a note on the regression analysis of censored data maximum likelihood estimates of the parameters in linear models with censored normal responses may be simply obtained using the em algorithm the iterative computations required for the regression coefficients are identical to those described by schmee and hahn for least squares estimates but those for the variance estimates are different the biases of the two variance estimates are discussed

online blind source separation using incremental nonnegative matrix factorization with volume constraint online blind source separation bss is proposed to overcome the high computational cost problem which limits the practical applications of traditional batch bss algorithms however the existing online bss methods are mainly used to separate independent or uncorrelated sources recently nonnegative matrix factorization nmf shows great potential to separate the correlative sources where some constraints are often imposed to overcome the non uniqueness of the factorization in this paper an incremental nmf with volume constraint is derived and utilized for solving online bss the volume constraint to the mixing matrix enhances the identifiability of the sources while the incremental learning mode reduces the computational cost the proposed method takes advantage of the natural gradient based multiplication updating rule and it performs especially well in the recovery of dependent sources simulations in bss for dual energy x ray images online encrypted speech signals and high correlative face images show the validity of the proposed method

learning overcomplete representations in an overcomplete basis the number of basis vectors is greater than the dimensionality of the input and the representation of an input is not a unique combination of basis vectors overcomplete representations have been advocated because they have greater robustness in the presence of noise can be sparser and can have greater flexibility in matching structure in the data overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex previous work has focused on finding the best representation of a signal using a fixed overcomplete basis or dictionary we present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data we show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency this can be viewed as a generalization of the technique of independent component analysis and provides a method for bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures

monte carlo deconvolution of digital signals guided by the inverse filter digital deconvolution concerns the restoration of an underlying discrete signal from a blurred noisy observation sequence the problem can be formulated in a bayesian framework as is usual in the bayesian context the computation of relevant posterior quantities is the major challenge previous work made substantial progress toward making this computation feasible most notably through the gibbs sampling approach of chen and li and the sequential importance sampling approach of liu and chen yet there is room for improvement because both global monte carlo strategies can be very slow to reach the target distribution we propose two new sampling strategies for efficient restoration of digital signals the key idea is to use inverse filtering to transform the posterior integration into a problem that is substantially more local than the direct formulation leading to stable monte carlo procedures that are very fast to converge in the final section we consider extensions to the case of blind deconvoluti

variational inference for watson mixture model this paper addresses modelling data using the watson distribution the watson distribution is one of the simplest distributions for analyzing axially symmetric data this distribution has gained some attention in recent years due to its modeling capability however its bayesian inference is fairly understudied due to difficulty in handling the normalization factor recent development of markov chain monte carlo mcmc sampling methods can be applied for this purpose however these methods can be prohibitively slow for practical applications a deterministic alternative is provided by variational methods that convert inference problems into optimization problems in this paper we present a variational inference for watson mixture models first the variational framework is used to side step the intractability arising from the coupling of latent states and parameters second the variational free energy is further lower bounded in order to avoid intractable moment computation the proposed approach provides a lower bound on the log marginal likelihood and retains distributional information over all parameters moreover we show that it can regulate its own complexity by pruning unnecessary mixture components while avoiding over fitting we discuss potential applications of the modeling with watson distributions in the problem of blind source separation and clustering gene expression data sets

single channel blind separation using pseudo stereo mixture and complex 2 d histogram a novel single channel blind source separation scbss algorithm is presented the proposed algorithm yields at least three benefits of the scbss solution 1 resemblance of a stereo signal concept given by one microphone 2 independent of initialization and a priori knowledge of the sources and 3 it does not require iterative optimization the separation process consists of two steps 1 estimation of source characteristics where the source signals are modeled by the autoregressive process and 2 construction of masks using only the single channel mixture a new pseudo stereo mixture is formulated by weighting and time shifting the original single channel mixture this creates an artificial mixing system whose parameters will be estimated through our proposed weighted complex 2 d histogram in this paper we derive the separability of the proposed mixture model conditions required for unique mask construction based on maximum likelihood are also identified finally experimental testing on both synthetic and real audio sources is conducted to verify that the proposed algorithm yields superior performance and is computationally very fast compared with existing methods

a new blind method for separating m 1 sources from m mixtures in this paper we consider the problem of underdetermined blind source separation ubss i e there are more sources than mixtures by exploiting the time frequency tf sparsity of the source signals some tf ubss algorithms have recently been proposed in the literature these algorithms require that the number of active sources at any tf point should not exceed one or be strictly less than the number of mixtures in this paper we show that if the number of sources is greater than the number of mixtures by one the sparsity assumption can be further relaxed especially it is allowed to have as many sources as mixtures at any tf point in this case then we propose a new tf ubss method to recover the sources the relaxation on the maximum number of active sources at tf points ensures that the tf based methods can be used in a wider range of applications

cramer rao bounds for complex valued independent component extraction determined and piecewise determined mixing models blind source extraction bse aims at recovering an unknown source signal of interest from the observation of instantaneous linear mixtures of the sources this paper presents cramer rao lower bounds crlb for the complex valued bse problem based on the assumption that the target signal is independent of the other signals the target source is assumed to be non gaussian or non circular gaussian while the other signals background are circular gaussian or non gaussian the results confirm some previous observations known for the real domain and yield new results for the complex domain also the crlb for independent component extraction ice is shown to coincide with that for independent component analysis ica when the non gaussianity of background is taken into account second we extend the crlb analysis to piecewise determined mixing models where the observed signals are assumed to obey the determined mixing model within short blocks where the mixing matrices can be varying from block to block this model has applications for instance when separating dynamic mixtures either the mixing vector or the separating vector corresponding to the target source is assumed to be constant across the blocks the crlbs for the parameters of these models bring new performance limits for the bse problem

