Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression relationships. We extend such models by imposing an eigen-decomposition on the multivariate error covariance matrix. By constraining parts of this decomposition, we obtain families of parsimonious mixtures of regressions and mixtures of regressions with concomitant variables. These families of models account for correlations between multiple responses. An expectation-maximization algorithm is presented for parameter estimation and performance is illustrated on simulated and real data.

An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among random variables. The undirected graphical model selection (UGMS) problem is to estimate the graph G* given observations drawn from the undirected graphical model. This paper proposes a framework for decomposing the UGMS problem into multiple subproblems over clusters and subsets of the separators in a junction tree. The junction tree is constructed using a graph that contains a superset of the edges in G*. We highlight three main properties of using junction trees for UGMS. First, different regularization parameters or different UGMS algorithms can be used to learn different parts of the graph. This is possible since the subproblems we identify can be solved independently of each other. Second, under certain conditions, a junction tree based UGMS algorithm can produce consistent results with fewer observations than the usual requirements of existing algorithms. Third, both our theoretical and experimental results show that the junction tree framework does a significantly better job at finding the weakest edges in a graph than existing methods. This property is a consequence of both the first and second properties. Finally, we note that our framework is independent of the choice of the UGMS algorithm and can be used as a wrapper around standard UGMS algorithms for more accurate graph estimation.

Relational classification on a single connected network has been of particular interest in the machine learning and data mining communities in the last decade or so. This is mainly due to the explosion in popularity of social networking sites such as Facebook, LinkedIn and Google+ amongst others. In statistical relational learning, many techniques have been developed to address this problem, where we have a connected unweighted homogeneous/heterogeneous graph that is partially labeled and the goal is to propagate the labels to the unlabeled nodes. In this paper, we provide a different perspective by enabling the effective use of graph transduction techniques for this problem. We thus exploit the strengths of this class of methods for relational learning problems. We accomplish this by providing a simple procedure for constructing a weight matrix that serves as input to a rich class of graph transduction techniques. Our procedure has multiple desirable properties. For example, the weights it assigns to edges between unlabeled nodes naturally relate to a measure of association commonly used in statistics, namely the Gamma test statistic. We further portray the efficacy of our approach on synthetic as well as real data, by comparing it with state-of-the-art relational learning algorithms, and graph transduction techniques with an adjacency matrix or a real valued weight matrix computed using available attributes as input. In these experiments we see that our approach consistently outperforms other approaches when the graph is sparsely labeled, and remains competitive with the best when the proportion of known labels increases.

In this paper we present a review of the existing typologies of Internet service users. We zoom in on social networking services including blogs and crowdsourcing websites. Based on the results of the analysis of the considered typologies obtained by means of FCA we developed a new user typology of a certain class of Internet services, namely a collaboration innovation platform. Cluster analysis of data extracted from the collaboration platform Witology was used to divide more than 500 participants into six groups based on three activity indicators: idea generation, commenting, and evaluation (assigning marks) The obtained groups and their percentages appear to follow the "90 - 9 - 1" rule.

One-class classification (OCC) algorithms aim to build classification models when the negative class is either absent, poorly sampled or not well defined. This unique situation constrains the learning of efficient classifiers by defining class boundary just with the knowledge of positive class. The OCC problem has been considered and applied under many research themes, such as outlier/novelty detection and concept learning. In this paper we present a unified view of the general problem of OCC by presenting a taxonomy of study for OCC problems, which is based on the availability of training data, algorithms used and the application domains applied. We further delve into each of the categories of the proposed taxonomy and present a comprehensive literature review of the OCC algorithms, techniques and methodologies with a focus on their significance, limitations and applications. We conclude our paper by discussing some open research problems in the field of OCC and present our vision for future research.

