solving mixed integer nonlinear programs by outer approximation a wide range of optimization problems arising from engineering applications can be formulated as mixed integer nonlinear programming problems minlps duran and grossmann 1986 suggest an outer approximation scheme for solving a class of minlps that are linear in the integer variables by a finite sequence of relaxed milp master programs and nlp subproblems

multiple window parallel adaptive boundary finding in computer vision the problem considered in this paper is the estimation of highly variable object boundaries in noisy images boundaries may be those of a tank in an ir image a spinal canal in a cat scan a cloud in a visible light image etc or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object the focus of the paper is on parallel multiple window boundary estimation algorithms here the image field is parti tioned into an array of rectangular windows and boundary finders are run simultaneously within the windows the boundary segments found within the windows are then seamed together to obtain meaningful global boundaries the entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding although our multiple window estimation approach can be used with a number of local boundary finding algorithms we concen trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary some theoretical considera tions for boundary model design and boundary finding runtime are covered included is the use of a low computational cost f test for test ing whether a window contains a boundary and an analytical treatment which shows that use of coarse pixels with a chi square test or an f test improves the probability of correctly recognizing whether a boundary is present in a window

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

multigrid tomographic inversion with variable resolution data and image spaces a multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements the proposed algorithm further reduces the computation relative to conventional multigrid approaches which change only the image space resolution at coarse scales the advantage is particularly important for data rich applications where data resolutions may differ for different scales applications of the approach to bayesian reconstruction algorithms in transmission and emission tomography with a generalized gaussian markov random field image prior are presented both with a poisson noise model and with a quadratic data term simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed grid iterative coordinate descent method and a multigrid method with fixed data resolution

a wavelet or lifting scheme based imputation method summary the paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis our method incorporates a bayesian mixture prior for these wavelet coefficients into a gibbs sampler to generate a complete posterior distribution for the variable of interest intuitively the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites we demonstrate the strong performance of our estimator in both one and two dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines

maximizing a class of submodular utility functions with constraints motivated by stochastic 0 1 integer programming problems with an expected utility objective we study the mixed integer nonlinear set p big w x in mathbb r times left 0 1 right n w le f a x d b x le b big p w x r 0 1n w f a x d b x b where n is a positive integer f mathbb r mapsto mathbb r f r r is a concave function a b in mathbb r n a b rn are nonnegative vectors d is a real number and b is a positive real number we propose a family of inequalities for the convex hull of p by exploiting submodularity of the function f a x d f a x d over 0 1 n 0 1 n and the knapsack constraint b x le b b x b computational effectiveness of the proposed inequalities within a branch and cut framework is illustrated using instances of an expected utility capital budgeting problem

approximate random variate generation from infinitely divisible distributions with applications to bayesian inference summary stochastic processes with independent increments play a central role in bayesian nonparametric inference the distributions of the increments of these processes aside from fixed points of discontinuity are infinitely divisible and their laplace and or fourier transforms in the levy representation are usually known conventional bayesian inference in this context has been limited largely to providing point estimates of the random quantities of interest although markov chain monte carlo methods have been used to obtain a fuller analysis in the context of dirichlet process priors in this paper we propose and implement a general method for simulating infinitely divisible random variates when their fourier or laplace transforms are available in the levy representation theoretical justification is established by proving a convergence theorem that is a sampling form of a classical theorem in probability the results provide a method for implementing bayesian nonparametric inference by using a wide range of stochastic processes as priors

a procedure for assessing the completeness of the q matrices of cognitively diagnostic tests the q matrix of a cognitively diagnostic test is said to be complete if it allows for the identification of all possible proficiency classes among examinees completeness of the q matrix is therefore a key requirement for any cognitively diagnostic test however completeness of the q matrix is often difficult to establish especially for tests with a large number of items involving multiple attributes as an additional complication completeness is not an intrinsic property of the q matrix but can only be assessed in reference to a specific cognitive diagnosis model cdm supposed to underly the data that is the q matrix of a given test can be complete for one model but incomplete for another in this article a method is presented for assessing whether a given q matrix is complete for a given cdm the proposed procedure relies on the theoretical framework of general cdms and is therefore legitimate for cdms that can be reparameterized as a general cdm

