Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of the multi-layer graph for improved clustering of the vertices compared to using layers independently. We propose two novel methods, which are based on joint matrix factorization and graph regularization framework respectively, to efficiently combine the spectrum of the multiple graph layers, namely the eigenvectors of the graph Laplacian matrices. In each case, the resulting combination, which we call a "joint spectrum" of multiple graphs, is used for clustering the vertices. We evaluate our approaches by simulations with several real world social network datasets. Results demonstrate the superior or competitive performance of the proposed methods over state-of-the-art technique and common baseline methods, such as co-regularization and summation of information from individual graphs.

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm.

In this paper, we first demonstrate that b-bit minwise hashing, whose estimators are positive definite kernels, can be naturally integrated with learning algorithms such as SVM and logistic regression. We adopt a simple scheme to transform the nonlinear (resemblance) kernel into linear (inner product) kernel; and hence large-scale problems can be solved extremely efficiently. Our method provides a simple effective solution to large-scale learning in massive and extremely high-dimensional datasets, especially when data do not fit in memory. We then compare b-bit minwise hashing with the Vowpal Wabbit (VW) algorithm (which is related the Count-Min (CM) sketch). Interestingly, VW has the same variances as random projections. Our theoretical and empirical comparisons illustrate that usually $b$-bit minwise hashing is significantly more accurate (at the same storage) than VW (and random projections) in binary data. Furthermore, $b$-bit minwise hashing can be combined with VW to achieve further improvements in terms of training speed, especially when $b$ is large.

This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-off function. The utility function encodes some a priori knowledge external to the system, it quantifies how bad it is to make mistakes. The intrinsic underlying structure of the system is modeled by an epsilon-machine and its causal states. The decisional states form a partition of the lower-level causal states that is defined according to the higher-level user's knowledge. In a complex systems perspective, the decisional states are thus the "emerging" patterns corresponding to the utility function. The transitions between these decisional states correspond to events that lead to a change of decision. The new REMAPF algorithm estimates both the epsilon-machine and the decisional states from data. Application examples are given for hidden model reconstruction, cellular automata filtering, and edge detection in images.

We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that imposing stationarity is enough to control the Gaussian complexity without further regularization. This lets us use structural risk minimization for model selection. We demonstrate our methods by predicting interest rate movements.

This paper addresses the problem of inferring sparse causal networks modeled by multivariate auto-regressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a "false connection score." In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that the false connection score is less than one. The false connection score is also demonstrated to be a useful metric of recovery in non-asymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach.

Elucidating the genetic basis of human diseases is a central goal of genetics and molecular biology. While traditional linkage analysis and modern high-throughput techniques often provide long lists of tens or hundreds of disease gene candidates, the identification of disease genes among the candidates remains time-consuming and expensive. Efficient computational methods are therefore needed to prioritize genes within the list of candidates, by exploiting the wealth of information available about the genes in various databases. Here we propose ProDiGe, a novel algorithm for Prioritization of Disease Genes. ProDiGe implements a novel machine learning strategy based on learning from positive and unlabeled examples, which allows to integrate various sources of information about the genes, to share information about known disease genes across diseases, and to perform genome-wide searches for new disease genes. Experiments on real data show that ProDiGe outperforms state-of-the-art methods for the prioritization of genes in human diseases.

This paper presents a new approach to identifying and eliminating mislabeled training instances for supervised learning. The goal of this approach is to improve classification accuracies produced by learning algorithms by improving the quality of the training data. Our approach uses a set of learning algorithms to create classifiers that serve as noise filters for the training data. We evaluate single algorithm, majority vote and consensus filters on five datasets that are prone to labeling errors. Our experiments illustrate that filtering significantly improves classification accuracy for noise levels up to 30 percent. An analytical and empirical evaluation of the precision of our approach shows that consensus filters are conservative at throwing away good data at the expense of retaining bad data and that majority filters are better at detecting bad data at the expense of throwing away good data. This suggests that for situations in which there is a paucity of data, consensus filters are preferable, whereas majority vote filters are preferable for situations with an abundance of data.

This paper introduces an elemental building block which combines Dictionary Learning and Dimension Reduction (DRDL). We show how this foundational element can be used to iteratively construct a Hierarchical Sparse Representation (HSR) of a sensory stream. We compare our approach to existing models showing the generality of our simple prescription. We then perform preliminary experiments using this framework, illustrating with the example of an object recognition task using standard datasets. This work introduces the very first steps towards an integrated framework for designing and analyzing various computational tasks from learning to attention to action. The ultimate goal is building a mathematically rigorous, integrated theory of intelligence.

A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonably-sized training sets. Typically such bias is supplied by hand through the skill and insights of experts. In this paper a model for automatically learning bias is investigated. The central assumption of the model is that the learner is embedded within an environment of related learning tasks. Within such an environment the learner can sample from multiple tasks, and hence it can search for a hypothesis space that contains good solutions to many of the problems in the environment. Under certain restrictions on the set of all hypothesis spaces available to the learner, we show that a hypothesis space that performs well on a sufficiently large number of training tasks will also perform well when learning novel tasks in the same environment. Explicit bounds are also derived demonstrating that learning multiple tasks within an environment of related tasks can potentially give much better generalization than learning a single task.