wavelet analysis for hopf bifurcations with aeroelastic applications abstract a wavelet analysis on the output signal of a non linear system in the neighbourhood of a hopf bifurcation i e a limit cycle oscillation has been performed to point out the linear and non linear signatures of the system indeed this kind of non linear behaviour is characterized not only by a simple harmonic oscillation in developed steady state condition but also by an initial transitory phase with a complex time evolution of the spectral signal content both these issues could be described in an analytical way via a singular perturbation analysis but they could be also directly analyzed by a signal processing tool via wavelet analysis continuous wavelet transform cwt this is obtained by using the wavelet capability in describing efficiently the time evolution of the spectrum of the signal i e a non linear signature of a hopf bifurcation furthermore the analytical results given by the singular perturbation analysis for the same class of non linear problems have allowed one to interpret correctly the results obtained by the wavelet analysis in this paper this theoretical link between the wavelet analysis and the output signal of a dynamical system recently achieved for linear mechanical damped systems has been extended to non linear systems in the neighbourhood of a hopf bifurcation this kind of analysis is of natural interest in aeroelastic applications where an efficient and noise insensitive analysis of the output signal recorded during the flight tests performed in the neighbourhood of the critical condition flutter may be desirable together with the capability to record the non linear system signature the time scale decompositions cwt have given the opportunity to analyze pre and post critical transient behaviour of a non linear aeroelastic system and thus upon considering the analytical tool given by the singular perturbation analysis to identify its linear and non linear features applications include either two non linear coupled oscillators or a typical section in a supersonic flow

explicit expressions for green ampt delta function diffusivity infiltration rate and cumulative storage the sharp wetting front model of infiltration green and ampt 1911 philip 1954 yields through simple integration an exact solution relating the infiltration rate i cumulative infiltration i and time t the relation however is implicit for i or i i e it is of the form t a i b ln 1 i b numerical iteration is required to find the infiltration rate and furthermore analytic manipulations are limited using this traditional formulation of the green ampt infiltration in this note we present an accurate expression for the infiltration rate in the form of a rapidly converging series in the variable t t truncating the series at four terms yields a useful expression for i t the proposed four term expression gives less than 2 error at all times and is readily integrated to yield the cumulative infiltration i t in conjunction with the exact expression for time t given i or i the proposed expression is useful in infiltration runoff calculations that necessitate the time compression approximation tca

matrix completion a la dempster by the principle of parsimony dempster s covariance selection method is extended first to general nonsingular matrices and then to full rank rectangular matrices dempster observed that his completion solved a maximum entropy problem we show that our generalized completions are also solutions of a suitable entropy like variational problem

reply to comment on explicit expressions for green ampt delta function diffusivity infiltration rate and cumulative storage by g d salvucci and d entekhabi

the isserlis matrix and its application to non decomposable graphical gaussian models the operations of matrix completion and isserlis matrix construction arise in the statistical analysis of graphical gaussian models in both the bayesian and frequentist approaches in this paper we study the properties of the isserlis matrix of the completion of a positive definite matrix and propose an edge set indexing notation which highlights the symmetry existing between and its isserlis matrix in this way well known properties of can be exploited to give an easy proof of certain asymptotic results for decomposable graphical gaussian models as well as to extend such results to the non decomposable case in particular we consider the asymptotic variance of maximum likelihood estimators the non informative jeffreys prior the laplace approximation to the bayes factor the asymptotic distribution of the maximum likelihood estimators and the asymptotic posterior distribution of the parameters in a bayesian conjugate analysis in dealing with distributions over non decomposable models an extension of the hyper markov property to models with non chordal graphs is required our proposed extension is justified by an analysis of the conditional independence structure of the sufficient statistic

an efficient algorithm for maximum entropy extension of block circulant covariance matrices article history this paper deals with maximum entropy completion of partially specified block circulant matrices since positive definite symmet ric circulants happen to be covariance matrices of stationary peri odic processes in particular of stationary reciprocal processes this problem has applications in signal processing in particular to im age modeling in fact it is strictly related to maximum likelihood estimation of bilateral ar type representations of acausal signals subject to certain conditional independence constraints the maxi mum entropy completion problem for block circulant matrices has recently been solved by the authors although leaving open the problem of an efficient computation of the solution in this pa per we provide an efficient algorithm for computing its solution which compares very favorably with existing algorithms designed for positive definite matrix extension problems the proposed al gorithm benefits from the analysis of the relationship between our problem and the band extension problem for block toeplitz matri ces also developed in this paper

on the identification of a single factor model with correlated residuals summary a necessary and sufficient condition for the identification of a single factor model with correlated residuals is derived by studying the zero elements of their concentration matrix in particular the new condition is expressed in terms of the complementary graph of the residuals this graphical condition can be simply checked by means of an efficient algorithm an example is also given showing that sometimes the single factor model with correlated residuals can be used to overcome the problem of non identification of a larger factor model

