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.

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.

Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is regularized minimization of the error entropy loss which has recently attracted quite some interest from the viewpoint of consistency and learning rates. This paper shows that such RPL methods have additionally good statistical robustness properties, if the loss function and the kernel are chosen appropriately. We treat two cases of particular interest: (i) a bounded and non-convex loss function and (ii) an unbounded convex loss function satisfying a certain Lipschitz type condition.

High frequency oscillations (HFOs) are a promising biomarker of epileptic brain tissue and activity. HFOs additionally serve as a prototypical example of challenges in the analysis of discrete events in high-temporal resolution, intracranial EEG data. Two primary challenges are 1) dimensionality reduction, and 2) assessing feasibility of classification. Dimensionality reduction assumes that the data lie on a manifold with dimension less than that of the feature space. However, previous HFO analyses have assumed a linear manifold, global across time, space (i.e. recording electrode/channel), and individual patients. Instead, we assess both a) whether linear methods are appropriate and b) the consistency of the manifold across time, space, and patients. We also estimate bounds on the Bayes classification error to quantify the distinction between two classes of HFOs (those occurring during seizures and those occurring due to other processes). This analysis provides the foundation for future clinical use of HFO features and buides the analysis for other discrete events, such as individual action potentials or multi-unit activity.

We study the problem of recovering the subspace spanned by the first $k$ principal components of $d$-dimensional data under the streaming setting, with a memory bound of $O(kd)$. Two families of algorithms are known for this problem. The first family is based on the framework of stochastic gradient descent. Nevertheless, the convergence rate of the family can be seriously affected by the learning rate of the descent steps and deserves more serious study. The second family is based on the power method over blocks of data, but setting the block size for its existing algorithms is not an easy task. In this paper, we analyze the convergence rate of a representative algorithm with decayed learning rate (Oja and Karhunen, 1985) in the first family for the general $k>1$ case. Moreover, we propose a novel algorithm for the second family that sets the block sizes automatically and dynamically with faster convergence rate. We then conduct empirical studies that fairly compare the two families on real-world data. The studies reveal the advantages and disadvantages of these two families.

In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a Hamiltonian Monte Carlo algorithm using a continuous time Markov jump process, and are thus able to escape this constraint. Transition rates in a Markov jump process need only be non-negative. We demonstrate that the new algorithm leads to improved mixing for several example problems, both by evaluating the spectral gap of the Markov operator, and by computing autocorrelation as a function of compute time. We release the algorithm as an open source Python package.

In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is crucial to select the appropriate number of states. We propose a new model selection technique based on the Gap statistics, which uses a null reference distribution on the stable AR filters to check whether adding a new AR state significantly improves the performance of the model. To that end, we define a new distance measure between AR filters based on mean squared prediction error (MSPE), and propose an efficient method to generate random stable filters that are uniformly distributed in the coefficient space. Numerical results are provided to evaluate the performance of the proposed approach.

In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online learning of the hyper-parameters have a constant (rather than cubic) time complexity and a constant (rather than squared) memory requirement in the number of observations, without resorting to approximations. Moreover, the proposed model is expressive in that the family of covariance functions of the implied latent process, namely the spectral Matern kernels, have recently been proven to be capable of approximating arbitrarily well any translation-invariant covariance function. The benefit of our approach compared to competing models is demonstrated using experiments on several real-life datasets.

We compare and contrast two approaches to validating a trained classifier while using all in-sample data for training. One is simultaneous validation over an organized set of hypotheses (SVOOSH), the well-known method that began with VC theory. The other is withhold and gap (WAG). WAG withholds a validation set, trains a holdout classifier on the remaining data, uses the validation data to validate that classifier, then adds the rate of disagreement between the holdout classifier and one trained using all in-sample data, which is an upper bound on the difference in error rates. We show that complex hypothesis classes and limited training data can make WAG a favorable alternative.

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approaches such as spectral mixture kernels and sparse spectrum kernels. Our extension has two primary advantages. Firstly, unlike existing spectral approaches that yield infinite differentiability, the kernels we introduce allow learning the degree of differentiability of the latent function in Gaussian process (GP) models and functions in the reproducing kernel Hilbert space (RKHS) in other kernel methods. Secondly, we show that some of the kernels we propose require fewer parameters than existing spectral kernels for the same accuracy, thereby leading to faster and more robust inference. Finally, we generalize our approach and propose a flexible and tractable family of spectral kernels that we prove can approximate any continuous bounded nonstationary kernel.