characterization of analytic wavelet transforms and a new phaseless reconstruction algorithm we obtain a characterization of all wavelets leading to analytic wavelet transforms wt the characterization is obtained as a byproduct of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude only coefficients the cornerstone of our analysis is an expression of the partial derivatives of the continuous wt which results in phase magnitude relationships similar to the short time fourier transform setting and valid for the generalized family of cauchy wavelets we show that the existence of such relations is equivalent to analyticity of the wt up to a multiplicative weight and a scaling of the mother wavelet the implementation of the new phaseless reconstruction method is considered in detail and compared to previous methods it is shown that the proposed method provides significant performance gains and a great flexibility regarding accuracy versus complexity in addition we discuss the relation between scalogram reassignment operators and the wavelet transform phase gradient and present an observation on the phase around zeros of the wt

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

anechoic blind source separation using wigner marginals blind source separation problems emerge in many applications where signals can be modeled as superpositions of multiple sources many popular applications of blind source separation are based on linear instantaneous mixture models if specific invariance properties are known about the sources for example translation or rotation invariance the simple linear model can be extended by inclusion of the corresponding transformations when the sources are invariant against translations spatial displacements or time shifts the resulting model is called an anechoic mixing model we present a new algorithmic framework for the solution of anechoic problems in arbitrary dimensions this framework is derived from stochastic time frequency analysis in general and the marginal properties of the wigner ville spectrum in particular the method reduces the general anechoic problem to a set of anechoic problems with non negativity constraints and a phase retrieval problem the first type of subproblem can be solved by existing algorithms for example by an appropriate modification of non negative matrix factorization nmf the second subproblem is solved by established phase retrieval methods we discuss and compare implementations of this new algorithmic framework for several example problems with synthetic and real world data including music streams natural 2d images human motion trajectories and two dimensional shapes

underdetermined blind source separation based on subspace representation this paper considers the problem of blindly separating sub and super gaussian sources from underdetermined mixtures the underlying sources are assumed to be composed of two orthogonal components one lying in the rowspace and the other in the nullspace of a mixing matrix the mapping from the rowspace component to the mixtures by the mixing matrix is invertible using the pseudo inverse of the mixing matrix the mapping from the nullspace component to zero by the mixing matrix is noninvertible and there are infinitely many solutions to the nullspace component the latent nullspace component which is of lower complexity than the underlying sources is estimated based on a mean square error mse criterion this leads to a source estimator that is optimal in the mse sense in order to characterize and model sub and super gaussian source distributions the parametric generalized gaussian distribution is used the distribution parameters are estimated based on the expectation maximization em algorithm when the mixing matrix is unavailable it must be estimated and a novel algorithm based on a single source detection algorithm which detects time frequency regions of single source occupancy is proposed in our simulations the proposed algorithm compared to other conventional algorithms estimated the mixing matrix with higher accuracy and separated various sources with higher signal to interference ratio

blind separation of speech mixtures via time frequency masking binary time frequency masks are powerful tools for the separation of sources from a single mixture perfect demixing via binary time frequency masks is possible provided the time frequency representations of the sources do not overlap a condition we call w disjoint orthogonality we introduce here the concept of approximate w disjoint orthogonality and present experimental results demonstrating the level of approximate w disjoint orthogonality of speech in mixtures of various orders the results demonstrate that there exist ideal binary time frequency masks that can separate several speech signals from one mixture while determining these masks blindly from just one mixture is an open problem we show that we can approximate the ideal masks in the case where two anechoic mixtures are provided motivated by the maximum likelihood mixing parameter estimators we define a power weighted two dimensional 2 d histogram constructed from the ratio of the time frequency representations of the mixtures that is shown to have one peak for each source with peak location corresponding to the relative attenuation and delay mixing parameters the histogram is used to create time frequency masks that partition one of the mixtures into the original sources experimental results on speech mixtures verify the technique example demixing results can be found online at http alum mit edu www rickard bss html

underdetermined blind separation of nondisjoint sources in the time frequency domain this paper considers the blind separation of nonstationary sources in the underdetermined case when there are more sources than sensors a general framework for this problem is to work on sources that are sparse in some signal representation domain recently two methods have been proposed with respect to the time frequency tf domain the first uses quadratic time frequency distributions tfds and a clustering approach and the second uses a linear tfd both of these methods assume that the sources are disjoint in the tf domain i e there is at most one source present at a point in the tf domain in this paper we relax this assumption by allowing the sources to be tf nondisjoint to a certain extent in particular the number of sources present at a point is strictly less than the number of sensors the separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding tfd values in particular we propose two subspace based algorithms for tf nondisjoint sources one uses quadratic tfds and the other a linear tfd another contribution of this paper is a new estimation procedure for the mixing matrix finally then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones

a convex geometry based blind source separation method for separating nonnegative sources this paper presents a convex geometry cg based method for blind separation of nonnegative sources first the unaccessible source matrix is normalized to be column sum to one by mapping the available observation matrix then its zero samples are found by searching the facets of the convex hull spanned by the mapped observations considering these zero samples a quadratic cost function with respect to each row of the unmixing matrix together with a linear constraint in relation to the involved variables is proposed upon which an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem unlike the traditional blind source separation bss methods the cg based method does not require the independence assumption nor the uncorrelation assumption compared with the bss methods that are specifically designed to distinguish between nonnegative sources the proposed method requires a weaker sparsity condition provided simulation results illustrate the performance of our method

