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Abstract: There is a growing interest in the literature for adaptive Markov chain Monte Carlo methods based on sequences of random transition kernels $\P_n\$ where the kernel $P_n$ is allowed to have an invariant distribution $\pi_n$ not necessarily equal to the distribution of interest $\pi$ (target distribution). The... |
Title: A D.C. Programming Approach to the Sparse Generalized Eigenvalue Problem |
Abstract: In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA), sparse can... |
Title: Joint universal lossy coding and identification of stationary mixing sources with general alphabets |
Abstract: We consider the problem of joint universal variable-rate lossy coding and identification for parametric classes of stationary $\beta$-mixing sources with general (Polish) alphabets. Compression performance is measured in terms of Lagrangians, while identification performance is measured by the variational dis... |
Title: Achievability results for statistical learning under communication constraints |
Abstract: The problem of statistical learning is to construct an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d. training sample from their joint distribution. Allowable predictors are constrained to lie in some specified class, and the goal is to approach... |
Title: Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems |
Abstract: Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that A... |
Title: SPADES and mixture models |
Abstract: This paper studies sparse density estimation via $\ell_1$ penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability de... |
Title: Hiding Quiet Solutions in Random Constraint Satisfaction Problems |
Abstract: We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the planted random ensemble. We study the structural phase transitions, a... |
Title: Discovering Global Patterns in Linguistic Networks through Spectral Analysis: A Case Study of the Consonant Inventories |
Abstract: Recent research has shown that language and the socio-cognitive phenomena associated with it can be aptly modeled and visualized through networks of linguistic entities. However, most of the existing works on linguistic networks focus only on the local properties of the networks. This study is an attempt to a... |
Title: Bayesian Computation and Model Selection in Population Genetics |
Abstract: Until recently, the use of Bayesian inference in population genetics was limited to a few cases because for many realistic population genetic models the likelihood function cannot be calculated analytically . The situation changed with the advent of likelihood-free inference algorithms, often subsumed under t... |
Title: Sparse Causal Discovery in Multivariate Time Series |
Abstract: Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to cau... |
Title: The Redundancy of a Computable Code on a Noncomputable Distribution |
Abstract: We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of sequences may be singled out almost surely with respect to certain pr... |
Title: Beyond word frequency: Bursts, lulls, and scaling in the temporal distributions of words |
Abstract: Background: Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication. More recent research has also identified scaling regularities in the dy... |
Title: A Limit Theorem in Singular Regression Problem |
Abstract: In statistical problems, a set of parameterized probability distributions is used to estimate the true probability distribution. If Fisher information matrix at the true distribution is singular, then it has been left unknown what we can estimate about the true distribution from random samples. In this paper,... |
Title: Maximum Entropy Discrimination Markov Networks |
Abstract: In this paper, we present a novel and general framework called \it Maximum Entropy Discrimination Markov Networks (MaxEnDNet), which integrates the max-margin structured learning and Bayesian-style estimation and combines and extends their merits. Major innovations of this model include: 1) It generalizes the... |
Title: State Space Realization Theorems For Data Mining |
Abstract: In this paper, we consider formal series associated with events, profiles derived from events, and statistical models that make predictions about events. We prove theorems about realizations for these formal series using the language and tools of Hopf algebras. |
Title: A process very similar to multifractional Brownian motion |
Abstract: In Ayache and Taqqu (2005), the multifractional Brownian (mBm) motion is obtained by replacing the constant parameter $H$ of the fractional Brownian motion (fBm) by a smooth enough functional parameter $H(.)$ depending on the time $t$. Here, we consider the process $Z$ obtained by replacing in the wavelet exp... |
Title: On finitely recursive programs |
Abstract: Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable model semantics is highly undecidable. In this paper we prove that a la... |
Title: Universal Complex Structures in Written Language |
Abstract: Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word frequencies. Zipf's law appears to be universal, and may not even be unique ... |
Title: An Upper Limit of AC Huffman Code Length in JPEG Compression |
