In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.1. INTRODUCTION Identification of systems from quantized data finds applications in a wide range of areas such as communications, networked control systems, bioinformatics (see e.g.

Social trust prediction addresses the significant problem of exploring interactions among users in social networks. Naturally, this problem can be formulated in the matrix completion framework, with each entry indicating the trustness or distrustness. However, there are two challenges for the social trust problem: 1) the observed data are with sign (1-bit) measurements; 2) they are typically sampled non-uniformly. Most of the previous matrix completion methods do not well handle the two issues. Motivated by the recent progress of max-norm, we propose to solve the problem with a 1-bit max-norm constrained formulation. Since max-norm is not easy to optimize, we utilize a reformulation of max-norm which facilitates an efficient projected gradient decent algorithm. We demonstrate the superiority of our formulation on two benchmark datasets.

Most of previous work in knowledge base (KB) completion has focused on the problem of relation extraction. In this work, we focus on the task of inferring missing entity type instances in a KB, a fundamental task for KB competition yet receives little attention. Due to the novelty of this task, we construct a large-scale dataset and design an automatic evaluation methodology. Our knowledge base completion method uses information within the existing KB and external information from Wikipedia. We show that individual methods trained with a global objective that considers unobserved cells from both the entity and the type side gives consistently higher quality predictions compared to baseline methods. We also perform manual evaluation on a small subset of the data to verify the effectiveness of our knowledge base completion methods and the correctness of our proposed automatic evaluation method.

There is rising interest in vector-space word embeddings and their use in NLP, especially given recent methods for their fast estimation at very large scale. Nearly all this work, however, assumes a single vector per word type--ignoring polysemy and thus jeopardizing their usefulness for downstream tasks. We present an extension to the Skip-gram model that efficiently learns multiple embeddings per word type. It differs from recent related work by jointly performing word sense discrimination and embedding learning, by non-parametrically estimating the number of senses per word type, and by its efficiency and scalability. We present new state-of-the-art results in the word similarity in context task and demonstrate its scalability by training with one machine on a corpus of nearly 1 billion tokens in less than 6 hours.

Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoyed great popularity. In the present paper, we argue that such regularization may no longer be necessary if the underlying matrix is symmetric positive semidefinite (\textsf{spd}) and the design satisfies certain conditions. In this situation, simple least squares estimation subject to an \textsf{spd} constraint may perform as well as regularization-based approaches with a proper choice of the regularization parameter, which entails knowledge of the noise level and/or tuning. By contrast, constrained least squares estimation comes without any tuning parameter and may hence be preferred due to its simplicity.

We developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to characterize the mechanisms underlying the time series. Motivated by the studies that show many normal physiological systems involve irregularity while the decrease of irregularity usually implies the abnormality, the statistics for "outliers" in the components are used as features measuring irregularity. Support vector machines are used to select the most relevant features that are able to differentiate the time series from normal and abnormal systems. This new approach is successfully used in the study of congestive heart failure by heart beat interval time series.

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussian quadrature based methods with suitably selected covariance functions. We show that this interpretation also extends to more general multivariate Gauss--Hermite integration methods and related spherical cubature rules. Additionally, we discuss different criteria for selecting the sigma-point locations: exactness for multivariate polynomials up to a given order, minimum average error, and quasi-random point sets. The performance of the different methods is tested in numerical experiments.

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory. Kernel methods use an implicit mapping of the input data into a high dimensional feature space defined by a kernel function, i.e., a function returning the inner product between the images of two data points in the feature space. Central to any kernel method is the kernel matrix, which is built by evaluating the kernel function on a given sample dataset. In this paper, we initiate the study of non-asymptotic spectral theory of random kernel matrices. These are n x n random matrices whose (i,j)th entry is obtained by evaluating the kernel function on $x_i$ and $x_j$, where $x_1,...,x_n$ are a set of n independent random high-dimensional vectors. Our main contribution is to obtain tight upper bounds on the spectral norm (largest eigenvalue) of random kernel matrices constructed by commonly used kernel functions based on polynomials and Gaussian radial basis. As an application of these results, we provide lower bounds on the distortion needed for releasing the coefficients of kernel ridge regression under attribute privacy, a general privacy notion which captures a large class of privacy definitions. Kernel ridge regression is standard method for performing non-parametric regression that regularly outperforms traditional regression approaches in various domains. Our privacy distortion lower bounds are the first for any kernel technique, and our analysis assumes realistic scenarios for the input, unlike all previous lower bounds for other release problems which only hold under very restrictive input settings.

The marginal log-likelihood is a key concept of Bayesian model identification of latent variable models (LVMs), such as mixture models (MMs), probabilistic principal component analysis, and hidden Markov models (HMMs). Determination of dimensionality of latent variables is an essential task to uncover hidden structures behind the observed data as well as to mitigate overfitting. In general, LVMs are singular (i.e., mapping between parameters and probabilistic models is not one-to-one) and such classical information criteria based on the regularity assumption as the Bayesian information criterion (BIC) [Schwarz, 1978] are no longer justified. Since exact evaluation of 1 the marginal log-likelihood is often not available, approximation techniques have been developed using sampling (i.e., Markov Chain Monte Carlo methods (MCMCs) [Hastings, 1970]), a variational lower bound (i.e., the variational Bayes methods (VB) [Attias, 1999, Jordan et al., 1999]), or algebraic geometry (i.e., the widely applicable BIC (WBIC) [Watanabe, 2013]). However, model selection using these methods typically requires heavy computational cost (e.g., a large number of MCMC sampling in a high-dimensional space, an outer loop for VB/WBIC.) In the last few years, a new approximation technique and an inference method, factorized information criterion (FIC) and factorized asymptotic Bayesian inference (FAB), have been developed for some binary LVMs [Fujimaki and Morinaga, 2012, Fujimaki and Hayashi, 2012, Hayashi and Fujimaki, 2013, Eto et al., 2014]. Unlike existing methods which evaluate approximated marginal log-likelihoods calculated for each latent variable dimensionality (and therefore need an outer loop for model selection), FAB finds an effective dimensionality via an EMstyle alternating optimization procedure.

Community detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging systems or folksonomies. A folksonomy is a tripartite 3-uniform hypergraph consisting of (user, tag, resource) hyperedges. We posit a probabilistic mixed membership community model, and prove that the tensor method consistently learns the communities under efficient sample complexity and separation requirements.