mixing matrix estimation from sparse mixtures with unknown number of sources in blind source separation many methods have been proposed to estimate the mixing matrix by exploiting sparsity however they often need to know the source number a priori which is very inconvenient in practice in this paper a new method namely nonlinear projection and column masking npcm is proposed to estimate the mixing matrix a major advantage of npcm is that it does not need any knowledge of the source number in npcm the objective function is based on a nonlinear projection and its maxima just correspond to the columns of the mixing matrix thus a column can be estimated first by locating a maximum and then deflated by a masking operation this procedure is repeated until the evaluation of the objective function decreases to zero dramatically thus the mixing matrix and the number of sources are estimated simultaneously because the masking procedure may result in some small and useless local maxima particle swarm optimization pso is introduced to optimize the objective function feasibility and efficiency of pso are also discussed comparative experimental results show the efficiency of npcm especially in the cases where the number of sources is unknown and the sources are relatively less sparse

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

subgroup growth and congruence subgroups letk be a global field o its ring of integers g an almost simple simply connected connected algebraic subgroups ofgl m defined overk and g o which is assumed to be infinite let n resp n be the number of all resp congruence subgroups of index at mostn in we show a if char k 0 then i c 1 frac log 2 n log log n leqq log gamma n gamma leqq c 2 frac log 2 n log log n for suitable constantsc1 andc2 under some mild assumptions we also have ii has the congruence subgroup property if and only if log n o log2n iii if is boundedly generated the has the congruence subgroup property this confirms a conjecture of rapinchuk r1 which was also proved by platonov and rapinchuk pr3 b if char k 0 and under somewhat stronger conditions ong then for suitable constantsc3 andc4 c3 log2n log n c4log3n

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

time frequency approach to underdetermined blind source separation this paper presents a new time frequency tf underdetermined blind source separation approach based on wigner ville distribution wvd and khatri rao product to separate n non stationary sources from m m n mixtures first an improved method is proposed for estimating the mixing matrix where the negative value of the auto wvd of the sources is fully considered then after extracting all the auto term tf points the auto wvd value of the sources at every auto term tf point can be found out exactly with the proposed approach no matter how many active sources there are as long as n 2m 1 further discussion about the extraction of auto term tf points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones

regression for skewed biomarker outcomes subject to pooling epidemiological studies involving biomarkers are often hindered by prohibitively expensive laboratory tests strategically pooling specimens prior to performing these lab assays has been shown to effectively reduce cost with minimal information loss in a logistic regression setting when the goal is to perform regression with a continuous biomarker as the outcome regression analysis of pooled specimens may not be straightforward particularly if the outcome is right skewed in such cases we demonstrate that a slight modification of a standard multiple linear regression model for poolwise data can provide valid and precise coefficient estimates when pools are formed by combining biospecimens from subjects with identical covariate values when these x homogeneous pools cannot be formed we propose a monte carlo expectation maximization mcem algorithm to compute maximum likelihood estimates mles simulation studies demonstrate that these analytical methods provide essentially unbiased estimates of coefficient parameters as well as their standard errors when appropriate assumptions are met furthermore we show how one can utilize the fully observed covariate data to inform the pooling strategy yielding a high level of statistical efficiency at a fraction of the total lab cost

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

on the statistical distributions of active intensity directions abstract pressure and pressure differences measured using closely spaced microphone pairs enable the calculation of active intensity directions these directions are exploited in various applications such as acoustical analysis and modelling multichannel audio systems source localization and real time blind source separation despite their widespread usage the distribution of the active intensity directions in the presence of interference has not been investigated before except for the diffuse sound field case for which the distribution becomes uniform in this paper the interference problem has been formulated using the pressure and pressure differences algebra of random variables fractional linear transformations and brownian motion have been used for the exposition of the model distributions it is shown that the distribution is wrapped cauchy for a single sound source in the presence of independent interference in an anechoic chamber in a direct plus diffuse sound field the distribution is offset cauchy for a nonstationary target source and von mises for the special case of a stationary target source related to the brownian motion in the presence of multiple independent sound sources the distribution can be modeled as mixtures of circular cauchy distributions and a uniform distribution

blind separation of instantaneous mixtures of nonstationary sources most source separation algorithms are based on a model of stationary sources however it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation this paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information these principles are exploited by efficient algorithms in both the off line case via a new joint diagonalization procedure and in the on line case via a newton like procedure some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented their ability to achieve a kind of super efficiency the paper concludes with a discussion contrasting separating methods for non gaussian and nonstationary models and emphasizing that as a matter of fact what makes the algorithms work is strictly speaking not the nonstationarity itself but rather the property that each realization of the source signals has a time varying envelope

robustness analysis of spatial time frequency distributions based on the influence function standard spatial time frequency distribution stfd estimators derived based on the gaussian noise assumption are known to have poor performance in the case of impulsive noise recently different stfd estimators have been proposed which based on simulations are claimed to be robust in this paper we provide an influence function robustness analysis of stfd estimators we derive the influence functions for the asymptotic and for the finite sample case and study robustness of the standard as well as for some recently proposed robust stfd estimators the empirical influence function gives practitioners a simple way to pre select stfd estimators for their scenario our analysis confirms that unlike for the standard estimator the proposed robust estimators yield a bounded influence function and are robust over a broad class of distributions future research on stfd estimation will allow for the design of robust and efficient estimators based on the influence function

