Current research on qualitative spatial representation and reasoning mainly focuses on one single aspect of space. In real world applications, however, multiple spatial aspects are often involved simultaneously. This paper investigates problems arising in reasoning with combined topological and directional information. We use the RCC8 algebra and the Rectangle Algebra (RA) for expressing topological and directional information respectively. We give examples to show that the bipath-consistency algorithm BIPATH is incomplete for solving even basic RCC8 and RA constraints. If topological constraints are taken from some maximal tractable subclasses of RCC8, and directional constraints are taken from a subalgebra, termed DIR49, of RA, then we show that BIPATH is able to separate topological constraints from directional ones. This means, given a set of hybrid topological and directional constraints from the above subclasses of RCC8 and RA, we can transfer the joint satisfaction problem in polynomial time to two independent satisfaction problems in RCC8 and RA. For general RA constraints, we give a method to compute solutions that satisfy all topological constraints and approximately satisfy each RA constraint to any prescribed precision.

To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation have been introduced. In this paper, we try to improve these axiomatic definitions and give a universal construction of information granulation by relating information granulations with a class of functions of multiple variables. We show that the improved axiomatic definition has some concrete information granulations in the literature as instances.

We present the nested Chinese restaurant process (nCRP), a stochastic process which assigns probability distributions to infinitely-deep, infinitely-branching trees. We show how this stochastic process can be used as a prior distribution in a Bayesian nonparametric model of document collections. Specifically, we present an application to information retrieval in which documents are modeled as paths down a random tree, and the preferential attachment dynamics of the nCRP leads to clustering of documents according to sharing of topics at multiple levels of abstraction. Given a corpus of documents, a posterior inference algorithm finds an approximation to a posterior distribution over trees, topics and allocations of words to levels of the tree. We demonstrate this algorithm on collections of scientific abstracts from several journals. This model exemplifies a recent trend in statistical machine learning--the use of Bayesian nonparametric methods to infer distributions on flexible data structures.

Traditional recommendation systems make recommendations based solely on the customer's past purchases, product ratings and demographic data without considering the profitability the items being recommended. In this work we study the question of how a vendor can directly incorporate the profitability of items into its recommender so as to maximize its expected profit while still providing accurate recommendations. Our approach uses the output of any traditional recommender system and adjust them according to item profitabilities. Our approach is parameterized so the vendor can control how much the recommendation incorporating profits can deviate from the traditional recommendation. We study our approach under two settings and show that it achieves approximately 22% more profit than traditional recommendations.

The explorative mind-map is a dynamic framework, that emerges automatically from the input, it gets. It is unlike a verificative modeling system where existing (human) thoughts are placed and connected together. In this regard, explorative mind-maps change their size continuously, being adaptive with connectionist cells inside; mind-maps process data input incrementally and offer lots of possibilities to interact with the user through an appropriate communication interface. With respect to a cognitive motivated situation like a conversation between partners, mind-maps become interesting as they are able to process stimulating signals whenever they occur. If these signals are close to an own understanding of the world, then the conversational partner becomes automatically more trustful than if the signals do not or less match the own knowledge scheme. In this (position) paper, we therefore motivate explorative mind-maps as a cognitive engine and propose these as a decision support engine to foster trust.

In this analytical study we derive the optimal unbiased value estimator (MVU) and compare its statistical risk to three well known value estimators: Temporal Difference learning (TD), Monte Carlo estimation (MC) and Least-Squares Temporal Difference Learning (LSTD). We demonstrate that LSTD is equivalent to the MVU if the Markov Reward Process (MRP) is acyclic and show that both differ for most cyclic MRPs as LSTD is then typically biased. More generally, we show that estimators that fulfill the Bellman equation can only be unbiased for special cyclic MRPs. The main reason being the probability measures with which the expectations are taken. These measure vary from state to state and due to the strong coupling by the Bellman equation it is typically not possible for a set of value estimators to be unbiased with respect to each of these measures. Furthermore, we derive relations of the MVU to MC and TD. The most important one being the equivalence of MC to the MVU and to LSTD for undiscounted MRPs in which MC has the same amount of information. In the discounted case this equivalence does not hold anymore. For TD we show that it is essentially unbiased for acyclic MRPs and biased for cyclic MRPs. We also order estimators according to their risk and present counter-examples to show that no general ordering exists between the MVU and LSTD, between MC and LSTD and between TD and MC. Theoretical results are supported by examples and an empirical evaluation.

We propose an extension of the concept of Expected Improvement criterion commonly used in Kriging based optimization. We extend it for more complex Kriging models, e.g. models using derivatives. The target field of application are CFD problems, where objective function are extremely expensive to evaluate, but the theory can be also used in other fields.

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization.

The perennial problem of "how many clusters?" remains an issue of substantial interest in data mining and machine learning communities, and becomes particularly salient in large data sets such as populational genomic data where the number of clusters needs to be relatively large and open-ended. This problem gets further complicated in a co-clustering scenario in which one needs to solve multiple clustering problems simultaneously because of the presence of common centroids (e.g., ancestors) shared by clusters (e.g., possible descents from a certain ancestor) from different multiple-cluster samples (e.g., different human subpopulations). In this paper we present a hierarchical nonparametric Bayesian model to address this problem in the context of multi-population haplotype inference. Uncovering the haplotypes of single nucleotide polymorphisms is essential for many biological and medical applications. While it is uncommon for the genotype data to be pooled from multiple ethnically distinct populations, few existing programs have explicitly leveraged the individual ethnic information for haplotype inference. In this paper we present a new haplotype inference program, Haploi, which makes use of such information and is readily applicable to genotype sequences with thousands of SNPs from heterogeneous populations, with competent and sometimes superior speed and accuracy comparing to the state-of-the-art programs. Underlying Haploi is a new haplotype distribution model based on a nonparametric Bayesian formalism known as the hierarchical Dirichlet process, which represents a tractable surrogate to the coalescent process. The proposed model is exchangeable, unbounded, and capable of coupling demographic information of different populations.

This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression methods. In the first stage we fit a set of candidate models. In the second stage we select one model by cross-validation. In the third stage we use hypothesis testing to eliminate some variables. We refer to the first two stages as "screening" and the last stage as "cleaning." We consider three screening methods: the lasso, marginal regression, and forward stepwise regression. Our method gives consistent variable selection under certain conditions.