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

the generalised autocovariance function the generalised autocovariance function is defined for a stationary stochastic process as the inverse fourier transform of the power transformation of the spectral density function depending on the value of the transformation parameter this function nests the inverse and the traditional autocovariance functions a frequency domain non parametric estimator based on the power transformation of the pooled periodogram is considered and its asymptotic distribution is derived the results are employed to construct classes of tests of the white noise hypothesis for clustering and discrimination of stochastic processes and to introduce a novel feature matching estimator of the spectrum

benders decomposition without separability a computational study for capacitated facility location problems abstract benders is one of the most famous decomposition tools for mathematical programming and it is the method of choice e g in mixed integer stochastic programming its hallmark is the capability of decomposing certain types of models into smaller subproblems each of which can be solved individually to produce local information notably cutting planes to be exploited by a centralized master problem as its name suggests the power of the technique comes essentially from the decomposition effect i e the separability of the problem into a master problem and several smaller subproblems in this paper we address the question of whether the benders approach can be useful even without separability of the subproblem i e when its application yields a single subproblem of the same size as the original problem in particular we focus on the capacitated facility location problem in two variants the classical linear case and a congested case where the objective function contains convex but non separable quadratic terms we show how to embed the benders approach within a modern branch and cut mixed integer programming solver addressing explicitly all the ingredients that are instrumental for its success in particular we discuss some computational aspects that are related to the negative effects derived from the lack of separability extensive computational results on various classes of instances from the literature are reported with a comparison with the state of the art exact and heuristic algorithms the outcome is that a clever but simple implementation of the benders approach can be very effective even without separability as its performance is comparable and sometimes even better than that of the most effective and sophisticated algorithms proposed in the previous literature

a coupling regeneration scheme for diagnosing convergence in markov chain monte carlo algorithms abstract here i propose a convergence diagnostic for markov chain monte carlo mcmc algorithms based on couplings of a markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value the diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains and provides a lower bound on the effective sample size of a mcmc run it also provides a simple procedure for obtaining what is with high probability an independent sample from the stationary distribution

a minimum distance estimator for long memory processes this paper considers a minimum distance estimator mde of the differencing para meter of the fractionally integrated white noise model the mde minimizes the differ ence between sample and population autocorrelations the paper presents calculations of asymptotic variances to examine the efficiency of the mde relative to that of the mle for values of the differencing parameter less than l 4 the mde is consistent and asymptotically normal and the asymptotic variance of the mde using the first n auto correlations approaches that of the mle as n increases however there is a substantial efficiency loss if low order autocorrelations are omitted this implies that a non parametric treatment of short run dynamics will involve a substantial loss of efficiency

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

application of the em algorithm for the multitarget multisensor tracking problem an important problem in surveillance and reconnaissance systems is the tracking of multiple moving targets in cluttered noise environments using outputs from a number of sensors possessing wide variations in individual characteristics and accuracies a number of approaches have been proposed for this multitarget multisensor tracking problem ranging from reasonably simple though ad hoc schemes to fairly complex but theoretically optimum approaches in this paper we describe an iterative procedure for time recursive multitarget multisensor tracking based on use of the expectation maximization em algorithm more specifically we pose the multitarget multisensor tracking problem as an incomplete data problem with the observable sensor outputs representing the incomplete data whereas the target associated sensor outputs constitute the complete data target updates at each time use an em based approach that calculates the maximum a posteriori map estimate of the target states under the assumption of appropriate motion models based on the outputs of disparate sensors the approach uses a markov random field mrf model of the associations between observations and targets and allows for estimation of joint association probabilities without explicit enumeration the advantage of this em based approach is that it provides a computationally efficient means for approaching the performance offered by theoretically optimum approaches that use explicit enumeration of the joint association probabilities we provide selected results illustrating the performance complexity characteristics of this em based approach compared with competing schemes

outperforming the gibbs sampler empirical estimator for nearest neighbor random fields given a markov chain sampling scheme does the standard empirical estimator make best use of the data we show that this is not so and construct better estimators we restrict attention to nearest neighbor random fields and to gibbs samplers with deterministic sweep but our approach applies to any sampler that uses reversible variable at a time updating with deterministic sweep the structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance the extra computational cost is negligible when the random field is spatially homogeneous symmetrizations of our estimator lead to further variance reduction the performance of the estimators is evaluated in a simulation study of the ising model

