Many networks are complex dynamical systems, where both attributes of nodes and topology of the network (link structure) can change with time. We propose a model of co-evolving networks where both node at- tributes and network structure evolve under mutual influence. Specifically, we consider a mixed membership stochastic blockmodel, where the probability of observing a link between two nodes depends on their current membership vectors, while those membership vectors themselves evolve in the presence of a link between the nodes. Thus, the network is shaped by the interaction of stochastic processes describing the nodes, while the processes themselves are influenced by the changing network structure. We derive an efficient variational inference procedure for our model, and validate the model on both synthetic and real-world data.

We present a novel Natural Evolution Strategy (NES) variant, the Rank-One NES (R1-NES), which uses a low rank approximation of the search distribution covariance matrix. The algorithm allows computation of the natural gradient with cost linear in the dimensionality of the parameter space, and excels in solving high-dimensional non-separable problems, including the best result to date on the Rosenbrock function (512 dimensions).

Due to space limitations, our submission "Source Separation and Clustering of Phase-Locked Subspaces", accepted for publication on the IEEE Transactions on Neural Networks in 2011, presented some results without proof. Those proofs are provided in this paper.

It is of increasing importance to develop learning methods for ranking. In contrast to many learning objectives, however, the ranking problem presents difficulties due to the fact that the space of permutations is not smooth. In this paper, we examine the class of rank-linear objective functions, which includes popular metrics such as precision and discounted cumulative gain. In particular, we observe that expectations of these gains are completely characterized by the marginals of the corresponding distribution over permutation matrices. Thus, the expectations of rank-linear objectives can always be described through locations in the Birkhoff polytope, i.e., doubly-stochastic matrices (DSMs). We propose a technique for learning DSM-based ranking functions using an iterative projection operator known as Sinkhorn normalization. Gradients of this operator can be computed via backpropagation, resulting in an algorithm we call Sinkhorn propagation, or SinkProp. This approach can be combined with a wide range of gradient-based approaches to rank learning. We demonstrate the utility of SinkProp on several information retrieval data sets.

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.

The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the Baire metric with (i) agglomerative hierarchical clustering, in terms of algorithm properties; (ii) generalized ultrametrics, in terms of definition; and (iii) fast clustering through k-means partititioning, in terms of quality of results. For the latter, we carry out an in depth astronomical study. We apply the Baire distance to spectrometric and photometric redshifts from the Sloan Digital Sky Survey using, in this work, about half a million astronomical objects. We want to know how well the (more costly to determine) spectrometric redshifts can predict the (more easily obtained) photometric redshifts, i.e. we seek to regress the spectrometric on the photometric redshifts, and we use clusterwise regression for this.

We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond-Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.

We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their \lova extensions. We show that the Lovasz extension may be seen as the convex envelope of a function that depends on level sets (i.e., the set of indices whose corresponding components of the underlying predictor are greater than a given constant): this leads to a class of convex structured regularization terms that impose prior knowledge on the level sets, and not only on the supports of the underlying predictors. We provide a unified set of optimization algorithms, such as proximal operators, and theoretical guarantees (allowed level sets and recovery conditions). By selecting specific submodular functions, we give a new interpretation to known norms, such as the total variation; we also define new norms, in particular ones that are based on order statistics with application to clustering and outlier detection, and on noisy cuts in graphs with application to change point detection in the presence of outliers.

This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a missing disease spreader node, and the rest, given a dataset on the number of cases. The spread is described by stochastic differential equations. A perturbation theory quantifies the impact of the missing spreader on the moments of the number of cases. Statistical discriminators examine the mid-body or tail-ends of the probability density function, and search for the disturbance from the missing spreader. They are tested with computationally synthesized datasets, and applied to the SARS outbreak and flu pandemic.

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.