measure of the system's performance. The advantages and disadvantages of the above measures are discussed and a combined use of them is suggested for achieving a worthy of credit mathematical analysis of the corresponding situation. An application is also developed for the Mathematical Modelling process illustrating the use of our results in practice.

A majority of scientific and commercial data is stored in relational databases. Probabilistic models over such datasets would allow probabilistic queries, error checking, and inference of missing values, but to this day machine learning expertise is required to construct accurate models. Fortunately, current probabilistic programming tools ease the task of constructing such models [1, 2, 3, 4, 5, 6] and work in statistical relational learning has focused on making it even easier to define models specific to relational data [7, 8, 9, 10]. However, within these frameworks the user still needs to specify all the probabilistic dependencies in the data, requiring a level of expertise in probability and statistics that domain experts often do not have, thus severely restricting the practical applications of such techniques. On the other hand, domain experts do spend considerable effort and expertise in designing the database schemata used to represent their data, providing type information for table columns and foreign key relations to specify dependencies.

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces. Keywords: Markov decision processes, hierarchical reinforcement learning, transfer, multiscale analysis.

The standard training method of Conditional Random Fields (CRFs) is very slow for large-scale applications. As an alternative, piecewise training divides the full graph into pieces, trains them independently, and combines the learned weights at test time. In this paper, we present \emph{separate} training for undirected models based on the novel Co-occurrence Rate Factorization (CR-F). Separate training is a local training method. In contrast to MEMMs, separate training is unaffected by the label bias problem. Experiments show that separate training (i) is unaffected by the label bias problem; (ii) reduces the training time from weeks to seconds; and (iii) obtains competitive results to the standard and piecewise training on linear-chain CRFs.

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter estimation problems arising in detailed combustion kinetics.

This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients to estimate, which renders conventional approaches computationally prohibitive when $d$ is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error for moderate sample sizes, and (2) the computational complexity is lower for sparser densities. Our method also allows for flexible control of the trade-off between mean-squared error and computational complexity.

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller.

In this paper, first we present a new explanation for the relation between logical circuits and artificial neural networks, logical circuits and fuzzy logic, and artificial neural networks and fuzzy inference systems. Then, based on these results, we propose a new neuro-fuzzy computing system which can effectively be implemented on the memristor-crossbar structure. One important feature of the proposed system is that its hardware can directly be trained using the Hebbian learning rule and without the need to any optimization. The system also has a very good capability to deal with huge number of input-out training data without facing problems like overtraining.

Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an appropriately constructed traveling salesman problem. In our approach, one computes an optimal ordering (partially ordered set) of random variables using methods for the traveling salesman problem. This ordering significantly reduces the search space for the subsequent greedy optimization that computes the final structure of the Bayesian network. We demonstrate our approach of learning Bayesian networks on real world census and weather datasets. In both cases, we demonstrate that the approach very accurately captures dependencies between random variables. We check the accuracy of the predictions based on independent studies in both application domains.