an outer approximation algorithm for a class of mixed integer nonlinear programs an outer approximation algorithm is presented for solving mixed integer nonlinear programming problems of a particular class linearity of the integer or discrete variables and convexity of the nonlinear functions involving continuous variables are the main features in the underlying mathematical structure based on principles of decomposition outer approximation and relaxation the proposed algorithm effectively exploits the structure of the problems and consists of solving an alternating finite sequence of nonlinear programming subproblems and relaxed versions of a mixed integer linear master program convergence and optimality properties of the algorithm are presented as well as a general discussion on its implementation numerical results are reported for several example problems to illustrate the potential of the proposed algorithm for programs in the class addressed in this paper finally a theoretical comparison with generalized benders decomposition is presented on the lower bounds predicted by the relaxed master programs

application of piece wise regression to detecting internal structure of signal abstract the problem of restoring the underlying structure of a signal with the help of piece wise regression is considered the case of interest is that the domain of definition of a response function consists of a number of regions of smoothness the number of regions and the location of change points are not fixed in advance and they should be found by analyzing the signal corrupted with noise for a given number of smooth regions the best piece wise regression may be found with the help of an approach based on dynamic programming the selection of the best model the best number of regions of smoothness is performed with the help of a probabilistic estimate some properties of the estimate and the whole procedure are studied and the results of experiments are presented

a branch and cut algorithm for the undirected traveling purchaser problem the purpose of this paper is to present a branch and cut algorithm for the undirectedtraveling purchaser problem which consists of determining a minimum cost route through a subset of markets where the cost is the sum of travel and purchase costs the problem is formulated as an integer linear program and several families of valid inequalities are derived to strengthen the linear relaxation the polyhedral structure of the formulation is analyzed and several classes of valid inequalities are proved to be facet defining a branch and cut procedure is developed and tested over four classes of randomly generated instances results show that the proposed algorithm outperforms all previous approaches and can optimally solve instances containing up to 200 markets

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

on the equivalence of soft wavelet shrinkage total variation diffusion total variation regularization and sides soft wavelet shrinkage total variation tv diffusion tv regularization and a dynamical system called sides are four useful techniques for discontinuity preserving denoising of signals and images in this paper we investigate under which circumstances these methods are equivalent in the one dimensional case first we prove that haar wavelet shrinkage on a single scale is equivalent to a single step of space discrete tv diffusion or regularization of two pixel pairs in the translationally invariant case we show that applying cycle spinning to haar wavelet shrinkage on a single scale can be regarded as an absolutely stable explicit discretization of tv diffusion we prove that space discrete tv diffusion and tv regularization are identical and that they are also equivalent to the sides system when a specific force function is chosen afterwards we show that wavelet shrinkage on multiple scales can be regarded as a single step diffusion filtering or regularization of the laplacian pyramid of the signal we analyze possibilities to avoid gibbs like artifacts for multiscale haar wavelet shrinkage by scaling the thresholds finally we present experiments where hybrid methods are designed that combine the advantages of wavelets and pde variational approaches these methods are based on iterated shift invariant wavelet shrinkage at multiple scales with scaled thresholds

optimization of integer wavelet transforms based on difference correlation structures in this paper a novel lifting integer wavelet transform based on difference correlation structure dccs liwt is proposed first we establish a relationship between the performance of a linear predictor and the difference correlations of an image the obtained results provide a theoretical foundation for the following construction of the optimal lifting filters then the optimal prediction lifting coefficients in the sense of least square prediction error are derived dccs liwt puts heavy emphasis on image inherent dependence a distinct feature of this method is the use of the variance normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources the proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations experimental evaluation shows that the proposed method produces better results than the other well known integer transforms for the lossless image compression

estimating the differencing parameter via the partial autocorrelation function this paper provides an explanation for the puzzling phenomenon in tieslau et al 1996 journal of econometrics 71 249 264 that a substantial e ciency loss occurs if low order autocorrelations are omitted when estimating the di erencing parameter d this is because for all n strictly bigger than 1 the nth order autocorrelation function does not depend uniquely on the di erencing parameter we construct a new estimator for the di erencing parameter based on the partial autocorrelation function comparisons of the asymptotic and nite sample variance of our estimator and those of tsb are made a substantial e ciency gain is achieved by our estimator as compared to tsb s 2000 elsevier science s a all rights reserved jel classixcation c22