penalized clustering of large scale functional data with multiple covariates in this article we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach in our proposed method responses and covariates are linked together through nonparametric multivariate functions fixed effects which have great flexibility in modeling various function features such as jump points branching and periodicity functional anova is used to further decompose multivariate functions in a reproducing kernel hilbert space and provide associated notions of main effect and interaction parsimonious random effects are used to capture various correlation structures the mixed effects models are nested under a general mixture model in which the heterogeneity of functional data is characterized we propose a penalized henderson s likelihood approach for model fitting and design a rejection controlled em algorithm for the estimation our method selects smoothing parameters through generalized cross validation furthermore bayesian confidence in

applications of multiple imputation to the analysis of censored regression data the first part of the article reviews the data augmentation algorithm and presents two approximations to the data augmentation algorithm for the analysis of missing data problems the poor man s data augmentation algorithm and the asymptotic data augmentation algorithm these two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology the performances of the censored regression algorithms are examined in a simulation study it is found up to the precision of the study that the bias of both the poor man s and asymptotic data augmentation estimators as well as the buckley james estimator does not appear to differ from zero however with regard to mean squared error over a wide range of settings examined in this simulation study the two data augmentation estimators have a smaller mean squared error than does the buckley james estimator in addition associated with the two data augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters it is shown how this device can be used to estimate the standard error of either data augmentation estimate of any parameter e g the correlation coefficient associated with the model in the simulation study the estimated standard error of the asymptotic data augmentation estimate of the regression parameter is found to be congruent with the monte carlo standard deviation of the corresponding parameter estimate the algorithms are illustrated using the updated stanford heart transplant data set

three dimensional elastic problems of three dimensional quasicrystals in this paper the three dimensional initial value problem for three dimensional quasicrystals is considered for special polynomial form of initial conditions and nonhomogeneous terms it is proved that the solution can be presented in a similar form an analytic method for finding the exact solution of the problem with this polynomial form of initial conditions and nonhomogeneous terms is presented

a technique for estimating marginal posterior densities in hierarchical models using mixtures of conditional densities abstract a technique called quantile integration is proposed for the estimation of marginal posterior densities arising in bayesian models having hierarchical representations the method is based on approximating marginal densities as mixtures of conditional densities where the conditioning variables are selected deterministically from the mixing distributions the form of the approximation makes it easy to implement and the resulting approximations are computationally efficient to obtain the technique leads to particularly simple approximations for the predictive and posterior densities in kalman filter or state space models and specific formulas are provided for the special case in which innovations belong to location scale families other applications include a hierarchical empirical bayes model for poisson rates and a hierarchical linear model with exchangeable regression parameters and unknown variance components

anisotropic elastodynamics in a half space an analytic method for polynomial data an initial boundary value problem for the dynamic system of anisotropic elasticity in a half space is studied in the paper a novel method of finding an exact solution of this problem for a special polynomial form of initial data and inhomogeneous term of the system is described on the base of this method the simulation of elastic waves in different homogeneous anisotropic half spaces is implemented

projection design for statistical compressive sensing a tight frame based approach in this paper we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error mse performance subject to sensing cost constraints by capitalizing on the mse of the oracle estimator whose performance has been shown to act as a benchmark to the performance of standard sparse recovery algorithms we use the fact that a parseval tight frame is the closest design in the frobenius norm sense to the solution of a convex relaxation of the optimization problem that relates to the minimization of the mse of the oracleestimator with respect to the equivalent sensing matrix subject to sensing energy constraints based on this result we then propose two sensing matrix designs that exhibit two key properties the designs are closed form rather than iterative the designs exhibit superior performance in relation to other designs in the literature which is revealed by our numerical investigation in various scenarios with different sparse recovery algorithms including basis pursuit de noise bpdn the dantzig selector and orthogonal matching pursuit omp

monte carlo em algorithm in logistic linear models involving non ignorable missing data abstract many data sets obtained from surveys or medical trials often include missing observations since ignoring the missing information usually cause bias and inefficiency an algorithm for estimating parameters is proposed based on the likelihood function of which the missing information is taken account a binomial response and normal exploratory model for the missing data are assumed we fit the model using the monte carlo em expectation and maximization algorithm the e step is derived by metropolis hastings algorithm to generate a sample for missing data and the m step is done by newton raphson to maximize the likelihood function asymptotic variances and the standard errors of the mle maximum likelihood estimates of parameters are derived using the observed fisher information

maximum likelihood estimation of nonlinear structural equation models the existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables however models with nonlinear relationships are often encountered in social and behavioral sciences in this article an em type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model to avoid computation of the complicated multiple integrals involved the e step is completed by a metropolis hastings algorithm it is shown that the m step can be completed efficiently by simple conditional maximization standard errors of the maximum likelihood estimates are obtained via louis s formula the methodology is illustrated with results from a simulation study and two real examples

a frailty model for informative censoring to account for the correlation between failure and censoring we propose a new frailty model for clustered data in this model the risk to be censored is affected by the risk of failure this model allows flexibility in the direction and degree of dependence between failure and censoring it includes the traditional frailty model as a special case it allows censoring by some causes to be analyzed as informative while treating censoring by other causes as noninformative it can also analyze data for competing risks to fit the model the em algorithm is used with markov chain monte carlo simulations in the e steps simulation studies and analysis of data for kidney disease patients are provided consequences of incorrectly assuming noninformative censoring are investigated

