Rough sets are efficient for data pre-process in data mining. Lower and upper approximations are two core concepts of rough sets. This paper studies generalized rough sets based on symmetric and transitive relations from the operator-oriented view by matroidal approaches. We firstly construct a matroidal structure of generalized rough sets based on symmetric and transitive relations, and provide an approach to study the matroid induced by a symmetric and transitive relation. Secondly, this paper establishes a close relationship between matroids and generalized rough sets. Approximation quality and roughness of generalized rough sets can be computed by the circuit of matroid theory. At last, a symmetric and transitive relation can be constructed by a matroid with some special properties.

The validity OF a causal model can be tested ONLY IF the model imposes constraints ON the probability distribution that governs the generated data. IN the presence OF unmeasured variables, causal models may impose two types OF constraints : conditional independencies, AS READ through the d - separation criterion, AND functional constraints, FOR which no general criterion IS available.This paper offers a systematic way OF identifying functional constraints AND, thus, facilitates the task OF testing causal models AS well AS inferring such models FROM data.

Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition function, based on convex combinations of distributions in the exponential domain, that is applicable to an arbitrary undirected graphical model. In the special case of convex combinations of tree-structured distributions, we obtain a family of variational problems, similar to the Bethe free energy, but distinguished by the following desirable properties: i. they are cnvex, and have a unique global minimum; and ii. the global minimum gives an upper bound on the log partition function. The global minimum is defined by stationary conditions very similar to those defining fixed points of belief propagation or tree-based reparameterization Wainwright et al., 2001. As with BP fixed points, the elements of the minimizing argument can be used as approximations to the marginals of the original model. The analysis described here can be extended to structures of higher treewidth e.g., hypertrees, thereby making connections with more advanced approximations e.g., Kikuchi and variants Yedidia et al., 2001; Minka, 2001.

We introduce Dimple, a fully open-source API for probabilistic modeling. Dimple allows the user to specify probabilistic models in the form of graphical models, Bayesian networks, or factor graphs, and performs inference (by automatically deriving an inference engine from a variety of algorithms) on the model. Dimple also serves as a compiler for GP5, a hardware accelerator for inference.

We propose a Bayesian methodology for one-mode projecting a bipartite network that is being observed across a series of discrete time steps. The resulting one mode network captures the uncertainty over the presence/absence of each link and provides a probability distribution over its possible weight values. Additionally, the incorporation of prior knowledge over previous states makes the resulting network less sensitive to noise and missing observations that usually take place during the data collection process. The methodology consists of computationally inexpensive update rules and is scalable to large problems, via an appropriate distributed implementation.

A number of modern learning tasks involve estimation from heterogeneous information sources. This includes classification with labeled and unlabeled data as well as other problems with analogous structure such as competitive (game theoretic) problems. The associated estimation problems can be typically reduced to solving a set of fixed point equations (consistency conditions). We introduce a general method for combining a preferred information source with another in this setting by evolving continuous paths of fixed points at intermediate allocations. We explicitly identify critical points along the unique paths to either increase the stability of estimation or to ensure a significant departure from the initial source. The homotopy continuation approach is guaranteed to terminate at the second source, and involves no combinatorial effort. We illustrate the power of these ideas both in classification tasks with labeled and unlabeled data, as well as in the context of a competitive (min-max) formulation of DNA sequence motif discovery.

In probabilistic approaches to classification and information extraction, one typically builds a statistical model of words under the assumption that future data will exhibit the same regularities as the training data. In many data sets, however, there are scope-limited features whose predictive power is only applicable to a certain subset of the data. For example, in information extraction from web pages, word formatting may be indicative of extraction category in different ways on different web pages. The difficulty with using such features is capturing and exploiting the new regularities encountered in previously unseen data. In this paper, we propose a hierarchical probabilistic model that uses both local/scope-limited features, such as word formatting, and global features, such as word content. The local regularities are modeled as an unobserved random parameter which is drawn once for each local data set. This random parameter is estimated during the inference process and then used to perform classification with both the local and global features--- a procedure which is akin to automatically retuning the classifier to the local regularities on each newly encountered web page. Exact inference is intractable and we present approximations via point estimates and variational methods. Empirical results on large collections of web data demonstrate that this method significantly improves performance from traditional models of global features alone.

In this paper, we introduce and evaluate a data-driven staged mixture modeling technique for building density, regression, and classification models. Our basic approach is to sequentially add components to a finite mixture model using the structural expectation maximization (SEM) algorithm. We show that our technique is qualitatively similar to boosting. This correspondence is a natural byproduct of the fact that we use the SEM algorithm to sequentially fit the mixture model. Finally, in our experimental evaluation, we demonstrate the effectiveness of our approach on a variety of prediction and density estimation tasks using real-world data.

Building models, or maps, of robot environments is a highly active research area; however, most existing techniques construct unstructured maps and assume static environments. In this paper, we present an algorithm for learning object models of non-stationary objects found in office-type environments. Our algorithm exploits the fact that many objects found in office environments look alike (e.g., chairs, recycling bins). It does so through a two-level hierarchical representation, which links individual objects with generic shape templates of object classes. We derive an approximate EM algorithm for learning shape parameters at both levels of the hierarchy, using local occupancy grid maps for representing shape. Additionally, we develop a Bayesian model selection algorithm that enables the robot to estimate the total number of objects and object templates in the environment. Experimental results using a real robot equipped with a laser range finder indicate that our approach performs well at learning object-based maps of simple office environments. The approach outperforms a previously developed non-hierarchical algorithm that models objects but lacks class templates.

Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When hidden variables are present, however, standard dimension might no longer be appropriate. One should instead use effective dimension (Geiger et al. 1996). This paper is concerned with the computation of effective dimension. First we present an upper bound on the effective dimension of a latent class (LC) model. This bound is tight and its computation is easy. We then consider a generalization of LC models called hierarchical latent class (HLC) models (Zhang 2002). We show that the effective dimension of an HLC model can be obtained from the effective dimensions of some related LC models. We also demonstrate empirically that using effective dimension in place of standard dimension improves the quality of models learned from data.