We describe a graphical model for probabilistic relationships|an alternative tothe Bayesian network|called a dependency network. The graph of a dependency network, unlike aBayesian network, is potentially cyclic. The probability component of a dependency network, like aBayesian network, is a set of conditional distributions, one for each nodegiven its parents. We identify several basic properties of this representation and describe a computationally e cient procedure for learning the graph and probability components from data. We describe the application of this representation to probabilistic inference, collaborative ltering (the task of predicting preferences), and the visualization of acausal predictive relationships.

For nearly a century, statisticians have been intrigued by the problems of developing a satisfactory methodology for the analysis of spatial data; see Student (1914), for an early example. It is only since the early 1970's, however, that the statistical analysis of large data sets, using flexible parametric models has become a feasible proposition. On the practical side, progress has been made possible by the availability of relatively cheap, computerised resources for the collection and analysis of data. The study of digital images and the use of satellite data for remote sensing are prominent examples in this respect. On the methodological side, substantial progress is associated with the introduction of Markov random fields (MRFs), as a class of parametric models for spatial data (Besag 1974). Shaped by these developments, spatial statistics has emerged as perhaps the most dynamic and computer intensive of all the areas of statistical endeavour; building upon models used originally...

The NRCSE was established in 1997 through a cooperative agreement with the United States Environmental Protection Agency which provides the Center's primary funding. A recursive algorithm for Markov random fields

Technological advances have led to new and automated data collection methods. Datasets once at a premium are often plentiful nowadays and sometimes indeed massive. A new breed of challenges are thus presented – primary among them is the need for methodology to analyze such masses of data with a view to understanding complex phenomena and relationships. Such capability is provided by data mining which combines core statistical techniques with those from machine intelligence. This article reviews the current state of the discipline from a statistician’s perspective, illustrates issues with real-life examples, discusses the connections with statistics, the differences, the failings and the challenges ahead. 1

Key words and phrases. Bayesian, Markov random field, maximum likelihood,

When used to learn high dimensional parametric probabilistic models, the classical maximum likelihood (ML) learning often suffers from computational intractability, which motivates the active developments of non-ML learning methods. Yet, because of their divergent motivations and forms, the objective functions of many non-ML learning methods are seemingly unrelated, and there lacks a unified framework to understand them. In this work, based on an information geometric view of parametric learning, we introduce a general non-ML learning principle termed as minimum KL contraction, where we seek optimal parameters that minimizes the contraction of the KL divergence between the two distributions after they are transformed with a KL contraction operator. We then show that the objective functions of several important or recently developed non-ML learning methods, including contrastive divergence [12], noise-contrastive estimation [11], partial likelihood [7], non-local contrastive objectives [31], score matching [14], pseudo-likelihood [3], maximum conditional likelihood [17], maximum mutual information [2], maximum marginal likelihood [9], and conditional and marginal composite likelihood [24], can be unified under the minimum KL contraction framework with different choices of the KL contraction operators. 1

Following the statistical mechanics methodology, firstly introduced in macroeconomics by Aoki [1, 2, 3], we provide some insights to the well known works of (author?) [7, 6]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean field interaction modeling and master equation techniques.