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

publication bias and meta analysis for 2x2 tables an average markov chain monte carlo em algorithm summary a major difficulty in meta analysis is publication bias studies with positive outcomes are more likely to be published than studies reporting negative or inconclusive results correcting for this bias is not possible without making untestable assumptions in this paper a sensitivity analysis is discussed for the meta analysis of 2 2 tables using exact conditional distributions a markov chain monte carlo em algorithm is used to calculate maximum likelihood estimates a rule for increasing the accuracy of estimation and automating the choice of the number of iterations is suggested

underdetermined blind source separation based on sparse representation this paper discusses underdetermined i e with more sources than sensors blind source separation bss using a two stage sparse representation approach the first challenging task of this approach is to estimate precisely the unknown mixing matrix in this paper an algorithm for estimating the mixing matrix that can be viewed as an extension of the duet and the tifrom methods is first developed standard clustering algorithms e g k means method also can be used for estimating the mixing matrix if the sources are sufficiently sparse compared with the duet the tifrom methods and standard clustering algorithms with the authors proposed method a broader class of problems can be solved because the required key condition on sparsity of the sources can be considerably relaxed the second task of the two stage approach is to estimate the source matrix using a standard linear programming algorithm another main contribution of the work described in this paper is the development of a recoverability analysis after extending the results in a necessary and sufficient condition for recoverability of a source vector is obtained based on this condition and various types of source sparsity several probability inequalities and probability estimates for the recoverability issue are established finally simulation results that illustrate the effectiveness of the theoretical results are presented

a deflation procedure for subspace decomposition a general deflation framework is described for the separation of a desired signal subspace of arbitrary dimensions from noisy multichannel observations the method simultaneously uses single and multichannel priors to split the desired and undesired subspaces even for coplanar intersecting subspaces by appropriate use of signal priors it can even extract signals from degenerate mixtures of signals and noise recorded from a few number of channels in low snr scenarios without the reduction of the data dimensions as a case study the performance of the proposed method is studied for the problem of extracting fetal cardiac signals from maternal abdominal recordings over simulated and real data a second case study deals with the degenerate problem of extracting diaphragmatic electromyogram from electrocardiograph artifacts a provisional patent application based on this method has been filed

second order blind separation of sources based on canonical partial innovations this paper is devoted to the study of the second order properties using partial autocorrelations of an instantaneous mixture of colored sources without additive noise we introduce the notion of symmetric recursive canonical partial innovation then their components for the observation process meet exactly with those of the source process from the order for which the autoregressive models underlying the sources are distinct this property leads to a new separation method based on the sample counterpart of partial autocorrelation matrices associated with these innovations simulation results show a notable improvement of the achievements of such an approach with respect to those of similar methods two other separation methods related to partial autocorrelation are also discussed

bounds on the number and sizes of conjugacy classes in finite chevalley groups with applications to derangements we present explicit upper bounds for the number and size of conjugacy classes in finite chevalley groups and their variations these results have been used by many authors to study zeta functions associated to representations of finite simple groups random walks on chevalley groups the final solution to the ore conjecture about commutators in finite simple groups and other similar problems in this paper we solve a strong version of the boston shalev conjecture on derangements in simple groups for most of the families of primitive permutation group representations of finite simple groups the remaining cases are settled in two other papers of the authors and applications are given in a third

monte carlo methods of inference for implicit statistical models a prescribed statistical model is a parametric specification of the distribution of a random vector whilst an implicit statistical model is one defined at a more fundamental level in terms of a generating stochastic mechanism this paper develops methods of inference which can be used for implicit statistical models whose distribution theory is intractable the kernel method of probability density estimation is advocated for estimating a log likelihood from simulations of such a model the development and testing of an algorithm for maximizing this estimated log likelihood function is described an illustrative example involving a stochastic model for quantal response assays is given possible applications of the maximization algorithm to ad hoc methods of parameter estimation are noted briefly and illustrated by an example involving a model for the spatial pattern of displaced amacrine cells in the retina of a rabbit

a variational method for learning sparse and overcomplete representations an expectation maximization algorithm for learning sparse and overcomplete data representations is presented the proposed algorithm exploits a variational approximation to a range of heavy tailed distributions whose limit is the laplacian a rigorous lower bound on the sparse prior distribution is derived which enables the analytic marginalization of a lower bound on the data likelihood this lower bound enables the development of an expectation maximization algorithm for learning the overcomplete basis vectors and inferring the most probable basis coefficients

enumerating finite groups of given order let f n denote the number of isomorphism classes of groups of order n let n hw p9ig be the prime factorization of n and let a a n ek and u ii n maxkl1 gi the function f n has been subject to considerable study g higman 15 and c c sims 26 showed that if n is a prime power say n p then f n n 2 27 o l a2 for a x oc p m neumann 22 proved that if the number of isomorphism classes of simple groups of order n is bounded by nca2 for some constant c then f n n 1 c a2 holds in general combining the methods of 22 with some consequences of the classification theorem of finite simple groups a mciver and neumann 21 obtained that in fact the estimates f n na2 2 and f n n1 2 1 2 hold recently d f holt 16 found a rather elegant proof for the bound