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

on the link between cognitive diagnostic models and knowledge space theory the present work explores the connections between cognitive diagnostic models cdm and knowledge space theory kst and shows that these two quite distinct approaches overlap it is proved that in fact the multiple strategy dina deterministic input noisy and gate model and the cblim a competence based extension of the basic local independence model blim are equivalent to demonstrate the benefits that arise from integrating the two theoretical perspectives it is shown that a fairly complete picture on the identifiability of these models emerges by combining results from both camps the impact of the results is illustrated by an empirical example and topics for further research are pointed out

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

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

the variance profile the variance profile is defined as the power mean of the spectral density function of a stationary stochastic process it is a continuous and nondecreasing function of the power parameter p which returns the minimum of the spectrum p the interpolation error variance harmonic mean p 1 the prediction error variance geometric mean p 0 the unconditional variance arithmetic mean p 1 and the maximum of the spectrum p the variance profile provides a useful characterization of a stochastic process we focus in particular on the class of fractionally integrated processes moreover it enables a direct and immediate derivation of the szego kolmogorov formula and the interpolation error variance formula the article proposes a nonparametric estimator of the variance profile based on the power mean of the smoothed sample spectrum and proves its consistency and its asymptotic normality from the empirical standpoint we propose and illustrate the use of the variance profile for estimating th

competitive facility location model with concave demand abstract we consider a spatial interaction model for locating a set of new facilities that compete for customer demand with each other as well as with some pre existing facilities to capture the market expansion and the market cannibalization effects customer demand is assumed to be a concave non decreasing function of the total utility derived by each customer from the service offered by the facilities the problem is formulated as a non linear knapsack problem for which we develop a novel solution approach based on constructing an efficient piecewise linear approximation scheme for the objective function this allows us to develop exact and optimal solution approaches capable of dealing with relatively large scale instances of the model we also develop a fast heuristic algorithm for which a tight worst case error bound is established

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

indirect estimation of arfima and varfima models indirect estimation methods are proposed for estimating arfima as well as more complex varfima models a general framework for conducting indirect estimation of fractional models is developed that covers simulation methods choice of auxiliary model and estimation algorithm special attention is given to comparing the finite sampling properties of the indirect estimator with sowell s 1992a exact time domain maximum likelihood estimator the spectral maximum likelihood estimator of fox and taqqu 1986 and the geweke and porter hudak 1983 spectral regression estimator the indirect estimator can be computationally faster than the exact time domain maximum likelihood estimator while generating similar small sample properties the computational gains of the indirect estimator over maximum likelihood increase as the complexity of the data generating process increases

the generalized dina model framework the g dina generalized deterministic inputs noisy and gate model is a generalization of the dina model with more relaxed assumptions in its saturated form the g dina model is equivalent to other general models for cognitive diagnosis based on alternative link functions when appropriate constraints are applied several commonly used cognitive diagnosis models cdms can be shown to be special cases of the general models in addition to model formulation the g dina model as a general cdm framework includes a component for item by item model estimation based on design and weight matrices and a component for item by item model comparison based on the wald test the paper illustrates the estimation and application of the g dina model as a framework using real and simulated data it concludes by discussing several potential implications of and relevant issues concerning the proposed framework

genetic algorithms for ambiguous labelling problems abstract consistent labelling problems frequently have more than one solution most work in the field has aimed at disambiguating early in the interpretation process using only local evidence this paper starts with a review of the literature on labelling problems and ambiguity based on this review we propose a strategy for simultaneously extracting multiple related solutions to the consistent labelling problem in a preliminary experimental study we show that an appropriately modified genetic algorithm is a robust tool for finding multiple solutions to the consistent labelling problem these solutions are related by common labellings of the most strongly constrained junctions we have proposed three run time measures of algorithm performance the maximum fitness of the genetic algorithm s population its shannon entropy and the total hamming distance between its distinct members the results to date indicate that when the shannon entropy falls below a certain threshold new solutions are unlikely to emerge and that most of the diversity in the population disappears within the first few generations

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 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

