bayesian estimation of dirichlet mixture model with variational inference in statistical modeling parameter estimation is an essential and challengeable task estimation of the parameters in the dirichlet mixture model dmm is analytically intractable due to the integral expressions of the gamma function and its corresponding derivatives we introduce a bayesian estimation strategy to estimate the posterior distribution of the parameters in dmm by assuming the gamma distribution as the prior to each parameter we approximate both the prior and the posterior distribution of the parameters with a product of several mutually independent gamma distributions the extended factorized approximation method is applied to introduce a single lower bound to the variational objective function and an analytically tractable estimation solution is derived moreover there is only one function that is maximized during iterations and therefore the convergence of the proposed algorithm is theoretically guaranteed with synthesized data the proposed method shows the advantages over the em based method and the previously proposed bayesian estimation method with two important multimedia signal processing applications the good performance of the proposed bayesian estimation method is demonstrated

3 d image denoising by local smoothing and nonparametric regression three dimensional 3 d images are becoming increasingly popular in image applications such as magnetic resonance imaging mri functional mri fmri and other image applications observed 3 d images often contain noise that should be removed beforehand for improving the reliability of subsequent image analyses in the literature most existing image denoising methods are for 2 d images their direct extensions to 3 d cases generally cannot handle 3 d images efficiently because the structure of 3 d images is often substantially more complicated than that of 2 d images for instance edge locations are surfaces in 3 d cases which are much more challenging to handle compared to edge curves in 2 d cases in this article we propose a novel 3 d image denoising procedure based on nonparametric estimation of a 3 d jump surface from noisy data one important feature of this method is its ability to preserve edges and major edge structures such as intersections of two edge surfaces pyramids pointed corn

comments with reply on fast convolution with laplacian of gaussian masks by j s chen et al in a recent paper by j s chen et al ibid vol pami 9 p 584 90 july 1987 the authors presented a means of decomposing the laplacian of gaussian log kernel into the product of a gaussian and a smaller log mask they then proceeded to develop a fast algorithm for convolution which exploits the spatial frequency properties of these operators to allow the image to be decimated subsampled although this approach is both novel and interesting it is contended that the exposition suffers from some inconsistencies and minor errors the commenters clarify matters for those who wish to implement this technique the original authors acknowledge two of the three points raised and provide further clarification of the other one namely the claim that the masks gaussian and log are too small

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

a weighted occupation time for a class of measured valued branching processes a weighted occupation time is defined for measure valued processes and a representation for it is obtained for a class of measure valued branching random motions on rd considered as a process in its own right the first and second order asymptotics are found as time t specifically the finiteness of the total weighted occupation time is determined as a function of the dimension d and when infinite a central limit type renormalization is considered yielding gaussian or asymmetric stable generalized random fields in the limit in one gaussian case the results are contrasted in high versus low dimensions

harmonic functions and exit boundary of superdiffusion abstract all positive harmonic functions in an arbitrary domain of a euclidean space can be described in terms of the so called exit boundary this was established in 1941 by r s martin a probabilistic approach to the martin theory is due to doob and hunt it was extended later to harmonic functions associated with a wide class of markov processes the subject of this paper are harmonic functions associated with a superdiffusion x we call them x harmonic the results of evans and perkins imply the existence and uniqueness of an integral representation of positive x harmonic functions through extreme functions an outstanding problem is to find all extremal functions they are in 1 1 correspondence with the points of the exit boundary an interest in x harmonic functions is motivated in part by the fact that each of them provides a way of conditioning a superprocess path properties of conditioned superprocesses corresponding to various special x harmonic functions were investigated by a number of authors important classes of x harmonic functions are related to positive solutions of semilinear partial differential equations almost nothing is known about their decomposition into extreme elements a progress in this direction may create new tools for investigating solutions of the equations the goal of this paper is to summarize all known facts about x harmonic functions to present the results of various authors in a more general setting in a unified form and to outline a program of further work

adaptive relaxation labeling current implementation of probabilistic relaxation labeling prl is based on stationary compatibility coefficients scc s such labeling frequently diverges from an achieved minimum labeling error in this correspondence it is shown that by having nonstationary compatibility coefficients nscc s the prl stabilizes about the minimum error which is obtained during the early iterations also a noniterative labeling algorithm which uses nscc and has a performance similar to that of the modified prl is suggested