analysis of structural equation model with ignorable missing continuous and polytomous data the main purpose of this article is to develop a bayesian approach for structural equation models with ignorable missing continuous and polytomous data joint bayesian estimates of thresholds structural parameters and latent factor scores are obtained simultaneously the idea of data augmentation is used to solve the computational difficulties involved in the posterior analysis in addition to the real missing data latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data an algorithm that embeds the metropolis hastings algorithm within the gibbs sampler is implemented to produce the bayesian estimates a goodness of fit statistic for testing the posited model is presented it is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small computational efficiency of the proposed procedure is illustrated by simulation studies and a real example

analysis of sparse representation and blind source separation in this letter we analyze a two stage cluster then l1 optimization approach for sparse representation of a data matrix which is also a promising approach for blind source separation bss in which fewer sensors than sources are present first sparse representation factorization of a data matrix is discussed for a given overcomplete basis matrix the corresponding sparse solution coefficient matrix with minimum l1 norm is unique with probability one which can be obtained using a standard linear programming algorithm the equivalence of the l1 norm solution and the l0 norm solution is also analyzed according to a probabilistic framework if the obtained l1 norm solution is sufficiently sparse then it is equal to the l0 norm solution with a high probability furthermore the l1 norm solution is robust to noise but the l0 norm solution is not showing that the l1 norm is a good sparsity measure these results can be used as a recoverability analysis of bss as discussed the basis matrix in this article is estimated using a clustering algorithm followed by normalization in which the matrix columns are the cluster centers of normalized data column vectors zibulevsky pearlmutter boll and kisilev 2000 used this kind of two stage approach in underdetermined bss our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed domain and with the case in which the source number is unknown it is also robust to additive noise and estimation error in the mixing matrix finally four simulation examples and an eeg data analysis example are presented to illustrate the algorithm s utility and demonstrate its performance

an adaptive method for subband decomposition ica subband decomposition ica sdica an extension of ica assumes that each source is represented as the sum of some independent subcomponents and dependent subcomponents which have different frequency bands in this article we first investigate the feasibility of separating the sdica mixture in an adaptive manner second we develop an adaptive method for sdica namely band selective ica bs ica which finds the mixing matrix and the estimate of the source independent subcomponents this method is based on the minimization of the mutual information between outputs some practical issues are discussed for better applicability a scheme to avoid the high dimensional score function difference is given third we investigate one form of the overcomplete ica problems with sources having specific frequency characteristics which bs ica can also be used to solve experimental results illustrate the success of the proposed method for solving both sdica and the overcomplete ica problems

equations of anisotropic elastodynamics as a symmetric hyperbolic system deriving the time dependent fundamental solution the dynamic system of anisotropic elasticity from three second order partial differential equations is written in the form of the time dependent first order symmetric hyperbolic system with respect to displacement velocity and stress components a new method of deriving the time dependent fundamental solution of the obtained system is suggested in this paper this method consists of the following the fourier transform image of the fundamental solution with respect to a space variable is presented as a power series expansion relative to the fourier parameters then explicit formulae for the coefficients of these power series are derived successively using these formulae the computer calculation of fundamental solution components displacement velocity and stress components arising from pulse point forces has been made for general anisotropic media orthorhombic and monoclinic and the simulation of elastic waves has been obtained these computational examples confirm the robustness of the suggested method

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

maximal subgroups in finite and profinite groups we prove that if a finitely generated profinite group g is not generated with positive probability by finitely many random elements then every finite group f is obtained as a quotient of an open subgroup of g the proof involves the study of maximal subgroups of profinite groups as well as techniques from finite permutation groups and finite chevalley groups confirming a conjecture from ann of math 137 1993 203 220 we then prove that a finite group g has at most igic maximal soluble subgroups and show that this result is rather useful in various enumeration problems

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

initial value problem for the dynamic system of anisotropic elasticity the main object of this paper is the cauchy problem for the dynamic system of anisotropic elasticity existence and uniqueness theorems of weak and smooth solutions of this problem are established by the reduction of the original elasticity system into a symmetric hyperbolic system of the first order the numerical method of the cauchy problem solving for anisotropic elastic system with polynomial data is obtained and its correctness is established the simulations of the numerical solutions are presented

underdetermined sparse blind source separation of nonnegative and partially overlapped data we study the solvability of sparse blind separation of n nonnegative sources from m linear mixtures in the underdetermined regime m n the geometric properties of the mixture matrix and the sparseness structure of the source matrix are closely related to the identification of the mixing matrix we first illustrate and establish necessary and sufficient conditions for the unique separation for the case of m mixtures and m 1 sources and develop a novel algorithm based on data geometry source sparseness and ell 1 minimization then we extend the results to any order m times n 3 leq m n based on the degree of degeneracy of the columns of the mixing matrix numerical results substantiate the proposed solvability conditions and show satisfactory performance of our approach

projection pursuit based method for blind separation of nonnegative sources this paper presents a projection pursuit pp based method for blind separation of nonnegative sources first the available observation matrix is mapped to construct a new mixing model in which the inaccessible source matrix is normalized to be column sum to 1 then the pp method is proposed to solve this new model where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions which leads to the recovery of the sources the proposed method is much faster than chan s method which has similar assumptions to ours due to the usage of optimal projection it is also more advantageous in separating cross correlated sources than the independence and uncorrelation based methods as it does not employ any statistical information of the sources furthermore the new method does not require the mixing matrix to be nonnegative simulation results demonstrate the superior performance of our method