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

the measure on the original space from a product measure abstract the measurability problems can arise in gaussian and empirical processes underlying nonparametric and semiparametric problems critical in modern statistics and machine learning the usual applications are high dimensional data in random fields to ensure the validity of recovering a true original complex object from its observed images treated in a product space that appears in existing high dimensional data applications widely arising in physical biological and social sciences and engineering we begin with the results on the algebra of the original space induced by a given map f t mapping from to a product measure space t f t t we study the certain measurability issues on with the induced measure from the image measure t of the product space by establishing the outer measure restricted to the trace algebra we further investigate the measure on under the map f t to obtain the conditions for the identifiability equality t f t 1 to hold so that a practical and rigorous foundation is provided for the nontrivial applications to work meaningfully

a class of globally convergent optimization methods based on conservative convex separable approximations this paper deals with a certain class of optimization methods based on conservative convex separable approximations ccsa for solving inequality constrained nonlinear programming problems each generated iteration point is a feasible solution with lower objective value than the previous one and it is proved that the sequence of iteration points converges toward the set of karush kuhn tucker points a major advantage of ccsa methods is that they can be applied to problems with a very large number of variables say 104 105 even if the hessian matrices of the objective and constraint functions are dense

modeling persistence in hydrological time series using fractional differencing the class of autoregressive integrated moving average arima time series models may be generalized by permitting the degree of differencing d to take fractional values models including fractional differencing are capable of representing persistent series d 0 or short memory series d 0 the class of fractionally differenced arima processes provides a more flexible way than has hitherto been available of simultaneously modeling the long term and short term behavior of a time series in this paper some fundamental properties of fractionally differenced arima processes are presented methods of simulating these processes are described estimation of the parameters of fractionally differenced arima models is discussed and an approximate maximum likelihood method is proposed the methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures

iterative reweighted total generalized variation based poisson noise removal model total generalized variation tgv regularization model is one of the most effective methods for denoising and eliminating staircase effect however the tgv regularization model tends to blur edges as the existence of high order derivative in order to avoid the staircase effect while alleviating the edge blurring an iterative reweighted tgv based poisson noise removal model is presented under the assumption that each pixel of noisy image follows a poisson distribution the weight function incorporated in the tgv regularization term is derived from the expectation maximization em algorithm we design a new iterative weighted primal dual algorithm which is an improvement of the classic iterative reweighted algorithm numerical experimental results show the better performance of our model in removing noise effectively while preserving edges and eliminating staircase effect

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

noncentral limit theorems for quadratic forms in random variables having long range dependence we study the weak convergence in d lbrack 0 1 rbrack of the quadratic form sum lbrack nt rbrack j 1 sum lbrack nt rbrack k 1 a j k h m x j h m x k adequately normalized here a s infty s infty is a symmetric sequence satisfying sum a s infty h m is the m th hermite polynomial and x j j geq 1 is a normalized gaussian sequence with covariances r k sim k d l k as k rightarrow infty where 0 d 1 and l is slowly varying we prove that for all m geq 1 the limit is brownian motion when 1 2 d 1 and it is the non gaussian rosenblatt process when 0 d 1 2

outer approximation and submodular cuts for maximum capture facility location problems with random utilities abstract we consider a family of competitive facility location problems in which a newcomer company enters the market and has to decide where to locate a set of new facilities so as to maximize its market share the multinomial logit model is used to estimate the captured customer demand we propose a first branch and cut approach for this family of difficult mixed integer non linear problems our approach combines two types of cutting planes that exploit particular properties of the objective function the first one are the outer approximation cuts and the second one are the submodular cuts the approach is computationally evaluated on three datasets from the recent literature the obtained results show that our new branch and cut drastically outperforms state of the art exact approaches both in terms of the computing times and in terms of the number of instances solved to optimality

the maximum capture problem with random utilities problem formulation and algorithms abstract a model for the optimal location of new facilities in a competitive market is introduced under the hypothesis that customers behavior can be modeled by random utility functions it means that the company that wished to locate uses a random utility model to forecast the market share of a location therefore the company cannot forecast the behavior of every customer in a deterministic fashion but is able to embed him by a probability distribution three formulations are proposed to compute upper bounds of the objective function and compared in a numerical simulation a branch and bound method is developed and tested on examples with up to 50 potential locations and a variable neighborhood search heuristic is proposed to solve larger instances