confidence and conflict in multivariate calibration summary multivariate calibration involves using an estimated relationship between a multivariate response y and an explanatory vector x to predict unknown x in future from further observed responses in controlled calibration with multivariate normal errors the profile likelihood function for the unknown x denoted 4 displays a term which measures the mutual inconsistency of the given response vector denoted z in predicting 4 this inconsistency diagnostic fundamentally differentiates the behaviour of likelihood based and bayes confidence regions from those of the unconditional sampling approach in addition the diagnostic serves to pinpoint an inadequate response vector z

variational inference for large scale models of discrete choice discrete choice models are commonly used by applied statisticians in numerous fields such as marketing economics finance and operations research when agents in discrete choice models are assumed to have differing preferences exact inference is often intractable markov chain monte carlo techniques make approximate inference possible but the computational cost is prohibitive on the large datasets now becoming routinely available variational methods provide a deterministic alternative for approximation of the posterior distribution we derive variational procedures for empirical bayes and fully bayesian inference in the mixed multinomial logit model of discrete choice the algorithms require only that we solve a sequence of unconstrained optimization problems which are shown to be convex one version of the procedures relies on a new approximation to the variational objective function based on the multivariate delta method extensive simulations along with an analysis of real world data demonstr

pathwise construction of additive h transforms of super brownian motion the pathwise construction of additiveh transforms of the super brownian motion is carried out as a modification of le gall s construction of superprocesses it provides then the explicit conditioning of the super brownian motion on its exit behaviour at its martin boundary which yields an additiveh transforms of the super brownian motion the condition turns out to be that the space time point of death of the super brownian motion converges in the martin topology of the brownian motion

absolute continuity results for superprocesses with some applications let x1 and x2 be instances of a measure valued dawsonwatanabe 4 super process where the underlying spatial motions are given by a borel right process x and where the branching mechanism has finite variance a necessary and sufficient condition on x0 and x2 is found for the law of xi 2 to be absolutely continuous with respect to the law of x2 the conditions are the natural absolute continuity conditions on s but some care must be taken with the set of times s t being considered the result is used to study the closed support of super brownian motion and give sufficient conditions for the existence of a nontrivial collision measure for a pair of independent superlevy processes or more generally for a super levy process and a fixed measure the collision measure gauges the extent of overlap of the two measures as a final application we give an elementary proof of the instantaneous propagation of a super levy process to all points to which the underlying levy process can jump this result is then extended to a much larger class of superprocesses using different techniques

combination tones in the response of single degree of freedom systems with quadratic and cubic non linearities abstract the method of multiple scales is used to analyze the response of a single degree of freedom system to either the combination resonance of the additive type 2 1 0 or the combination resonance of the difference type 2 1 0 where 1 and 2 are the frequencies of the excitation and 0 is the linear undamped natural frequency of the system to the second approximation the combination resonance of the additive type has three effects on the steady state response first it produces terms having the frequencies 1 2 and 2 1 at first order and terms having the frequencies 0 2 1 2 2 2 1 2 2 1 2 2 1 and 2 2 1 at second order second it produces a shift in the natural frequency of the system third it produces a virtual primary resonant excitation having the frequency 2 1 0 that makes the component having the frequency 2 1 be of first rather than second order similar effects are produced by a combination resonance of the difference type or a superharmonic resonance of order two

combination resonances in the non linear response of bowed structures to a harmonic excitation a second order uniform expansion is obtained for the response of a bowed structure systems with quadratic and cubic non linearities to a combination resonance the results show that combination resonances of the difference type can never be excited moreover the results show that the steady state amplitudes depend strongly on the second mode excitation amplitude f2 two threshold values 1 and 2 for f2 are identified when f2 2 combination resonances are always excited and when 2 f2 2 combination resonances may or may not be excited depending on the initial conditions the results also show that combination resonances are very sensitive to the addition of a first mode excitation amplitude f1 for a certain range of values of f1f2 and the phase angle between the two excitations combination resonances are quenched and the response consistes essentially of the linear response the quenching of combination resonances has been verified by numerically integrating the original differential equations in the presence as well as the absence of internal resonances the analysis also identifies a range of values of f1f2 and for which the response is significantly enhanced this result has also been verified by numerically integrating the original equations in the presence as well as the absence of internal resonances

link sign prediction by variational bayesian probabilistic matrix factorization with student t prior abstract in signed social networks link sign prediction refers to using the observed link signs to infer the signs of the remaining links which is important for mining and analyzing the evolution of social networks the widely used matrix factorization based approach bayesian probabilistic matrix factorization bmf assumes that the noise between the real and predicted entry is gaussian noise and the prior of latent features is multivariate gaussian distribution however gaussian noise model is sensitive to outliers and is not robust gaussian prior model neglects the differences between latent features that is it does not distinguish between important and non important features thus gaussian assumption based models perform poorly on real world sparse datasets to address these issues a novel variational bayesian probabilistic matrix factorization with student t prior model tbmf is proposed in this paper a univariate student t distribution is used to fit the prediction noise and a multivariate student t distribution is adopted for the prior of latent features due to the high kurtosis of student t distribution tbmf can select informative latent features automatically characterize long tail cases and obtain reasonable representations on many real world datasets experimental results show that tbmf improves the prediction performance significantly compared with the state of the art algorithms especially when the observed links are few

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

local extinction versus local exponential growth for spatial branching processes let x be either the branching diffusion corresponding to the operator lu u2 u on d rd where x 0 and 0 is bounded from above or the superprocess corresponding to the operator lu u u2 on d rd with 0 and is bounded from above but no restriction on its sign let c denote the generalized principal eigenvalue for the operator l on d we prove the following dichotomy either c 0 and x exhibits local extinction or c 0 and there is exponential growth of mass on compacts of d with rate c for superdiffusions this completes the local extinction criterion obtained by pinsky ann probab 24 1996 237 267 and a recent result on the local growth of mass under a spectral assumption given by englander and turaev ann probab 30 2002 683 722 the proofs in the above two papers are based on pde techniques however the proofs we offer are probabilistically conceptual for the most part they are based on spine decompositions or immortal particle representations along with martingale convergence and the law of large numbers further they are generic in the sense that they work for both types of processes

insights into multiple single lower bound approximation for extended variational inference in non gaussian structured data modeling for most of the non gaussian statistical models the data being modeled represent strongly structured properties such as scalar data with bounded support e g beta distribution vector data with unit length e g dirichlet distribution and vector data with positive elements e g generalized inverted dirichlet distribution in practical implementations of non gaussian statistical models it is infeasible to find an analytically tractable solution to estimating the posterior distributions of the parameters variational inference vi is a widely used framework in bayesian estimation recently an improved framework namely the extended vi evi has been introduced and applied successfully to a number of non gaussian statistical models evi derives analytically tractable solutions by introducing lower bound approximations to the variational objective function in this paper we compare two approximation strategies namely the multiple lower bounds mlbs approximation and the single lower bound slb approximation which can be applied to carry out the evi for implementation two different conditions the weak and the strong conditions are discussed convergence of the evi depends on the selection of the lower bound regardless of the choice of weak or strong condition we also discuss the convergence properties to clarify the differences between mlb and slb extensive comparisons are made based on some evi based non gaussian statistical models theoretical analysis is conducted to demonstrate the differences between the weak and strong conditions experimental results based on real data show advantages of the slb approximation over the mlb approximation

regular transition functions and regular superprocesses the class of regular markov processes is very close to the class of right processes studied by meyer getoor and others we say that a transition function p is regular if it is the transition function of a well defined regular markov process a characterization of regular transition functions is given which implies that if p is regular then the dawson watanabe and the flemingviot supertransition functions over p belong to the same class

comments on application of the conditional population mixture model to image segmentation in the above correspondence1 a maximum likelihood method is proposed for estimating class memberships and underlying statistical parameters within the context of distribution mixtures in the present comment it is pointed out that biases are incurred in parameter estimation that the class memberships and parameters are conceptually different and therefore that the so called standard mixture likelihood is to be preferred also in the correspondence 1 akaike s information criterion aic is used to choose the number of classes in the mixture here a brief theoretical caveat is issued

superprocesses and their linear additive functionals let x x t p be a measure valued stochastic process linear functionals of x are the elements of the minimal closed subspace l of l 2 p which contains all x t b with x t b 2 dp we represent such functionals in terms of stochastic integrals and we derive integral and differential equations for their laplace transforms we consider markov processes with nonstationary transition functions to reveal better the principal role of the backward equations

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

response of self excited two degree of freedom systems to multifrequency excitations the response to multifrequency excitation of a two degree of freedom self excited system is analyzed by using the method of multiple scales three cases of resonance are considered superharmonic primary and subharmonic also considered is the case of simultaneous superharmonic and subharmonic resonance steady state and stability analyses are carried out for each case and numerical results are presented showing the influences of the several parameters

turbo segmentation of textured images we consider the problem of semi supervised segmentation of textured images existing model based approaches model the intensity field of textured images as a gauss markov random field to take into account the local spatial dependencies between the pixels classical bayesian segmentation consists of also modeling the label field as a markov random field to ensure that neighboring pixels correspond to the same texture class with high probability well known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion but these techniques are usually computationally intensive because they require a large number of iterations to converge in this paper we propose a new bayesian framework by modeling two dimensional textured images as the concatenation of two one dimensional hidden markov autoregressive models for the lines and the columns respectively a segmentation algorithm which is similar to turbo decoding in the context of error correcting codes is obtained based on a factor graph approach the proposed method estimates the unknown parameters using the expectation maximization algorithm

conditioned super brownian motion we investigate classes of conditioned super brownian motions namely h transformsp h with non negative finitely based space time harmonic functionsh t we prove thath h is the unique solution of a martingale problem with interaction and is a weak limit of a sequence of rescaled interacting branching brownian motions we identify the limit behaviour of h transforms with functionsh t h t 1 depending only on the total mass 1 using the palm measures of the super brownian motion we describe for an additive spacetime harmonic functionh t h t x dx theh transformp h as a conditioned super brownian motion in which an immortal particle moves like an h transform of brownian motion

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

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

decorrelation of neutral vector variables theory and applications in this paper we propose novel strategies for neutral vector variable decorrelation two fundamental invertible transformations namely serial nonlinear transformation and parallel nonlinear transformation are proposed to carry out the decorrelation for a neutral vector variable which is not multivariate gaussian distributed the conventional principal component analysis cannot yield mutually independent scalar variables with the two proposed transformations a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom we also evaluate the decorrelation performances for the vectors generated from a single dirichlet distribution and a mixture of dirichlet distributions the mutual independence is verified with the distance correlation measurement the advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations

bayes smoothing algorithms for segmentation of binary images modeled by markov random fields a new image segmentation algorithm is presented based on recursive bayes smoothing of images modeled by markov random fields and corrupted by independent additive noise the bayes smoothing algorithm yields the a posteriori distribution of the scene value at each pixel given the total noisy image in a recursive way the a posteriori distribution together with a criterion of optimality then determine a bayes estimate of the scene the algorithm presented is an extension of a 1 d bayes smoothing algorithm to 2 d and it gives the optimum bayes estimate for the scene value at each pixel computational concerns in 2 d however necessitate certain simplifying assumptions on the model and approximations on the implementation of the algorithm in particular the scene noiseless image is modeled as a markov mesh random field a special class of markov random fields and the bayes smoothing algorithm is applied on overlapping strips horizontal vertical of the image consisting of several rows columns it is assumed that the signal scene values vector sequence along the strip is a vector markov chain since signal correlation in one of the dimensions is not fully used along the edges of the strip estimates are generated only along the middle sections of the strips the overlapping strips are chosen such that the union of the middle sections of the strips gives the whole image the bayes smoothing algorithm presented here is valid for scene random fields consisting of multilevel discrete or continuous random variables

super brownian motion path properties and hitting probabilities sample path properties of super brownian motion including a one sided modulus of continuity and exact hausdorff measure function of the range and closed support are obtained analytic estimates for the probability of hitting balls lead to upper bounds on the hausdorff measure of the set of k multiple points and a sufficient condition for a set to be polar

on a problem of modified lindstedt poincare for certain strongly non linear oscillators in the present paper concerns the modified lindstedt poincare method is presented for extending the rang of the validity of perturbation expansion to strongly non linear oscillation it is an effective method for dealing with strongly non linear vibration of single degree of freedom system which cannot be treated by the standard l p method therefore a strongly non linear system with large parameter m is transformed into a small parameter system with respect to a this method is suitable for the system with even non linearities as well as with odd non linearities all numerical results computed are in pretty good and displayed graphysically this method is suitable for the system with even non linearities as well as with odd non linearities all numerical results computed are in pretty good and displayed graphysically

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

mean field approaches to independent component analysis we develop mean field approaches for probabilistic independent component analysis ica the sources are estimated from the mean of their posterior distribution and the mixing matrix and noise level is estimated by maximum a posteriori map the latter requires the computation of a good approximation to the correlations between sources for this purpose we investigate three increasingly advanced mean field methods the variational also known as naive mean field approach linear response corrections and an adaptive version of the thouless anderson and palmer 1977 tap mean field approach which is due to opper and winther 2001 the resulting algorithms are tested on a number of problems on synthetic data the advanced mean field approaches are able to recover the correct mixing matrix in cases where the variational mean field theory fails for handwritten digits sparse encoding is achieved using nonnegative source and mixing priors for speech the mean field method is able to separate in the underdetermined overcomplete case of two sensors and three sources one major advantage of the proposed method is its generality and algorithmic simplicity finally we point out several possible extensions of the approaches developed here

parametrically excited non linear systems a comparison of two methods subharmonic resonance of two degree of freedom systems with cubic non linearities to multifrequency parametric excitations in the presence of three to one internal resonance is investigated two approximate methods the multiple scales and the generalized synchronization are used to construct first order non linear ordinary differential equations governing the modulation of the amplitudes and phases steady state solutions and their stability are computed for selected values of the system parameters the results obtained by the two methods are in excellent agreement numerical solutions are carried out and graphical representations of the results are presented and discussed

segmentation registration and measurement of shape variation via image object shape a model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives metrics are described that compute an object representation s prior probability of local geometry by reflecting variabilities in the net s node and link parameter values and that compute a likelihood function measuring the degree of match of an image to that object representation a paradigm for image analysis of deforming such a model to optimize a posteriori probability is described and this paradigm is shown to be usable as a uniform approach for object definition object based registration between images of the same or different imaging modalities and measurement of shape variation of an abnormal anatomical object compared with a normal anatomical object examples of applications of these methods in radiotherapy surgery and psychiatry are given

maximum likelihood discriminant analysis on the plane using a markovian model of spatial context abstract a method is presented for utilising spatial information in performing discriminant analysis on multivariate data at each point on a regular lattice as for example with landsat the spatial information is modelled as a particularly simple markov random field the discriminant analysis is based on the maximum likelihood method the results are compared with alternatives by monte carlo simulation and seem to be encouraging

parameter estimation and tissue segmentation from multispectral mr images a statistical method is developed to classify tissue types and to segment the corresponding tissue regions from relaxation time t sub 1 t sub 2 and proton density p sub d weighted magnetic resonance images the method assumes that the distribution of image intensities associated with each tissue type can be expressed as a multivariate likelihood function of three weighted signal intensity values t sub 1 t sub 2 p sub d at each location within that tissue regions the method further assumes that the underlying tissue regions are piecewise contiguous and can be characterized by a markov random field prior in classifying the tissue types the method models the likelihood of realizing the images as a finite multivariate mixture function the class parameters associated with the tissue types i e the weighted intensity means variances and correlation coefficients of the multivariate function as well as the number of voxels within regions of the tissue types of are estimated by maximum likelihood the estimation fits the class parameters to the image data via the expectation maximization algorithm the number of classes associated with the tissue types is determined by the information criterion of minimum description length the method segments the tissue regions given the estimated class parameters by maximum a posteriori probability the prior is constructed by the tissue region membership of the first and second order neighborhood the method is tested by a few sets of t sub 1 t sub 2 and p sub d weighted images of the brain acquired with a 1 5 tesla whole body scanner the number of classes and the associated class parameters are automatically estimated the regions of different brain tissues are satisfactorily segmented

nonnegative matrix factorization with the itakura saito divergence with application to music analysis this letter presents theoretical algorithmic and experimental results about nonnegative matrix factorization nmf with the itakura saito is divergence we describe how is nmf is underlaid by a well defined statistical model of superimposed gaussian components and is equivalent to maximum likelihood estimation of variance parameters this setting can accommodate regularization constraints on the factors through bayesian priors in particular inverse gamma and gamma markov chain priors are considered in this work estimation can be carried out using a space alternating generalized expectation maximization sage algorithm this leads to a novel type of nmf algorithm whose convergence to a stationary point of the is cost function is guaranteed we also discuss the links between the is divergence and other cost functions used in nmf in particular the euclidean distance and the generalized kullback leibler kl divergence as such we describe how is nmf can also be performed using a gradient multiplicative algorithm a standard algorithm structure in nmf whose convergence is observed in practice though not proven finally we report a furnished experimental comparative study of euclidean nmf kl nmf and is nmf algorithms applied to the power spectrogram of a short piano sequence recorded in real conditions with various initializations and model orders then we show how is nmf can successfully be employed for denoising and upmix mono to stereo conversion of an original piece of early jazz music these experiments indicate that is nmf correctly captures the semantics of audio and is better suited to the representation of music signals than nmf with the usual euclidean and kl costs

interval estimation in discrimination the multivariate normal equal covariance case summary a general approach to discrimination problems is described which emphasizes the viewpoint of individual cases and expresses the uncertainty with which individual decisions are made it is applied to the particular case of two multivariate normal distributions with a common covariance matrix an affine transformation to which the key quantities are invariant simplifies discussion of the distribution of the estimated log odds ratio and suggests a practically useful plot which generalizes the usual display of discriminant scores and has several attractive features an illustration is given two approximate interval estimation techniques for the true log odds ratio are described and evaluated in a range of practical situations by a simulation study some further applications of our general approach are briefly indicated

persistence of critical multitype particle and measure branching processes we consider a class of systems of particles ofk types inr d undergoing spatial diffusion and critical multitype branching where the diffusions the particle lifetimes and the branching laws depend on the types we prove persistence criteria for such systems and for their corresponding high density limits known as multitype dawson watanabe processes the main tool is a representation of the palm distributions for a general class of inhomogeneous critical branching particle systems constructed by means of a backward tree

on the covariance of two noncentral f random variables and the variance of the estimated liner discriminant function summary the covariance of two noncentral f random variables with a common covariance matrix is obtained from which the variance of their difference follows easily an application of this latter result in discriminant analysis is then given

bayesian estimation of beta mixture models with variational inference bayesian estimation of the parameters in beta mixture models bmm is analytically intractable the numerical solutions to simulate the posterior distribution are available but incur high computational cost in this paper we introduce an approximation to the prior posterior distribution of the parameters in the beta distribution and propose an analytically tractable closed form bayesian approach to the parameter estimation the approach is based on the variational inference vi framework following the principles of the vi framework and utilizing the relative convexity bound the extended factorized approximation method is applied to approximate the distribution of the parameters in bmm in a fully bayesian model where all of the parameters of the bmm are considered as variables and assigned proper distributions our approach can asymptotically find the optimal estimate of the parameters posterior distribution also the model complexity can be determined based on the data the closed form solution is proposed so that no iterative numerical calculation is required meanwhile our approach avoids the drawback of overfitting in the conventional expectation maximization algorithm the good performance of this approach is verified by experiments with both synthetic and real data

variational bayesian matrix factorization for bounded support data a novel bayesian matrix factorization method for bounded support data is presented each entry in the observation matrix is assumed to be beta distributed as the beta distribution has two parameters two parameter matrices can be obtained which matrices contain only nonnegative values in order to provide low rank matrix factorization the nonnegative matrix factorization nmf technique is applied furthermore each entry in the factorized matrices i e the basis and excitation matrices is assigned with gamma prior therefore we name this method as beta gamma nmf bg nmf due to the integral expression of the gamma function estimation of the posterior distribution in the bg nmf model can not be presented by an analytically tractable solution with the variational inference framework and the relative convexity property of the log inverse beta function we propose a new lower bound to approximate the objective function with this new lower bound we derive an analytically tractable solution to approximately calculate the posterior distributions each of the approximated posterior distributions is also gamma distributed which retains the conjugacy of the bayesian estimation in addition a sparse bg nmf can be obtained by including a sparseness constraint to the gamma prior evaluations with synthetic data and real life data demonstrate the good performance of the proposed method

a markov random field model based approach to image interpretation an image is segmented into a collection of disjoint regions that form the nodes of an adjacency graph and image interpretation is achieved through assigning object labels or interpretations to the segmented regions or nodes using domain knowledge extracted feature measurements and spatial relationships between the various regions the interpretation labels are modeled as a markov random field mrf on the corresponding adjacency graph and the image interpretation problem is then formulated as a maximum a posteriori map estimation rule given domain knowledge and region based measurements simulated annealing is used to find this best realization or optimal map interpretation this approach also provides a systematic method for organizing and representing domain knowledge through appropriate design of the clique functions describing the gibbs distribution representing the pdf of the underlying mrf a general methodology is provided for the design of the clique functions results of image interpretation experiments on synthetic and real world images are described

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

object based estimation of dense motion fields motion estimation belongs to key techniques in image sequence processing segmentation of the motion fields such that ideally each independently moving object uniquely corresponds to one region is one of the essential elements in object based image processing this paper is concerned with unsupervised simultaneous estimation of dense motion fields and their segmentations it is based on a stochastic model relating image intensities to motion information based on the analysis of natural images a region based model of motion compensated prediction error is proposed in each region the error is modeled by a white stationary generalized gaussian random process the motion field and its segmentation are themselves modeled by a compound gibbs markov random field accounting for statistical bindings in spatial direction and along the direction of motion trajectories the a posteriori distribution of the motion field for a given image sequence is formulated as an objective function such that its maximization results in the map estimate a deterministic multiscale relaxation technique with regular structure is employed for optimization of the objective function simulation results are in a good agreement with human perception for both the motion fields and their segmentations

3 d contextual bayesian classifiers we extend a series of multivariate bayesian two dimensional 2 d contextual classifiers to three dimensional 3 d by specifying a simultaneous gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its six nearest 3 d neighbors

on the conditioned exit measures of super brownian motion in this paper we present a martingale related to the exit measures of super brownian motion by changing measure with this martingale in the canonical way we have a new process associated with the conditioned exit measure this measure is shown to be identical to a measure generated by a non homogeneous branching particle system with immigration of mass an application is given to the problem of conditioning the exit measure to hit a number of specified points on the boundary of a domain the results are similar in flavor to the immortal particle picture of conditioned super brownian motion but more general as the change of measure is given by a martingale which need not arise from a single harmonic function

a tree structured markov random field model for bayesian image segmentation we present a new image segmentation algorithm based on a tree structured binary mrf model the image is recursively segmented in smaller and smaller regions until a stopping condition local to each region is met each elementary binary segmentation is obtained as the solution of a map estimation problem with the region prior modeled as an mrf since only binary fields are used and thanks to the tree structure the algorithm is quite fast and allows one to address the cluster validation problem in a seamless way in addition all field parameters are estimated locally allowing for some spatial adaptivity to improve segmentation accuracy a split and merge procedure is also developed and a spatially adaptive mrf model is used numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on flat mrf models and its performance in terms of segmentation accuracy and map smoothness is comparable or even superior

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

algorithms for nonnegative matrix factorization with the β divergence this letter describes algorithms for nonnegative matrix factorization nmf with the divergence nmf the divergence is a family of cost functions parameterized by a single shape parameter that takes the euclidean distance the kullback leibler divergence and the itakura saito divergence as special cases 2 1 0 respectively the proposed algorithms are based on a surrogate auxiliary function a local majorization of the criterion function we first describe a majorization minimization algorithm that leads to multiplicative updates which differ from standard heuristic multiplicative updates by a dependent power exponent the monotonicity of the heuristic algorithm can however be proven for 0 1 using the proposed auxiliary function then we introduce the concept of the majorization equalization me algorithm which produces updates that move along constant level sets of the auxiliary function and lead to larger steps than mm simulations on synthetic and real data illustrate the faster convergence of the me approach the letter also describes how the proposed algorithms can be adapted to two common variants of nmf penalized nmf when a penalty function of the factors is added to the criterion function and convex nmf when the dictionary is assumed to belong to a known subspace

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

graphical and recursive models for contingency tables summary we discuss two classes of models for contingency tables graphical and recursive models both of which arise from restrictions that are expressible as conditional independencies of variable pairs the first of these is a subclass of hierarchical log linear models each of its models can be represented by an undirected graph in the second class each model corresponds to a particular kind of a directed graph instead and can be characterized by a nontrivial factorization of the joint distribution in terms of response variables we derive decomposable or multiplicative models as the intersecting class this result has useful consequences for exploratory types of analysis as well as for the model interpretation we can give an aid for detecting well fitting decomposable models in a transformation of the observed contingency table and each decomposable model may be interpreted with the help of an undirected or directed graph