VT (Viterbi training), or hard EM, is an efficient way of parameter learning for probabilistic models with hidden variables. Given an observation $y$, it searches for a state of hidden variables $x$ that maximizes $p(x,y \mid \theta)$ by coordinate ascent on parameters $\theta$ and $x$. In this paper we introduce VT to PRISM, a logic-based probabilistic modeling system for generative models. VT improves PRISM in three ways. First VT in PRISM converges faster than EM in PRISM due to the VT's termination condition. Second, parameters learned by VT often show good prediction performance compared to those learned by EM. We conducted two parsing experiments with probabilistic grammars while learning parameters by a variety of inference methods, i.e.\ VT, EM, MAP and VB. The result is that VT achieved the best parsing accuracy among them in both experiments. Also we conducted a similar experiment for classification tasks where a hidden variable is not a prediction target unlike probabilistic grammars. We found that in such a case VT does not necessarily yield superior performance. Third since VT always deals with a single probability of a single explanation, Viterbi explanation, the exclusiveness condition that is imposed on PRISM programs is no more required if we learn parameters by VT. Last but not least we can say that as VT in PRISM is general and applicable to any PRISM program, it largely reduces the need for the user to develop a specific VT algorithm for a specific model. Furthermore since VT in PRISM can be used just by setting a PRISM flag appropriately, it makes VT easily accessible to (probabilistic) logic programmers. To appear in Theory and Practice of Logic Programming (TPLP).

Community Question Answering (CQA) websites have become valuable repositories which host a massive volume of human knowledge. To maximize the utility of such knowledge, it is essential to evaluate the quality of an existing question or answer, especially soon after it is posted on the CQA website. In this paper, we study the problem of inferring the quality of questions and answers through a case study of a software CQA (Stack Overflow). Our key finding is that the quality of an answer is strongly positively correlated with that of its question. Armed with this observation, we propose a family of algorithms to jointly predict the quality of questions and answers, for both quantifying numerical quality scores and differentiating the high-quality questions/answers from those of low quality. We conduct extensive experimental evaluations to demonstrate the effectiveness and efficiency of our methods.

A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the GP model is itself parameterized using the exponential family distribution (EFD). In this paper, we consider efficient algorithms for approximate inference on GGPMs using the general form of the EFD. A particular GP model and its associated inference algorithms can then be formed by changing the parameters of the EFD, thus greatly simplifying its creation for task-specific output domains. We demonstrate the efficacy of this framework by creating several new GP models for regressing to non-negative reals and to real intervals. We also consider a closed-form Taylor approximation for efficient inference on GGPMs, and elaborate on its connections with other model-specific heuristic closed-form approximations. Finally, we present a comprehensive set of experiments to compare approximate inference algorithms on a wide variety of GGPMs.

This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. Statist. Math. 37 (1966) 577-580]. Equipped with this tool, we develop four interconnected procedures for inference: (i) pointwise confidence interval; (ii) local likelihood ratio testing; (iii) simultaneous confidence band; (iv) global likelihood ratio testing. In particular, our confidence intervals are proved to be asymptotically valid at any point in the support, and they are shorter on average than the Bayesian confidence intervals proposed by Wahba [J. R. Stat. Soc. Ser. B Stat. Methodol. 45 (1983) 133-150] and Nychka [J. Amer. Statist. Assoc. 83 (1988) 1134-1143]. We also discuss a version of the Wilks phenomenon arising from local/global likelihood ratio testing. It is also worth noting that our simultaneous confidence bands are the first ones applicable to general quasi-likelihood models. Furthermore, issues relating to optimality and efficiency are carefully addressed. As a by-product, we discover a surprising relationship between periodic and nonperiodic smoothing splines in terms of inference.

We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this setting, these procedures require that individuals provide a complete ranking of all items, which is rarely feasible in practice. Instead, individuals routinely provide partial preference information, such as pairwise comparisons of items, and more practical approaches to ranking have aimed at modeling this partial preference data directly. As we show, however, such an approach raises serious theoretical challenges. Indeed, we demonstrate that many commonly used surrogate losses for pairwise comparison data do not yield consistency; surprisingly, we show inconsistency even in low-noise settings. With these negative results as motivation, we present a new approach to supervised ranking based on aggregation of partial preferences, and we develop $U$-statistic-based empirical risk minimization procedures. We present an asymptotic analysis of these new procedures, showing that they yield consistency results that parallel those available for classification. We complement our theoretical results with an experiment studying the new procedures in a large-scale web-ranking task.