Abstract: We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to solve the regularized maximum likelihood estimation problem. We show that our method is significantly faster than the widely used graphical lasso method, which is based on blockwise coordinate descent, on both artificial and real-world data.

Product take-back legislation forces manufacturers to bear the costs of collection and disposal of products that have reached the end of their useful lives. In order to reduce these costs, manufacturers can consider reuse, remanufacturing and/or recycling of components as an alternative to disposal. The implementation of such alternatives usually requires an appropriate reverse supply chain management. With the concepts of reverse supply chain are gaining popularity in practice, the use of artificial intelligence approaches in these areas is also becoming popular. As a result, the purpose of this paper is to give an overview of the recent publications concerning the application of artificial intelligence techniques to reverse supply chain with emphasis on certain types of product returns.

A growing number of challenging machine learning applications require decision-making from incomplete data (e.g., stochastic optimization, active sampling, robotics), which relies on quantitative representations of uncertainty (e.g., Bayesian posterior, belief state) and is out of reach of the commonly used paradigm of learning as point estimation on hand-selected data. While Bayesian inference is harder than point estimation in general, it can be relaxed to variational optimization problems which can be computationally competitive, if only they are treated with the algorithmic state-of-the-art established for the latter. In this paper, we propose a novel algorithm for the expectation propagation (EP; or adaptive TAP, or expectation consistent (EC)) relaxation [11, 8, 12], which is both much faster than the commonly used sequential EP algorithm, and is provably convergent (the sequential algorithm lacks such a guarantee). Our method builds on the convergent double loop algorithm of [12], but runs orders of magnitude faster. We gain a deeper understanding of EP (or EC) as optimization problem, unifying it with covariance decoupling ideas [19, 10], and allowing for "point estimation" algorithmic progress to be brought to bear on this powerful approximate inference formulation.

Translating potential disease biomarkers between multi-species 'omics' experiments is a new direction in biomedical research. The existing methods are limited to simple experimental setups such as basic healthy-diseased comparisons. Most of these methods also require an a priori matching of the variables (e.g., genes or metabolites) between the species. However, many experiments have a complicated multi-way experimental design often involving irregularly-sampled time-series measurements, and for instance metabolites do not always have known matchings between organisms. We introduce a Bayesian modelling framework for translating between multiple species the results from 'omics' experiments having a complex multi-way, time-series experimental design. The underlying assumption is that the unknown matching can be inferred from the response of the variables to multiple covariates including time.

The notion of distance between two objects is very general. Distance metrics and distances have now become an essential tool in many areas of mathematics and its applications including geometry, probability, statistics, coding/graph theory, data analysis, pattern recognition. For a comprehensive source on this subject see [4]. The notion of a fuzzy set was introduced by [8]. It is a class of objects with continuous values of membership and hence extends the classical definition of a set (to distinguish it from a fuzzy set we refer to it as a crisp set).

A learning algorithm based on primary school teaching and learning is presented. The methodology is to continuously evaluate a student and to give them training on the examples for which they repeatedly fail, until, they can correctly answer all types of questions. This incremental learning procedure produces better learning curves by demanding the student to optimally dedicate their learning time on the failed examples. When used in machine learning, the algorithm is found to train a machine on a data with maximum variance in the feature space so that the generalization ability of the network improves. The algorithm has interesting applications in data mining, model evaluations and rare objects discovery.

Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphismis provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.

There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy finite automata. However, the results obtained are applicable only to finite-state systems. In this paper, we consider bisimulation for general fuzzy systems which may be infinite-state or infinite-event, by modeling them as fuzzy transition systems. To help understand and check bisimulation, we characterize it in three ways by enumerating whole transitions, comparing individual transitions, and using a monotonic function. In addition, we address composition operations, subsystems, quotients, and homomorphisms of fuzzy transition systems and discuss their properties connected with bisimulation. The results presented here are useful for comparing the behavior of general fuzzy systems. In particular, this makes it possible to relate an infinite fuzzy system to a finite one, which is easier to analyze, with the same behavior.

Statistical models of natural stimuli provide an important tool for researchers in the fields of machine learning and computational neuroscience. A canonical way to quantitatively assess and compare the performance of statistical models is given by the likelihood. One class of statistical models which has recently gained increasing popularity and has been applied to a variety of complex data are deep belief networks. Analyses of these models, however, have been typically limited to qualitative analyses based on samples due to the computationally intractable nature of the model likelihood. Motivated by these circumstances, the present article provides a consistent estimator for the likelihood that is both computationally tractable and simple to apply in practice. Using this estimator, a deep belief network which has been suggested for the modeling of natural image patches is quantitatively investigated and compared to other models of natural image patches. Contrary to earlier claims based on qualitative results, the results presented in this article provide evidence that the model under investigation is not a particularly good model for natural images

The Monty Hall problem is the TV game scenario where you, the contestant, are presented with three doors, with a car hidden behind one and goats hidden behind the other two. After you select a door, the host (Monty Hall) opens a second door to reveal a goat. You are then invited to stay with your original choice of door, or to switch to the remaining unopened door, and claim whatever you find behind it. Assuming your objective is to win the car, is your best strategy to stay or switch, or does it not matter? Jason Rosenhouse has provided the definitive analysis of this game, along with several intriguing variations, and discusses some of its psychological and philosophical implications. This extended review examines several themes from the book in some detail from a Bayesian perspective, and points out one apparently inadvertent error.