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

generalized flows for optimal inference in higher order mrf map use of higher order clique potentials in mrf map problems has been limited primarily because of the inefficiencies of the existing algorithmic schemes we propose a new combinatorial algorithm for computing optimal solutions to 2 label mrf map problems with higher order clique potentials the algorithm runs in time o 2 kn 3 in the worst case k is size of clique and n is the number of pixels a special gadget is introduced to model flows in a higher order clique and a technique for building a flow graph is specified based on the primal dual structure of the optimization problem the notions of the capacity of an edge and a cut are generalized to define a flow problem we show that in this flow graph when the clique potentials are submodular the max flow is equal to the min cut which also is the optimal solution to the problem we show experimentally that our algorithm provides significantly better solutions in practice and is hundreds of times faster than solution schemes like dual decomposition 1 trws 2 and reduction 3 4 5 the framework represents a significant advance in handling higher order problems making optimal inference practical for medium sized cliques

phase unwrapping of mr phase images using poisson equation the authors have developed a technique based on a solution of the poisson equation to unwrap the phase in magnetic resonance mr phase images the method is based on the assumption that the magnitude of the inter pixel phase change is less than spl pi per pixel therefore the authors obtain an estimate of the phase gradient by wrapping the gradient of the original phase image the problem is then to obtain the absolute phase given the estimate of the phase gradient the least squares ls solution to this problem is shown to be a solution of the poisson equation allowing the use of fast poisson solvers the absolute phase is then obtained by mapping the ls phase to the nearest multiple of 2 k from the measured phase the proposed technique is evaluated using mr phase images and is proven to be robust in the presence of noise an application of the proposed method to the 3 point dixon technique for water and fat separation is demonstrated

algorithmic stability and sanity check bounds for leave one out cross validation in this article we prove sanity check bounds for the error of the leave one out cross validation estimate of the generalization error that is bounds showing that the worst case error of this estimate is not much worse than that of the training error estimate the name sanity check refers to the fact that although we often expect the leave one out estimate to perform considerably better than the training error estimate we are here only seeking assurance that its performance will not be considerably worse perhaps surprisingly such assurance has been given only for limited cases in the prior literature on cross validation any nontrivial bound on the error of leave one out must rely on some notion of algorithmic stability previous bounds relied on the rather strong notion of hypothesis stability whose application was primarily limited to nearest neighbor and other local algorithms here we introduce the new and weaker notion of error stability and apply it to obtain sanity check bounds for leave one out for other classes of learning algorithms including training error minimization procedures and bayesian algorithms we also provide lower bounds demonstrating the necessity of some form of error stability for proving bounds on the error of the leave one out estimate and the fact that for training error minimization algorithms in the worst case such bounds must still depend on the vapnik chervonenkis dimension of the hypothesis class

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

bayesian lasso for semiparametric structural equation models there has been great interest in developing nonlinear structural equation models and associated statistical inference procedures including estimation and model selection methods in this paper a general semiparametric structural equation model ssem is developed in which the structural equation is composed of nonparametric functions of exogenous latent variables and fixed covariates on a set of latent endogenous variables a basis representation is used to approximate these nonparametric functions in the structural equation and the bayesian lasso method coupled with a markov chain monte carlo mcmc algorithm is used for simultaneous estimation and model selection the proposed method is illustrated using a simulation study and data from the affective dynamics and individual differences adid study results demonstrate that our method can accurately estimate the unknown parameters and correctly identify the true underlying model

a comparison of linear reformulations for multinomial logit choice probabilities in facility location models abstract in the last decade several papers appeared on facility location problems that incorporate customer demand by the multinomial logit model three linear reformulations of the original non linear model have been proposed so far in this paper we discuss these models in terms of solvability we present empirical findings based on synthetic data

estimating multiple classification latent class models this paper presents a new class of models for persons by items data the essential new feature of this class is the representation of the persons every person is represented by its membership tomultiple latent classes each of which belongs to onelatent classification the models can be considered as a formalization of the hypothesis that the responses come about in a process that involves the application of a number ofmental operations two algorithms for maximum likelihood ml and maximum a posteriori map estimation are described they both make use of the tractability of the complete data likelihood to maximize the observed data likelihood properties of the map estimators i e uniqueness and goodness of recovery and the existence of asymptotic standard errors were examined in a simulation study then one of these models is applied to the responses to a set of fraction addition problems finally the models are compared to some related models in the literature

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

the indian buffet process an introduction and review the indian buffet process is a stochastic process defining a probability distribution over equivalence classes of sparse binary matrices with a finite number of rows and an unbounded number of columns this distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features or that involve bipartite graphs in which the size of at least one class of nodes is unknown we give a detailed derivation of this distribution and illustrate its use as a prior in an infinite latent feature model we then review recent applications of the indian buffet process in machine learning discuss its extensions and summarize its connections to other stochastic processes

a branch and bound algorithm for the maximum capture problem with random utilities abstract the maximum capture problem with random utilities seeks to locate new facilities in a competitive market such that the captured demand of users is maximized assuming that each individual chooses among all available facilities according to the well know a random utility model namely the multinomial logit the problem is complex mostly due to its integer nonlinear objective function currently the most efficient approaches deal with this complexity by either using a nonlinear programing solver or reformulating the problem into a mixed integer linear programing milp model in this paper we show how the best milp reformulation available in the literature can be strengthened by using tighter coefficients in some inequalities we also introduce a new branch and bound algorithm based on a greedy approach for solving a relaxation of the original problem extensive computational experiments are presented benchmarking the proposed approach with other linear and non linear relaxations of the problem the computational experiments show that our proposed algorithm is competitive with all other methods as there is no method which outperforms the others in all instances we also show a large scale real instance of the problem which comes from an application in park and ride facility location where our proposed branch and bound algorithm was the most effective method for solving this type of problem

asymptotic distributions of the sample mean autocovariances and autocorrelations of long memory time series we derive the asymptotic distributions of the sample mean autocovariances and autocorrelations for a time series whose autocovariance function has the powerlaw decay 0 o 1 as the results differ in important respects from the corresponding results for short memory processes whose autocovariance functions are absolutely summable for long memory processes the variances of the sample mean and of the sample autocovariances and autocorrelations for 0 12 are not of asymptotic order n 1 when 0 12 the asymptotic distributions of the sample autocovariances and autocorrelations are not normal

maximum likelihood estimation of stationary univariate fractionally integrated time series models abstract to estimate the parameters of a stationary univariate fractionally integrated time series the unconditional exact likelihood function is derived this allows the simultaneous estimation of all the parameters of the model by exact maximum likelihood issues involved in obtaining maximum likelihood estimates are discussed particular attention is given to efficient procedures to evaluate the likelihood function obtaining starting values and the small sample properties of the estimators limitations of previous estimation procedures are also discussed

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

convergence analysis of reweighted sum product algorithms markov random fields are designed to represent structured dependencies among large collections of random variables and are well suited to capture the structure of real world signals many fundamental tasks in signal processing e g smoothing denoising segmentation etc require efficient methods for computing approximate marginal probabilities over subsets of nodes in the graph the marginalization problem though solvable in linear time for graphs without cycles is computationally intractable for general graphs with cycles this intractability motivates the use of approximate ldquomessage passingrdquo algorithms this paper studies the convergence and stability properties of the family of reweighted sum product algorithms a generalization of the widely used sum product or belief propagation algorithm in which messages are adjusted with graph dependent weights for pairwise markov random fields we derive various conditions that are sufficient to ensure convergence and also provide bounds on the geometric convergence rates when specialized to the ordinary sum product algorithm these results provide strengthening of previous analyses we prove that some of our conditions are necessary and sufficient for subclasses of homogeneous models but not for general models the experimental simulations on various classes of graphs validate our theoretical results

gradient tree boosting for training conditional random fields conditional random fields crfs provide a flexible and powerful model for sequence labeling problems however existing learning algorithms are slow particularly in problems with large numbers of potential input features and feature combinations this paper describes a new algorithm for training crfs via gradient tree boosting in tree boosting the crf potential functions are represented as weighted sums of regression trees which provide compact representations of feature interactions so the algorithm does not explicitly consider the potentially large parameter space as a result gradient tree boosting scales linearly in the order of the markov model and in the order of the feature interactions rather than exponentially as in previous algorithms based on iterative scaling and gradient descent gradient tree boosting also makes it possible to use instance weighting as in c4 5 and surrogate splitting as in cart to handle missing values experimental studies of the effectiveness of these two methods as well as standard imputation and indicator feature methods show that instance weighting is the best method in most cases when feature values are missing at random