Abstract: A strategy for computing upper code-length limits of AC Huffman codes for an 8x8 block in JPEG Baseline coding is developed. The method is based on a geometric interpretation of the DCT, and the calculated limits are as close as 14% to the maximum code-lengths. The proposed strategy can be adapted to other tr... |
Title: The Benefit of Group Sparsity |
Abstract: This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group str... |
Title: Detection of Change--Points in the Spectral Density. With Applications to ECG Data |
Abstract: We propose a new method for estimating the change-points of heart rate in the orthosympathetic and parasympathetic bands, based on the wavelet transform in the complex domain and the study of the change-points in the moments of the modulus of these wavelet transforms. We observe change-points in the distribut... |
Title: Statistical analysis of the Indus script using $n$-grams |
Abstract: The Indus script is one of the major undeciphered scripts of the ancient world. The small size of the corpus, the absence of bilingual texts, and the lack of definite knowledge of the underlying language has frustrated efforts at decipherment since the discovery of the remains of the Indus civilisation. Recen... |
Title: Matrix Completion from a Few Entries |
Abstract: Let M be a random (alpha n) x n matrix of rank r<<n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(rn) observed entries with relative root mean square error RMSE <= C(rn/|E|)^0.5 . Further, if r=O(1), M can be recons... |
Title: Model-Consistent Sparse Estimation through the Bootstrap |
Abstract: We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in low-dimensional settings. For various decays of the regularization pa... |
Title: Approaching the linguistic complexity |
Abstract: We analyze the rank-frequency distributions of words in selected English and Polish texts. We compare scaling properties of these distributions in both languages. We also study a few small corpora of Polish literary texts and find that for a corpus consisting of texts written by different authors the basic sc... |
Title: Unsupervised bayesian convex deconvolution based on a field with an explicit partition function |
Abstract: This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function. To the best of our knowledge, this is an original contribution. Moreover, the explicit expression of the partition function enables the development of an unsupervised edge-preserving convex deconvolution me... |
Title: Zonal polynomials and hypergeometric functions of quaternion matrix argument |
Abstract: We define zonal polynomials of quaternion matrix argument and deduce some important formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we give the distributions of the largest and smallest eigenvalues of a quaternion central Wishart matrix $W\simW(n,\S... |
Title: Infinitesimally Robust Estimation in General Smoothly Parametrized Models |
Abstract: We describe the shrinking neighborhood approach of Robust Statistics, which applies to general smoothly parametrized models, especially, exponential families. Equal generality is achieved by object oriented implementation of the optimally robust estimators. We evaluate the estimates on real datasets from lite... |
Title: Automating Access Control Logics in Simple Type Theory with LEO-II |
Abstract: Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory (which is also known as higher-order logic... |
Title: Resource Adaptive Agents in Interactive Theorem Proving |
Abstract: We introduce a resource adaptive agent mechanism which supports the user in interactive theorem proving. The mechanism uses a two layered architecture of agent societies to suggest appropriate commands together with possible command argument instantiations. Experiments with this approach show that its effecti... |
Title: On the Dual Formulation of Boosting Algorithms |
Abstract: We study boosting algorithms from a new perspective. We show that the Lagrange dual problems of AdaBoost, LogitBoost and soft-margin LPBoost with generalized hinge loss are all entropy maximization problems. By looking at the dual problems of these boosting algorithms, we show that the success of boosting alg... |
Title: A remark on higher order RUE-resolution with EXTRUE |
Abstract: We show that a prominent counterexample for the completeness of first order RUE-resolution does not apply to the higher order RUE-resolution approach EXTRUE. |
Title: Equations for hidden Markov models |
Abstract: We will outline novel approaches to derive model invariants for hidden Markov and related models. These approaches are based on a theoretical framework that arises from viewing random processes as elements of the vector space of string functions. Theorems available from that framework then give rise to novel ... |
Title: Enhancing the capabilities of LIGO time-frequency plane searches through clustering |
Abstract: One class of gravitational wave signals LIGO is searching for consists of short duration bursts of unknown waveforms. Potential sources include core collapse supernovae, gamma ray burst progenitors, and mergers of binary black holes or neutron stars. We present a density-based clustering algorithm to improve ... |
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