Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we introduce novel statistics based on block sizes for representing sample sets of partitionings and feature allocations. We develop an element-based definition of entropy to quantify segmentation among their elements. Then we propose a simple algorithm called entropy agglomeration (EA) to summarize and visualize this information. Experiments on various infinite mixture posteriors as well as a feature allocation dataset demonstrate that the proposed statistics are useful in practice.

Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables. However, there has been remarkably little theoretical statistical foundation on sparse CCA in high-dimensional settings despite active methodological and applied research activities. In this paper, we introduce an elementary sufficient and necessary characterization such that the solution of CCA is indeed sparse, propose a computationally efficient procedure, called CAPIT, to estimate the canonical directions, and show that the procedure is rate-optimal under various assumptions on nuisance parameters. The procedure is applied to a breast cancer dataset from The Cancer Genome Atlas project. We identify methylation probes that are associated with genes, which have been previously characterized as prognosis signatures of the metastasis of breast cancer.

In the past decade, high-dimensional data analysis has received broad research interests in data mining and scientific discovery, with many significant results obtained in theory, algorithm and applications. The major driven force is the rapid development of data collection technologies in many applications domains such as social networks, natural language processing, bioinformatics and computer vision. In these applications it is not unusual that data samples are represented with millions or even billions of features using which an underlying statistical learning model must be fit. In many circumstances, however, the number of collected samples is substantially smaller than the dimensionality of the feature, implying that consistent estimators cannot be hoped for unless additional assumptions are imposed on the model. One of the widely acknowledged prior assumptions is that the data exhibit low-dimensional structure, which can often be captured by imposing sparsity constraint on the model parameter space. It is thus crucial to develop robust and efficient computational procedures for solving, even just approximately, these optimization problems with sparsity constraint.

This article considers the performance of the MOA* multiobjective search algorithm with heuristic information. It is shown that in certain cases blind search can be more efficient than perfectly informed search, in terms of both node and label expansions. A class of simple graph search problems is defined for which the number of nodes grows linearly with problem size and the number of nondominated labels grows quadratically. It is proved that for these problems the number of node expansions performed by blind MOA* grows linearly with problem size, while the number of such expansions performed with a perfectly informed heuristic grows quadratically. It is also proved that the number of label expansions grows quadratically in the blind case and cubically in the informed case.

We present NaturalOWL, a natural language generation system that produces texts describing individuals or classes of OWL ontologies. Unlike simpler OWL verbalizers, which typically express a single axiom at a time in controlled, often not entirely fluent natural language primarily for the benefit of domain experts, we aim to generate fluent and coherent multi-sentence texts for end-users. With a system like NaturalOWL, one can publish information in OWL on the Web, along with automatically produced corresponding texts in multiple languages, making the information accessible not only to computer programs and domain experts, but also end-users. We discuss the processing stages of NaturalOWL, the optional domain-dependent linguistic resources that the system can use at each stage, and why they are useful. We also present trials showing that when the domain-dependent llinguistic resources are available, NaturalOWL produces significantly better texts compared to a simpler verbalizer, and that the resources can be created with relatively light effort.

Multitask learning can be effective when features useful in one task are also useful for other tasks, and the group lasso is a standard method for selecting a common subset of features. In this paper, we are interested in a less restrictive form of multitask learning, wherein (1) the available features can be organized into subsets according to a notion of similarity and (2) features useful in one task are similar, but not necessarily identical, to the features best suited for other tasks. The main contribution of this paper is a new procedure called Sparse Overlapping Sets (SOS) lasso, a convex optimization that automatically selects similar features for related learning tasks. Error bounds are derived for SOSlasso and its consistency is established for squared error loss. In particular, SOSlasso is motivated by multi- subject fMRI studies in which functional activity is classified using brain voxels as features. Experiments with real and synthetic data demonstrate the advantages of SOSlasso compared to the lasso and group lasso.

Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a hierarchically structured model. We propose two non-parametric Bayesian hierarchical network models based on Gibbs fragmentation tree priors, and demonstrate their ability to capture nested patterns in simulated networks. On real networks we demonstrate detection of hierarchical structure and show predictive performance on par with the state of the art. We envision that our methods can be employed in exploratory analysis of large scale complex networks for example to model human brain connectivity.

Reasoning, the most important human brain operation, is characterized by a degree of fuzziness. In the present paper we construct a fuzzy model for the reasoning process giving through the calculation of probabilities and possibilities of all possible individuals' profiles a quantitative/qualitative view of their behaviour during the above process. In this model the main stages of human reasoning (imagination, visualisation and generation of ideas) are represented as fuzzy subsets of a set of linguistic labels characterizing a person's performance in each stage. Further, using the coordinates of the centre of gravity of the graph of the corresponding membership function we develop a method of measuring the reasoning skills of a group of individuals. We also present a number of classroom experiments with student groups' of T. E. I. of Patras, Greece, illustrating our results in practice.

In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$, of elements from an overcomplete dictionary. While many algorithms are competitive at both problems when $x$ is very sparse, it can be challenging to recover $x$ when it is less sparse. We present the Difference Map, which excels at sparse recovery when sparseness is lower and noise is higher. The Difference Map out-performs the state of the art with reconstruction from random measurements and natural image reconstruction via sparse coding.

Due to the nature of the individual experiments, based on eliciting neural response from a small number of stimuli, this link is incomplete, and unidirectional from the causal point of view. To come to conclusions on the function implied by the activation of brain regions, it is necessary to combine a wide exploration of the various brain functions and some inversion of the statistical inference. Here we introduce a methodology for accumulating knowledge towards a bidirectional link between observed brain activity and the corresponding function. We rely on a large corpus of imaging studies and a predictive engine. Technically, the challenges are to find commonality between the studies without denaturing the richness of the corpus. The key elements that we contribute are labeling the tasks performed with a cognitive ontology, and modeling the long tail of rare paradigms in the corpus. To our knowledge, our approach is the first demonstration of predicting the cognitive content of completely new brain images. To that end, we propose a method that predicts the experimental paradigms across different studies.