underdetermined blind source separation based on relaxed sparsity condition of sources recently aissa el bey et al have proposed two subspace based methods for underdetermined blind source separation ubss in time frequency tf domain these methods allow multiple active sources at tf points so long as the number of active sources at any tf point is strictly less than the number of sensors and the column vectors of the mixing matrix are pairwise linearly independent in this correspondence we first show that the subspace based methods must also satisfy the condition that any m times m submatrix of the mixing matrix is of full rank then we present a new ubss approach which only requires that the number of active sources at any tf point does not exceed that of sensors an algorithm is proposed to perform the ubss

permutation characters and fixed point free elements in permutation groups abstract let g be a finite group with two transitive permutation representations on the sets 1 and 2 respectively we are concerned with the case that the set of fixed point free elements of g on 1 coincides with the set of fixed point free elements of g on 2 we prove that if g has nilpotency class 2 then the permutation character 1 of g on 1 equals the permutation character 2 of g on 2 furthermore for these groups we prove that the stabilizer of a point in 1 is conjugate under an automorphism of g to the stabilizer of a point of 2 in section 3 we present the following conjecture let g act primitively on 1 and on 2 and assume that the set of fixed point free elements of g on 1 coincides with the set of fixed point free elements of g on 2 then the permutation character 1 of g on 1 and the permutation character 2 of g on 2 are comparable i e if 1 2 then either 1 2 or 2 1 is a character we show that if the conjecture is false then a minimal counterexample must be an almost simple group further results concerning other classes of groups are presented

conditional likelihood inference under complex ascertainment using data augmentation summary in many applications particularly in genetics samples are drawn under complex ascertainment rules for example families may only be selected for study if two or more siblings have trait values exceeding some threshold the correct likelihood for inference in such situations involves the probabilities of ascertainment and these are frequently intractable a consistent but not fully efficient method of analysis of such studies is proposed the main idea is to augment the data with additional pseudo observations simulated under the ascertainment scheme and to analyse using a conditional likelihood for discrimination between true observations and pseudoobservations ascertainment probabilities cancel in this likelihood the method is illustrated with a simple example involving left truncated failure times

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

differential fast fixed point algorithms for underdetermined instantaneous and convolutive partial blind source separation this paper concerns underdetermined linear instantaneous and convolutive blind source separation bss i e the case when the number of observed mixed signals is lower than the number of sources we propose partial bss methods which separate supposedly nonstationary sources of interest while keeping residual components for the other supposedly stationary ldquonoiserdquo sources these methods are based on the general differential bss concept that we introduced before in the instantaneous case the approach proposed in this paper consists of a differential extension of the fastica method which does not apply to underdetermined mixtures in the convolutive case we extend our recent time domain fast fixed point c fica algorithm to underdetermined mixtures both proposed approaches thus keep the attractive features of the fastica and c fica methods our approaches are based on differential sphering processes followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper experimental tests show that these differential algorithms are much more robust to noise sources than the standard fastica and c fica algorithms

comparing measures of sparsity sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation compression sampling and signal analysis the aim of this paper is to compare several commonly used sparsity measures based on intuitive attributes intuitively a sparse representation is one in which a small number of coefficients contain a large proportion of the energy in this paper six properties are discussed robin hood scaling rising tide cloning bill gates and babies each of which a sparsity measure should have the main contributions of this paper are the proofs and the associated summary table which classify commonly used sparsity measures based on whether or not they satisfy these six propositions only two of these measures satisfy all six the pq mean with p les 1 q 1 and the gini index

a fast improvement to the em algorithm on its own terms the em algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models it is easy to apply in many problems and is stable but slow the algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the louis method is performed newton type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and at least approximations to the fisher information matrix the purpose of this paper is to expand on a result by fisher that permits a unification of em methodology and newton methods the evaluation of the individual observation by observation score functions of the incomplete data is a byproduct of the application of the e step of the em algorithm once these become available the fisher information matrix may be consistently estimated and the m step may be replaced by a fast newton type step

monte carlo state space likelihoods by weighted posterior kernel density estimation maximum likelihood estimation and likelihood ratio tests for nonlinear non gaussian state space models require numerical integration for likelihood calculations several methods including monte carlo mc expectation maximization mc likelihood ratios direct mc integration and particle filter likelihoods are inefficient for the motivating problem of stage structured population dynamics models in experimental settings an mc kernel likelihood mckl method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of bayesian posteriors mckl is derived by using bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals mc error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed zooming in on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant based approximation of mode bias a simulated example show

underdetermined blind modal identification of structures by earthquake and ambient vibration measurements via sparse component analysis abstract sparse component analysis sca approach was adopted to handle underdetermined blind modal identification of structures where the number of sensors is less than the number of active modes to exploit the sparsity of structural responses in time frequency domain short time fourier transform stft was used in this study the proposed sca based approach has two main stages modal matrix estimation and modal displacement estimation in the first stage hierarchical clustering algorithm was used to estimate the modal matrix the clustering algorithm was preceded by a preprocessing step to select the points in time frequency domain that only one mode makes contribution in the responses these points were fed to the clustering algorithm as an input performing this analysis enhanced the modal matrix estimation accuracy and reduced the computational cost while conducting clustering analysis having estimated mixing matrix the complex valued modal responses in the transformed domain were recovered via smoothed zero norm sl 0 algorithm in a broad sense using the sl 0 algorithm permits researchers to use any kind of transform in seeking sparsity regardless of obtaining real valued or complex valued signals in transformed domain natural frequencies and damping ratios were extracted from the recovered modal responses performance of the proposed method was investigated using a synthetic example and a benchmark structure with earthquake and ambient excitation respectively

