We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of all Herbrand models of the program and the least fixed-point of an immediate consequence operator. We also propose an SLD-resolution proof procedure which is proven sound and complete with respect to the minimum model semantics. In other words, we provide a purely extensional theoretical framework for higher-order logic programming which generalizes the familiar theory of classical (first-order) logic programming.

We introduce new online and batch algorithms that are robust to data with missing features, a situation that arises in many practical applications. In the online setup, we allow for the comparison hypothesis to change as a function of the subset of features that is observed on any given round, extending the standard setting where the comparison hypothesis is fixed throughout. In the batch setup, we present a convex relation of a non-convex problem to jointly estimate an imputation function, used to fill in the values of missing features, along with the classification hypothesis. We prove regret bounds in the online setting and Rademacher complexity bounds for the batch i.i.d. setting. The algorithms are tested on several UCI datasets, showing superior performance over baselines.

We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.

In the current study we examine an application of the machine learning methods to model the retention constants in the thin layer chromatography (TLC). This problem can be described with hundreds or even thousands of descriptors relevant to various molecular properties, most of them redundant and not relevant for the retention constant prediction. Hence we employed feature selection to significantly reduce the number of attributes. Additionally we have tested application of the bagging procedure to the feature selection. The random forest regression models were built using selected variables. The resulting models have better correlation with the experimental data than the reference models obtained with linear regression. The cross-validation confirms robustness of the models.

Aim of this paper is to address the problem of learning Boolean functions from training data with missing values. We present an extension of the BRAIN algorithm, called U-BRAIN (Uncertainty-managing Batch Relevance-based Artificial INtelligence), conceived for learning DNF Boolean formulas from partial truth tables, possibly with uncertain values or missing bits. Such an algorithm is obtained from BRAIN by introducing fuzzy sets in order to manage uncertainty. In the case where no missing bits are present, the algorithm reduces to the original BRAIN.

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.

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.

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.

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).

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.