miscellanea on the generation of the chordless four cycle in the theory of markov graphical representations of conditional independencies a special role is played by the chordless four cycle representing for four random variables the conditional independencies x v u w and w u x v it is not immediately clear how such systems are to be generated here we sketch some possible data generating mechanisms

markov properties of nonrecursive causal models this paper aims to solve an often noted incompatibility between graphical chain models which elucidate the conditional independence structure of a set of random variables and simultaneous equations systems which focus on direct linear interactions and correlations between random variables various authors have argued that the incompatibility arises mainly from the fact that in a simultaneous equations system e g a lisrel model reciprocal causality is possible whereas this is not so in the case of graphical chain models in this article it is shown that this view is not correct in fact the definition of the markov property embodied in a graph can be generalized to a wider class of graphs which includes certain nonrecursive graphs the resulting class of reciprocal graph probability models strictly includes the class of chain graph probability models the class of lattice conditional independence probability models is also strictly included it is shown that the resulting methodology is directly applicable to quite general simultaneous equations systems that are subject to mild restrictions only provided some adjustments are made general simultaneous equations systems can be handled as well in all cases consistency with the lisrel methodology is maintained

a convex pseudolikelihood framework for high dimensional partial correlation estimation with convergence guarantees author s khare k oh sy rajaratnam b abstract 2014 royal statistical society sparse high dimensional graphical model selection is a topic of much interest in modern day statistics a popular approach is to apply l1 penalties to either parametric likelihoods or regularized regression pseudolikelihoods with the latter having the distinct advantage that they do not explicitly assume gaussianity as none of the popular methods proposed for solving pseudolikelihood based objective functions have provable convergence guarantees it is not clear whether corresponding estimators exist or are even computable or if they actually yield correct partial correlation graphs we propose a new pseudolikelihood based graphical model selection method that aims to overcome some of the shortcomings of current methods but at the same time retain all their respective strengths in particular we introduce a novel framework that leads to a convex formulation of the partial covariance regression graph problem resulting in an objective function comprised of quadratic forms the objective is then optimized via a co ordinatewise approach the specific functional form of the objective function facilitates rigorous convergence analysis leading to convergence guarantees an important property that cannot be established by using standard results when the dimension is larger than the sample size as is often the case in high dimensional applications these convergence guarantees ensure that estimators are well defined under very general conditions and are always computable in addition the approach yields estimators that have good large sample properties and also respect symmetry furthermore application to simulated and real data timing comparisons and numerical convergence is demonstrated we also present a novel unifying framework that places all graphical pseudolikelihood methods as special cases of a more general formulation leading to important insights

embedded trees estimation of gaussian processes on graphs with cycles graphical models provide a powerful general framework for encoding the structure of large scale estimation problems however the graphs describing typical real world phenomena contain many cycles making direct estimation procedures prohibitively costly in this paper we develop an iterative inference algorithm for general gaussian graphical models it operates by exactly solving a series of modified estimation problems on spanning trees embedded within the original cyclic graph when these subproblems are suitably chosen the algorithm converges to the correct conditional means moreover and in contrast to many other iterative methods the tree based procedures we propose can also be used to calculate exact error variances although the conditional mean iteration is effective for quite densely connected graphical models the error variance computation is most efficient for sparser graphs in this context we present a modeling example suggesting that very sparsely connected graphs with cycles may provide significant advantages relative to their tree structured counterparts thanks both to the expressive power of these models and to the efficient inference algorithms developed herein the convergence properties of the proposed tree based iterations are characterized both analytically and experimentally in addition by using the basic tree based iteration to precondition the conjugate gradient method we develop an alternative accelerated iteration that is finitely convergent simulation results are presented that demonstrate this algorithm s effectiveness on several inference problems including a prototype distributed sensing application

a junction tree framework for undirected graphical model selection an undirected graphical model is a joint probability distribution defined on an undirected graph g where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among random variables the undirected graphical model selection ugms problem is to estimate the graph g given observations drawn from the undirected graphical model this paper proposes a framework for decomposing the ugms problem into multiple subproblems over clusters and subsets of the separators in a junction tree the junction tree is constructed using a graph that contains a superset of the edges in g we highlight three main properties of using junction trees for ugms first different regularization parameters or different ugms algorithms can be used to learn different parts of the graph this is possible since the subproblems we identify can be solved independently of each other second under certain conditions a junction tree based ugms algorithm can produce consistent results with fewer observations than the usual requirements of existing algorithms third both our theoretical and experimental results show that the junction tree framework does a significantly better job at finding the weakest edges in a graph than existing methods this property is a consequence of both the first and second properties finally we note that our framework is independent of the choice of the ugms algorithm and can be used as a wrapper around standard ugms algorithms for more accurate graph estimation

a recursive model reduction method for approximate inference in gaussian markov random fields this paper presents recursive cavity modeling a principled tractable approach to approximate near optimal inference for large gauss markov random fields the main idea is to subdivide the random field into smaller subfields constructing cavity models which approximate these subfields each cavity model is a concise yet faithful model for the surface of one subfield sufficient for near optimal inference in adjacent subfields this basic idea leads to a tree structured algorithm which recursively builds a hierarchy of cavity models during an ldquoupward passrdquo and then builds a complementary set of blanket models during a reverse ldquodownward pass rdquo the marginal statistics of individual variables can then be approximated using their blanket models model thinning plays an important role allowing us to develop thinned cavity and blanket models thereby providing tractable approximate inference we develop a maximum entropy approach that exploits certain tractable representations of fisher information on thin chordal graphs given the resulting set of thinned cavity models we also develop a fast preconditioner which provides a simple iterative method to compute optimal estimates thus our overall approach combines recursive inference variational learning and iterative estimation we demonstrate the accuracy and scalability of this approach in several challenging large scale remote sensing problems

partial correlation matrix estimation using ridge penalty followed by thresholding and re estimation motivated by the problem of construction gene co expression network we propose a statistical framework for estimating high dimensional partial correlation matrix by a three step approach we first obtain a penalized estimate of a partial correlation matrix using ridge penalty next we select the non zero entries of the partial correlation matrix by hypothesis testing finally we reestimate the partial correlation coefficients at these non zero entries in the second step the null distribution of the test statistics derived from penalized partial correlation estimates has not been established we address this challenge by estimating the null distribution from the empirical distribution of the test statistics of all the penalized partial correlation estimates extensive simulation studies demonstrate the good performance of our method application on a yeast cell cycle gene expression data shows that our method delivers better predictions of the protein protein interactions than the graphic lasso

the gaussian many help one distributed source coding problem jointly gaussian memoryless sources are observed at n distinct terminals the goal is to efficiently encode the observations in a distributed fashion so as to enable reconstruction of any one of the observations say the first one at the decoder subject to a quadratic fidelity criterion our main result is a precise characterization of the rate distortion region when the covariance matrix of the sources satisfies a tree structure condition in this situation a natural analog digital separation scheme optimally trades off the distributed quantization rate tuples and the distortion in the reconstruction each encoder consists of a point to point gaussian vector quantizer followed by a slepian wolf binning encoder we also provide a partial converse that suggests that the tree structure condition is fundamental

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

wavelet analysis of time series for the duffing oscillator the detection of order within chaos we consider a wavelet analysis of various time series for the duffing oscillator for which there is a potential maximum and a harmonic forcing term and we focus on time series that return to the region of the potential maximum when the dynamics is chaotic and the time series is highly nonstationary there are many significant higher harmonics in a fourier expansion and the usual fourier analysis is problematic especially for short total times we show that the wavelet analysis is a robust tool that may be used to obtain qualitative information for highly nonstationary time series specifically that it may be used to detect a small amplitude harmonic forcing term even when the dynamics is chaotic and even for short total times

a generalized levinson algorithm for covariance extension with application to multiscale autoregressive modeling efficient computation of extensions of banded partially known covariance matrices is provided by the classical levinson algorithm one contribution of this paper is the introduction of a generalization of this algorithm that is applicable to a substantially broader class of extension problems this generalized algorithm can compute unknown covariance elements in any order that satisfies certain graph theoretic properties which we describe this flexibility which is not provided by the classical levinson algorithm is then harnessed in a second contribution of this paper the identification of a multiscale autoregressive mar model for the maximum entropy me extension of a banded partially known covariance matrix the computational complexity of mar model identification is an order of magnitude below that of explicitly computing a full covariance extension and is comparable to that required to build a standard autoregressive ar model using the classical levinson algorithm

covariance decomposition in undirected gaussian graphical models the covariance between two variables in a multivariate gaussian distribution is decomposed into a sum of path weights for all paths connecting the two variables in an undirected independence graph these weights are useful in determining which variables are important in mediating correlation between the two path endpoints the decomposition arises in undirected gaussian graphical models and does not require or involve any assumptions of causality this covariance decomposition is derived using basic linear algebra the decomposition is feasible for very large numbers of variables if the corresponding precision matrix is sparse a circumstance that arises in examples such as gene expression studies in functional genomics additional computational efficiences are possible when the undirected graph is derived from an acyclic directed graph

an incomplete data approach to the analysis of covariance structures in this paper linear structural equation models with latent variables are considered it is shown how many common models arise from incomplete observation of a relatively simple system subclasses of models with conditional independence interpretations are also discussed using an incomplete data point of view the relationships between the incomplete and complete data likelihoods assuming normality are highlighted for computing maximum likelihood estimates the em algorithm and alternatives are surveyed for the alternative algorithms simplified expressions for computing function values and derivatives are given likelihood ratio tests based on complete and incomplete data are related and an example on using their relationship to improve the fit of a model is given

state space realizations and optimal smoothing for gaussian generalized reciprocal processes this technical note derives stochastic realization and optimal smoothing algorithms for a class of gaussian generalized reciprocal processes ggrp the note exploits the interplay between reciprocal processes and markov bridges which underpin the ggrp model a forward backward algorithm for stochastic realization of ggrp is described the form on the inverse covariance matrix for the ggrp is used via cholesky factorization to derive a procedure for optimal mmse smoothing of ggrp observed in noise the note demonstrates that the associated smoothing error is also a ggrp with known covariance which may be used to assess the performance of smoothing as a function of the model parameters a numerical example is provided to illustrate the performance of the mmse smoother compared to those derived from compatible markov and reciprocal model based algorithms

estimation in gaussian graphical models using tractable subgraphs a walk sum analysis graphical models provide a powerful formalism for statistical signal processing due to their sophisticated modeling capabilities they have found applications in a variety of fields such as computer vision image processing and distributed sensor networks in this paper we present a general class of algorithms for estimation in gaussian graphical models with arbitrary structure these algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables this framework includes parallel iterations such as embedded trees serial iterations such as block gauss seidel and hybrid versions of these iterations we also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications we analyze these algorithms based on the recently developed walk sum interpretation of gaussian inference we describe the walks ldquocomputedrdquo by the algorithms using walk sum diagrams and show that for iterations based on a very large and flexible set of sequences of subgraphs convergence is guaranteed in walk summable models consequently we are free to choose spanning trees and subsets of variables adaptively at each iteration this leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional one tree and two tree iterations

analysis of wavelets in chaotic states for a one degree of freedom system with viscoelastic restraints a qualitative numerical technique is presented for identifying chaotic states of a non linear one sided constrained one degree of freedom 1 d o f deterministic system under a dynamic non conservative load discrete wavelet analysis in its classic and packet versions was used to search for the boundaries of chaotic and non chaotic solutions the results obtained were verified by an analysis of the lyapunov exponents of the investigated system on the basis of numerical tests one can state that wavelet analysis may be a fast and reliable tool suitable for searching for the boundaries of chaotic and non chaotic solutions

on the geometry of maximum entropy problems we show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite dimensional maximum entropy problems concerning probability distributions spectral densities and covariance matrices these include burg s spectral estimation method and dempster s covariance completion as well as various recent generalizations of the above we then apply this orthogonality principle to the new problem of completing a block circulant covariance matrix when an a priori estimate is available

hierarchical interaction models lauritzen and wermuth have proposed a class of models for mixed qualitative and continuous data defined by two properties that the continuous variables are normally distributed given the qualitative variables and that a set of conditional independence relations hold between specified pairs of variables the present paper examines an extension to this class called hierarchical interaction models a compact form for model representation is described and an estimation algorithm is given some properties of the models a compact form for model representation is described and an estimation algorithm is given some properties of the models concerning marginalization and conditioning are examined the class includes and generalizes hierarchical log linear models standard fixed effect anova multivariate anova and multivariate regression models

robust distributed estimation using the embedded subgraphs algorithm we propose a new iterative distributed approach for linear minimum mean square error lmmse estimation in graphical models with cycles the embedded subgraphs algorithm esa decomposes a loopy graphical model into a number of linked embedded subgraphs and applies the classical parallel block jacobi iteration comprising local lmmse estimation in each subgraph involving inversion of a small matrix followed by an information exchange between neighboring nodes and subgraphs our primary application is sensor networks where the model encodes the correlation structure of the sensor measurements which are assumed to be gaussian the resulting lmmse estimation problem involves a large matrix inverse which must be solved in network with distributed computation and minimal intersensor communication by invoking the theory of asynchronous iterations we prove that esa is robust to temporary communication faults such as failing links and sleeping nodes and enjoys guaranteed convergence under relatively mild conditions simulation studies demonstrate that esa compares favorably with other recently proposed algorithms for distributed estimation simulations also indicate that energy consumption for iterative estimation increases substantially as more links fail or nodes sleep thus somewhat surprisingly sensor network energy conservation strategies such as low powered transmission and aggressive sleep schedules could actually prove counterproductive our results can be replicated using matlab code from www dsp rice edu software

damping identification in multi degree of freedom systems via a wavelet logarithmic decrement part 1 theory a wavelet based formula similar to the logarithmic decrement formula is introduced to estimate damping in multi degree of freedom systems from time domain responses both analytical and numerical approaches are investigated

robust gaussian graphical modeling via l1 penalization gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks however gene expression data typically have heavier tails or more outlying observations than the standard gaussian distribution such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes we propose a l1 penalized estimation procedure for the sparse gaussian graphical models that is robustified against possible outliers the likelihood function is weighted according to how the observation is deviated where the deviation of the observation is measured based on its own likelihood an efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified likelihood where nonzero elements of the concentration matrix represents the graphical links among the genes after the graphical structure is obtained we re estimate the positive definite concentration matrix using an iterative proportional fitting algorithm through simulations we demonstrate that the proposed robust method performs much better than the graphical lasso for the gaussian graphical models in terms of both graph structure selection and estimation when outliers are present we apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical lasso

numerical evaluation of a set of analytical infiltration equations in this paper a set of analytical infiltration equations that are commonly used to evaluate one and three dimensional water infiltration from a surface disc source is studied both the quasi exact analytical formulation and the related approximations for short and long times are assessed the analytical properties of the quasi exact formulation are evaluated using a proposed scaling procedure in order to define the validity domains of related approximations both quasi exact and approximate analytical equations are then studied with respect to their ability to reproduce numerically generated cumulative infiltrations from a 10 cm radius disc source for four soils sand loam silt and silty clay at several initial saturations the quasi exact formulation is suitable for sand loam and silt when their soil dependent and saturation independent shape parameters and are properly chosen between 0 75 and 1 and 0 3 and 1 7 respectively approximations derived for the same shape parameters can also be used provided that their use is restricted to proposed validity intervals however none of these equations applies for silty clay since its hydraulic properties do not fulfill the conditions required for the use of the quasi exact formulation

completing a block diagonal matrix with a partially prescribed inverse abstract a complete solution of the matrix completion problem a b 1 c d is obtained in terms of solutions of a riccati type matrix equation several special cases are described in detail

series solution for richards equation under concentration boundary conditions and uniform initial conditions a series solution which expresses the moisture profiles and surface fluxes during infiltration and exfiltration is derived the solution applies for conditions of fixed surface moisture content and uniform initial moisture content within an unbounded homogeneous nonhysteretic soil column the series derivation is similar to j r philip s but with a transformed time variable the series converges for infiltration problems involving soils which exhibit steep increase in capillary pressure near saturation under these conditions the solution captures the transition from early square root of time behavior to the longtime traveling wave solution without the use of approximate joining techniques the soil water retention models for which convergence occurs include the widely applied brooks corey and van genuchten models with minor restrictions on the shape parameters of the latter other cases examined include infiltration and exfiltration assuming power law linear quadratic and constant dependence of diffusivity and conductivity on moisture content for these cases the convergence limits were finite the solution is particularly well suited for infiltration into sandy soils for which the transition between short time and longtime behavior occurs relatively early

an analytical solution of richards equation providing the physical basis of scs curve number method and its proportionality relationship the empirical proportionality relationship which indicates that the ratio of cumulative surface runoff and infiltration to their corresponding potentials are equal is the basis of the extensively used soil conservation service curve number scs cn method the objective of this paper is to provide the physical basis of the scs cn method and its proportionality hypothesis from the infiltration excess runoff generation perspective to achieve this purpose an analytical solution of richards equation is derived for ponded infiltration in shallow water table environment under the following boundary conditions 1 the soil is saturated at the land surface and 2 there is a no flux boundary which moves downward the solution is established based on the assumptions of negligible gravitational effect constant soil water diffusivity and hydrostatic soil moisture profile between the no flux boundary and water table based on the derived analytical solution the proportionality hypothesis is a reasonable approximation for rainfall partitioning at the early stage of ponded infiltration in areas with a shallow water table for coarse textured soils this article is protected by copyright all rights reserved

robust estimators for nondecomposable elliptical graphical models robust estimators of the restricted covariance matrices associated with elliptical graphical models are studied general asymptotic results which apply to both decomposable and nondecomposable graphical models are presented for robust plug in type estimators these extend results previously established only for the decomposable case furthermore a class of graphical m estimators for the restricted covariance matrices is introduced and compared with the corresponding plug in m estimators the two approaches are shown to be asymptotically equivalent under random sampling from an elliptical distribution a simulation study demonstrates the superiority of the graphical m estimators for small samples

partial gaussian graphical model estimation this paper studies the partial estimation of gaussian graphical models from high dimensional empirical observations we derive a convex formulation for this problem using l1 regularized maximum likelihood estimation which can be solved via a smoothing approximation algorithm statistical estimation performance can be established for our method the proposed approach has competitive empirical performance compared with existing methods as demonstrated by various experiments on synthetic and real data sets

exponential dispersion models on etudie les proprietes generales de la classe des modeles de dispersion exponentiels qui est la generalisation multivariable des modeles de distribution d erreur de nelder et wedderburn 1972

wavelet based compression and feature selection for vibration analysis this paper is concerned with wavelet based linear transformations for data compression and feature selection in vibration analysis recent developments in wavelet data compression are summarized a discussion of various types of data including periodic continuous non stationary and transient non stationary signals are used to show practical aspects of wavelet compression the analysis employs smooth wavelets and compactly supported wavelets it has been shown that compression in vibration analysis can be used not only for effective storage and transmission of the data but also for feature selection a number of different approaches have been presented to show coefficient selection procedures this includes procedures based on truncated wavelet coefficients according to their amplitude position and frequency location and a data compression technique based on optimal wavelet coefficients

covariance estimation in decomposable gaussian graphical models graphical models are a framework for representing and exploiting prior conditional independence structures within distributions using graphs in the gaussian case these models are directly related to the sparsity of the inverse covariance concentration matrix and allow for improved covariance estimation with lower computational complexity we consider concentration estimation with the mean squared error mse as the objective in a special type of model known as decomposable this model includes for example the well known banded structure and other cases encountered in practice our first contribution is the derivation and analysis of the minimum variance unbiased estimator mvue in decomposable graphical models we provide a simple closed form solution to the mvue and compare it with the classical maximum likelihood estimator mle in terms of performance and complexity next we extend the celebrated stein s unbiased risk estimate sure to graphical models using sure we prove that the mse of the mvue is always smaller or equal to that of the biased mle and that the mvue itself is dominated by other approaches in addition we propose the use of sure as a constructive mechanism for deriving new covariance estimators similarly to the classical mle all of our proposed estimators have simple closed form solutions but result in a significant reduction in mse

decomposition of maximum likelihood in mixed graphical interaction models summary we show how decompositions of marked graphs induce corresponding decompositions of maximum likelihood estimates in mixed graphical interaction models we use this result to obtain explicit formulae for the estimates in decomposable models and to obtain factorizations of likelihood ratio statistics

elliptical graphical modelling we propose elliptical graphical models based on conditional uncorrelatedness as a gen eralization of gaussian graphical models by letting the population distribution be elliptical instead of normal allowing the tting of data with arbitrarily heavy tails we study the class of propor tionally ane equivariant scatter estimators and show how they can be used to perform elliptical graphical modelling leading to a new class of partial correlation estimators and analogues of the classical deviance test general expressions for the asymptotic variance of partial correlation esti mators unconstrained and under decomposable models are given and the asymptotic chi square approximation of the pseudo deviance test statistic is proved the feasibility of our approach is demonstrated by a simulation study using among others tyler s scatter estimator which is distribution free within the elliptical model our approach provides a robustication of gauss ian graphical modelling the latter is likelihood based and known to be very sensitive to model misspecication and outlying observations 1 introduction and notation the statistical theory of undirected graphical models for continuous variables is usually based on the assumption of multivariate normality in practice data may deviate from the normal model in various ways outliers and heavy tails pose a problem of particular gravity they frequently occur and the normal likelihood methods such as the sample covariance matrix are very susceptible to them our objective is to deal with heavy tailed data and to safeguard graphical modelling against the impact of faulty outliers we restrict our attention to the case where we have only continuous variables and only undirected edges joint multivariate normality is often assumed in this situation and the statistical methodology is called gaussian graphical modelling we propose the class of elliptical distributions as a more general model and call our approach elliptical graphical modelling the lack of robustness of gaussian graphical modelling has been noted by several authors four proposals of robust approaches to gaussian graphical modelling are known to us becker 2005 and gottard and pacillo 2010 suggest replacing the sample covariance matrix by the reweighted minimum covariance determinant estimator miyamura and kano 2006 propose an alternative m type estimation and finegold drton arxiv 1009 3669 consider robustied versions of the graphical lasso by friedman et al 2008 this article delivers a systematic treatment of the plug in approach used in the rst two ref erences we show that the sample covariance matrix may be replaced by any ane equivariant

wavelet based analysis of the non stationary response of a slipping foundation a wavelet based stochastic formulation has been presented in this paper for the seismic analysis of a rigid block resting on a friction base the ground motion has been modelled as a non stationary process both in amplitude and frequency by using wavelets the proposed formulation is based on replacing the non linear system by an equivalent linear system with time dependent properties the expressions of the instantaneous damping root mean square r m s velocity response and the power spectral density function psdf of the velocity response have been obtained in terms of the input wavelet coefficients for validation of the formulation simulation based on twenty synthetically generated time histories corresponding to an example ground motion process has been carried out the effectiveness of the base isolation system and the effect of the frequency non stationarity on the non linear response have also been studied in detail it has been clearly shown how the frequency non stationarity in the ground motion changes the non linear response

walk sums and belief propagation in gaussian graphical models we present a new framework based on walks in a graph for analysis and inference in gaussian graphical models the key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph the weight of each walk is given by a product of edgewise partial correlation coefficients this representation holds for a large class of gaussian graphical models which we call walk summable we give a precise characterization of this class of models and relate it to other classes including diagonally dominant attractive non frustrated and pairwise normalizable we provide a walk sum interpretation of gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles the walk sum perspective leads to a better understanding of gaussian belief propagation and to stronger results for its convergence in loopy graphs

an efficient approach to graphical modeling of time series a method for selecting a graphical model for p vector valued stationary gaussian time series was recently proposed by matsuda and uses the kullback leibler divergence measure to define a test statistic this statistic was used in a backward selection procedure but the algorithm is prohibitively expensive for large p a high degree of sparsity is not assumed we show that reformulation in terms of a multiple hypothesis test reduces computation time by o p 2 and simulations support the assertion that power levels are attained at least as good as those achieved by matsuda s much slower approach moreover the new scheme is readily parallelizable for even greater speed gains

partial factor modeling predictor dependent shrinkage for linear regression we develop a modified gaussian factor model for the purpose of inducing predictor dependent shrinkage for linear regression the new model predicts well across a wide range of covariance structures on real and simulated data furthermore the new model facilitates variable selection in the case of correlated predictor variables which often stymies other methods

positive definite completions and determinant maximization abstract a method is described for determining whether a positive definite completion of a given partial hermitian matrix exists and if so for finding the determinant maximizing positive definite completion no assumption is made about the arrangement of the specified entries the method employs iterative application to a modified problem of an explicit formula for the maximum determinant in case there is only one symmetrically placed pair of unspecified entries a robust and fast algorithm based upon this approach is shown to have global convergence to the necessarily unique solution

comment on explicit expressions for green ampt delta function diffusivity infiltration rate and cumulative storage by g d salvucci and d entekhabi reference ecol article 1995 002doi 10 1029 95wr00092 url http www agu org record created on 2005 12 09 modified on 2016 11 26

telescoping recursive representations and estimation of gauss markov random fields we present telescoping recursive representations for both continuous and discrete indexed noncausal gauss markov random fields our recursions start at the boundary a hypersurface in and telescope inwards for example for images the telescoping representation reduce recursions from to i e to recursions on a single dimension under appropriate conditions the recursions for the random field are linear stochastic differential difference equations driven by white noise for which we derive recursive estimation algorithms that extend standard algorithms like the kalman bucy filter and the rauch tung striebel smoother to noncausal markov random fields

high dimensional sparse inverse covariance estimation using greedy methods in this paper we consider the task of estimating the non zero pattern of the sparse inverse covariance matrix of a zero mean gaussian random vector from a set of iid samples note that this is also equivalent to recovering the underlying graph structure of a sparse gaussian markov random field gmrf we present two novel greedy approaches to solving this problem the first estimates the non zero covariates of the overall inverse covariance matrix using a series of global forward and backward greedy steps the second estimates the neighborhood of each node in the graph separately again using greedy forward and backward steps and combines the intermediate neighborhoods to form an overall estimate the principal contribution of this paper is a rigorous analysis of the sparsistency of these two greedy procedures that is their consistency in recovering the sparsity pattern of the inverse covariance matrix surprisingly we show that both the local and global greedy methods learn the full structure of the model with high probability given just o d log p samples which is a significant improvement over state of the art 1 regularized gaussian mle graphical lasso that requires o d 2 log p samples moreover the restricted eigenvalue and smoothness conditions imposed by our greedy methods are much weaker than the strong irrepresentable conditions required by the 1 regularization based methods we corroborate our results with extensive simulations and examples comparing our local and

identification of damping in mdof systems using time scale decomposition abstract a method of damping identification in multi degree of freedom systems is presented the method is based on the time scale decomposition of the system impulse response the continuous wavelet transform is used to decompose the impulse response into the time scale domain three techniques based on the wavelet tranform are used to estimate damping these are the wavelet transform cross section procedure the impulse response recovery procedure based on wavelet domain filtering and the wavelet ridge detection procedure the methods are applied to simulated multi degree of freedom systems

graphical models via univariate exponential family distributions undirected graphical models or markov networks are a popular class of statistical models used in a wide variety of applications popular instances of this class include gaussian graphical models and ising models in many settings however it might not be clear which subclass of graphical models to use particularly for non gaussian and non categorical data in this paper we consider a general sub class of graphical models where the node wise conditional distributions arise from exponential families this allows us to derive multivariate graphical model distributions from univariate exponential family distributions such as the poisson negative binomial and exponential distributions our key contributions include a class of m estimators to fit these graphical model distributions and rigorous statistical analysis showing that these m estimators recover the true graphical model structure exactly with high probability we provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from poisson and exponential distributions

learning gradients predictive models that infer geometry and statistical dependence the problems of dimension reduction and inference of statistical dependence are addressed by the modeling framework of learning gradients the models we propose hold for euclidean spaces as well as the manifold setting the central quantity in this approach is an estimate of the gradient of the regression or classification function two quadratic forms are constructed from gradient estimates the gradient outer product and gradient based diffusion maps the first quantity can be used for supervised dimension reduction on manifolds as well as inference of a graphical model encoding dependencies that are predictive of a response variable the second quantity can be used for nonlinear projections that incorporate both the geometric structure of the manifold as well as variation of the response variable on the manifold we relate the gradient outer product to standard statistical quantities such as covariances and provide a simple and precise comparison of a variety of supervised dimensionality reduction methods we provide rates of convergence for both inference of informative directions as well as inference of a graphical model of variable dependencies

gaussian markov distributions over finite graphs on s interesse aux modeles de selection de covariance introduites par dempster 1972 et etudies par wermuth 1976

cholesky decomposition of a hyper inverse wishart matrix the canonical parameter of a covariance selection model is the inverse covariance matrix 1 whose zero pattern gives the conditional independence structure characterising the model in this paper we consider the upper triangular matrix obtained by the cholesky decomposition 1 t this provides an interesting alternative parameterisation of decomposable models since its upper triangle has the same zero structure as 1 and its elements have an interpretation as parameters of certain conditional distributions for a distribution for the strong hyper markov property is shown to be characterised by the mutual independence of the rows of this is further used to generalise to the hyper inverse wishart distribution some well known properties of the inverse wishart distribution in particular we show that a hyper inverse wishart matrix can be decomposed into independent normal and chi squared random variables and we describe a family of transformations under which the family of hyper inverse wishart distributions is closed

globally convergent algorithms for maximizing a likelihood function summary in this paper we show global convergence under very general assumptions of iterative maximization procedures with cyclic fixing of groups of parameters maximizing over the remaining parameters further we show that a slightly modified newton procedure applied to the derivative of the reciprocal likelihood function in a one dimensional exponential family is globally convergent we also prove that if the distribution of the sufficient statistic is infinitely divisible then the newton method applied to the derivative of the log likelihood function converges by combining these results we obtain general globally convergent iterative procedures for maximizing the likelihood function in any regular k dimensional exponential family the likelihood function can be maximized either by successively maximizing over one parameter at a time or by maximizing in the newton direction

graphical gaussian models with edge and vertex symmetries summary we introduce new types of graphical gaussian models by placing symmetry restrictions on the concentration or correlation matrix the models can be represented by coloured graphs where parameters that are associated with edges or vertices of the same colour are restricted to being identical we study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates we identify conditions for restrictions on the concentration and correlation matrices being equivalent this is for example the case when symmetries are generated by permutation of variable labels for such models a particularly simple maximization of the likelihood function is available

on substantive research hypotheses conditional independence graphs and graphical chain models summary graphs consisting of points and lines or arrows as connections between selected pairs of points are used to formulate hypotheses about relations between variables points stand for variables connections represent associations when a missing connection is interpreted as a conditional independence the graph characterizes a conditional independence structure as well statistical models called graphical chain models correspond to special types of graphs which are interpreted in this fashion examples are used to illustrate how conditional independences are reflected in summary statistics derived from the models and how the graphs help to identify analogies and equivalences between different models graphical chain models are shown to provide a unifying concept for many statistical techniques that in the past have proven to be useful in analyses of data they also provide tools for new types of analysis

model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data we consider the problem of estimating the parameters of a gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse our approach is to solve a maximum likelihood problem with an added l1 norm penalty term the problem as formulated is convex but the memory requirements and complexity of existing interior point methods are prohibitive for problems with more than tens of nodes we present two new algorithms for solving problems with at least a thousand nodes in the gaussian case our first algorithm uses block coordinate descent and can be interpreted as recursive l1 norm penalized regression our second algorithm based on nesterov s first order method yields a complexity estimate with a better dependence on problem size than existing interior point methods using a log determinant relaxation of the log partition function wainwright and jordan 2006 we show that these same algorithms can be used to solve an approximate sparse maximum likelihood problem for the binary case we test our algorithms on synthetic data as well as on gene expression and senate voting records data