bayesian blind separation of generalized hyperbolic processes in noisy and underdeterminate mixtures in this paper we propose a bayesian sampling solution to the noisy blind separation of generalized hyperbolic signals generalized hyperbolic models introduced by barndorff nielsen in 1977 represent a parametric family able to cover a wide range of real signal distributions the alternative construction of these distributions as a normal mean variance continuous mixture leads to an efficient implementation of the markov chain monte carlo method applied to source separation the incomplete data structure of the generalized hyperbolic distribution is indeed compatible with the hidden variable nature of the source separation problem both overdeterminate and underdeterminate noisy mixtures are solved by the same algorithm without a prewhitening step our algorithm involves hyperparameters estimation as well therefore it can be used independently to fitting the parameters of the generalized hyperbolic distribution to real data

linear quadratic blind source separation using nmf to unmix urban hyperspectral images in this work we propose algorithms to perform blind source separation bss for the linear quadratic mixing model the linear quadratic model is less studied in the literature than the linear one in this paper we propose original methods that are based on non negative matrix factorization nmf this class of methods is well suited to many applications where the data are non negative we are here particularly interested in spectral unmixing extracting reflectance spectra of materials present in pixels and associated abundance fractions for urban hyperspectral images the originality of our work is that we developed extensions of nmf which is initially suited to the linear model for the linear quadratic model the proposed algorithms are tested with simulated hyperspectral images using real reflectance spectra and the obtained results are very satisfactory

asymptotic results for primitive permutation groups abstract we prove that the number of conjugacy classes of primitive permutation groups of degreenis at mostnc n where n denotes the maximal exponent occurring in the prime factorization ofn this result is applied to investigating maximal subgroup growth of infinite groups we then proceed by showing that if the point stabilizerg of a primitive groupgof degreendoes not have the alternating group alt d as a section then the order ofgis bounded by a polynomial inn this result extends a well known theorem of babai cameron and palfy it is used to prove for example that ifhis a subgroup of indexnin a groupg andhis a product ofbcyclic groups then g hg ncwherecdepends onb

the synchronized short time fourier transform properties and definitions for multichannel source separation this paper proposes the use of a synchronized linear transform the synchronized short time fourier transform sstft for time frequency analysis of anechoic mixtures we address the short comings of the commonly used time frequency linear transform in multichannel settings namely the classical short time fourier transform cstft we propose a series of desirable properties for the linear transform used in a multichannel source separation scenario stationary invertibility relative delay relative attenuation and finally delay invariant relative windowed disjoint orthogonality dirwdo multisensor source separation techniques which operate in the time frequency domain have an inherent error unless consideration is given to the multichannel properties proposed in this paper the sstft preserves these relationships for multichannel data the crucial innovation of the sstft is to locally synchronize the analysis to the observations as opposed to a global clock improvement in separation performance can be achieved because assumed properties of the time frequency transform are satisfied when it is appropriately synchronized numerical experiments show the sstft improves instantaneous subsample relative parameter estimation in low noise conditions and achieves good synthesis

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

a frequency bin wise nonlinear masking algorithm in convolutive mixtures for speech segregation a frequency bin wise nonlinear masking algorithm is proposed in the spectrogram domain for speech segregation in convolutive mixtures the contributive weight from each speech source to a time frequency unit of the mixture spectrogram is estimated by a nonlinear function based on location cues for each sound source a non binary mask is formed from the estimated weights and is multiplied to the mixture spectrogram to extract the sound head related transfer functions hrtfs are used to simulate convolutive sound mixtures perceived by listeners simulation results show our proposed method outperforms convolutive independent component analysis and degenerate unmixing and estimation technique methods in almost all test conditions

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

two microphone separation of speech mixtures based on interclass variance maximization sparse methods for speech separation have become a discussed issue in acoustic signal processing these sparse methods provide a powerful approach to the separation of several signals in the underdetermined case i e when there are more sources than sensors in this paper a two microphone separation method is presented the proposed algorithm is based on grouping time frequency points with similar direction of arrival doa using a multi level thresholding approach the thresholds are calculated via the maximization of the interclass variance between doa estimates and allow to identify angular sections wherein the speakers are located with a strong likelihood these sections define a set of time frequency masks that are able to separate several sound sources in realistic scenarios and with little computational cost several experiments carried out under different mixing situations are discussed showing the validity of the proposed approach

blind separation of quasi stationary sources exploiting convex geometry in covariance domain this paper revisits blind source separation of instantaneously mixed quasi stationary sources bss qss motivated by the observation that in certain applications e g speech there exist time frames during which only one source is active or locally dominant combined with nonnegativity of source powers this endows the problem with a nice convex geometry that enables elegant and efficient bss solutions local dominance is tantamount to the so called pure pixel separability assumption in hyperspectral unmixing nonnegative matrix factorization respectively building on this link a very simple algorithm called successive projection algorithm spa is considered for estimating the mixing system in closed form to complement spa in the specific bss qss context an algebraic preprocessing procedure is proposed to suppress short term source cross correlation interference the proposed procedure is simple effective and supported by theoretical analysis solutions based on volume minimization volmin are also considered by theoretical analysis it is shown that volmin guarantees perfect mixing system identifiability under an assumption more relaxed than exact local dominance which means wider applicability in practice exploiting the specific structure of bss qss a fast volmin algorithm is proposed for the overdetermined case careful simulations using real speech sources showcase the simplicity efficiency and accuracy of the proposed algorithms

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea