Multi-cell cooperative processing with limited backhaul traffic is studied for cellular uplinks. Aiming at reduced backhaul overhead, a sparsity-regularized multi-cell receive-filter design problem is formulated. Both unstructured distributed cooperation as well as clustered cooperation, in which base station groups are formed for tight cooperation, are considered. Dynamic clustered cooperation, where the sparse equalizer and the cooperation clusters are jointly determined, is solved via alternating minimization based on spectral clustering and group-sparse regression. Furthermore, decentralized implementations of both unstructured and clustered cooperation schemes are developed for scalability, robustness and computational efficiency. Extensive numerical tests verify the efficacy of the proposed methods.

The EM training algorithm of the classical i-vector extractor is often incorrectly described as a maximum-likelihood method. The i-vector model is however intractable: the likelihood itself and the hidden-variable posteriors needed for the EM algorithm cannot be computed in closed form. We show here that the classical i-vector extractor recipe is actually a mean-field variational Bayes (VB) recipe. This theoretical VB interpretation turns out to be of further use, because it also offers an interpretation of the newer phonetic i-vector extractor recipe, thereby unifying the two flavours of extractor. More importantly, the VB interpretation is also practically useful: it suggests ways of modifying existing i-vector extractors to make them more accurate. In particular, in existing methods, the approximate VB posterior for the GMM states is fixed, while only the parameters of the generative model are adapted. Here we explore the possibility of also mildly adjusting (calibrating) those posteriors, so that they better fit the generative model.

In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such group-invariant subspaces are also referred to as submodules. Similar to the well known Sparse Subspace Clustering approach where the data is assumed to come from a union of subspaces, we analyze an algorithm which, following a recent work [1], we refer to as Sparse Sub-module Clustering (SSmC). The method is based on finding group-sparse self-representation of data points. In this paper we primarily derive general conditions under which such a group-invariant subspace identification is possible. In particular we extend the geometric analysis in [2] and in the process we identify a related problem in geometric functional analysis.

We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this conditional. Varying-coefficient models subsume hierarchical Bayesian multitask models, but also generalizations in which the conditional varies continuously, for instance, in time or space. However, Bayesian inference in varying-coefficient models is generally intractable. We show that inference for varying-coefficient models with isotropic Gaussian process priors resolves to standard inference for a Gaussian process that can be solved efficiently. MAP inference in this model resolves to multitask learning using task and instance kernels, and inference for hierarchical Bayesian multitask models can be carried out efficiently using graph-Laplacian kernels. We report on experiments for geospatial prediction.

This paper contains the consideration of inheritance mechanism in such knowledge representation models as object-oriented programming, frames and object-oriented dynamic networks. In addition, inheritance within representation of vague and imprecise knowledge are also discussed. New types of inheritance, general classification of all known inheritance types and approach, which allows avoiding in many cases problems with exceptions, redundancy and ambiguity within object-oriented dynamic networks and their fuzzy extension, are introduced in the paper. The proposed approach bases on conception of homogeneous and inhomogeneous or heterogeneous class of objects, which allow building of inheritance hierarchy more flexibly and efficiently.

Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL $\mathcal{SROIQ}$ based on finite chains of degrees of truth. To answer such queries, we extend a well-known technique that reduces the fuzzy ontology to a classical one, and use classical DL reasoners as a black box. We improve the complexity of previous reduction techniques for finitely valued fuzzy DLs, which allows us to prove tight complexity results for answering certain kinds of fuzzy CQs. We conclude with an experimental evaluation of a prototype implementation, showing the feasibility of our approach.

This paper contains the consideration of knowledge extraction mechanisms of such object-oriented knowledge representation models as frames, object-oriented programming and object-oriented dynamic networks. In addition, conception of universal exploiters within object-oriented dynamic networks is also discussed. The main result of the paper is introduction of new exploiters-based knowledge extraction approach, which provides generation of a finite set of new classes of objects, based on the basic set of classes. The methods for calculation of quantity of new classes, which can be obtained using proposed approach, and of quantity of types, which each of them describes, are proposed. Proof that basic set of classes, extended according to proposed approach, together with union exploiter create upper semilattice is given. The approach always allows generating of finitely defined set of new classes of objects for any object-oriented dynamic network. A quantity of these classes can be precisely calculated before the generation. It allows saving of only basic set of classes in the knowledge base.

We propose a method combining relational-logic representations with neural network learning. A general lifted architecture, possibly reflecting some background domain knowledge, is described through relational rules which may be handcrafted or learned. The relational rule-set serves as a template for unfolding possibly deep neural networks whose structures also reflect the structures of given training or testing relational examples. Different networks corresponding to different examples share their weights, which co-evolve during training by stochastic gradient descent algorithm. The framework allows for hierarchical relational modeling constructs and learning of latent relational concepts through shared hidden layers weights corresponding to the rules. Discovery of notable relational concepts and experiments on 78 relational learning benchmarks demonstrate favorable performance of the method.

Common Representation Learning (CRL), wherein different descriptions (or views) of the data are embedded in a common subspace, is receiving a lot of attention recently. Two popular paradigms here are Canonical Correlation Analysis (CCA) based approaches and Autoencoder (AE) based approaches. CCA based approaches learn a joint representation by maximizing correlation of the views when projected to the common subspace. AE based methods learn a common representation by minimizing the error of reconstructing the two views. Each of these approaches has its own advantages and disadvantages. For example, while CCA based approaches outperform AE based approaches for the task of transfer learning, they are not as scalable as the latter. In this work we propose an AE based approach called Correlational Neural Network (CorrNet), that explicitly maximizes correlation among the views when projected to the common subspace. Through a series of experiments, we demonstrate that the proposed CorrNet is better than the above mentioned approaches with respect to its ability to learn correlated common representations. Further, we employ CorrNet for several cross language tasks and show that the representations learned using CorrNet perform better than the ones learned using other state of the art approaches.

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space that spans the conditional means, it is possible to consistently recover the structure using only information up to the second moments of these random variables. This finding, specialized to one-parameter exponential families whose variance function is quadratic in their means, allows for the derivation of an explicit estimator of such latent structure. This approach serves as a latent variable model estimator and as a tool for dimension reduction for a high-dimensional matrix of data composed of many related variables. Our theoretical results are verified by simulation studies and an application to genomic data.