an integrated approach for scene understanding based on markov random field model in this paper we propose a markov random field model based approach as a unified and systematic way for modeling encoding and applying scene knowledge to the image understanding problem in our proposed scheme we formulate the image segmentation and interpretation problem as an integrated scheme and solve it through a general optimization algorithm more specifically the image is first segmented into a set of disjoint regions by a conventional region based segmentation technique which operates on image pixels and a region adjacency graph rag is then constructed from the resulting segmented regions based on the spatial adjacencies between regions our scheme then proceeds on the rag by defining the region merging and labeling problem based on the mrf models in the mrf model we specify the a priori knowledge about the optimal segmentation and interpretation in the form of clique functions and those clique functions are incorporated into the energy function to be minimized by a general optimization technique in the proposed scheme the image segmentation and interpretation processes cooperate in the simultaneous optimization process such that the erroneous segmentation and misinterpretation due to incomplete knowledge about each problem domain can be compensately recovered by continuous estimation of the single unified energy function we exploit the proposed scheme to segment and interpret natural outdoor scene images

bayes inference in the tobit censored regression model we consider the bayes estimation of the tobit censored regression model with normally distributed errors a simple condition for the existence of posterior moments is provided suitable versions of monte carlo procedures based on symmetric multivariate t distributions and laplacian approximations in a certain parametrization are developed and illustrated ideas involving data augmentation and gibbs sampling cf tanner and wong 1987 and gelfand and smith 1990 are also developed the methods are compared in two examples with diffuse priors and various combinations of sample sizes and degrees of censoring

a fractional dickey fuller test for unit roots this paper presents a new test for fractionally integrated fi processes in particular we propose a testing procedure in the time domain that extends the well known dickey fuller approach originally designed for the i 1 versus i 0 case to the more general setup of fid 0 versus fid 1 with d1 d 0 when d0 1 the proposed test statistics are based on the ols estimator or its t ratio of the coefficient on d1 yt 1 in a regression of y t on d1 yt 1 and possibly some lags ofy t when d1 is not taken to be known a priori a pre estimation of d1 is needed to implement the test we show that the choice of any t 1 2 consistent estimator of d1 0 1 suffices to make the test feasible while achieving asymptotic normality monte carlo simulations support the analytical results derived in the paper and show that proposed tests fare very well both in terms of power and size when compared with others available in the literature the paper ends with two empirical applications

voxel based bayesian lesion symptom mapping most existing voxel based lesion symptom mapping methods are based on the same statistical foundation null hypothesis significance testing nhst the two major limitations of these methods are the inability to infer that there is no difference in lesion proportions and a requirement for multiple comparison correction we propose a bayesian approach that directly models the posterior distribution of lesion proportion difference and makes decisions based on inference on this posterior distribution compared to nhst based approaches our bayesian approach yields inference results with clearer semantics and does not require multiple comparison correction we evaluated our bayesian method using simulated data and data from a study of acute ischemic left hemispheric stroke results of both experiments indicate that the bayesian approach is sensitive in detecting regions that characterize group differences

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time

relation between optimal nonlinearity and non gaussian noise enhancing a weak signal in a nonlinear system in the study of stochastic resonance it is often mentioned that nonlinearity can enhance a weak signal embedded in noise in order to give a systematic proof of the signal enhancement in nonlinear systems we derive an optimal nonlinearity that maximizes a signal to noise ratio snr the obtained optimal nonlinearity yields the maximum unbiased signal estimation performance which is known in the context of information theory it is found that a linear system is optimal for a gaussian noise but for a non gaussian noise there exist nonlinear systems that can achieve an snr higher than that obtained from linear systems this analysis refers to a system subjected to an additive non gaussian noise with a small signal input

selecting the number of classes under latent class regression a factor analytic analogue recently the regression extension of latent class analysis rlca model has received much attention in the field of medical research the basic rlca model summarizes shared features of measured multiple indicators as an underlying categorical variable and incorporates the covariate information in modeling both latent class membership and multiple indicators themselves to reduce complexity and enhance interpretability one usually fixes the number of classes in a given rlca often goodness of fit methods comparing various estimated models are used as a criterion to select the number of classes in this paper we propose a new method that is based on an analogous method used in factor analysis and does not require repeated fitting two ideas with application to many settings other than ours are synthesized in deriving the method a connection between latent class models and factor analysis and techniques of covariate marginalization and elimination a monte carlo simulation study is presented to evaluate the behavior of the selection procedure and compare to alternative approaches data from a study of how measured visual impairments affect older persons functioning are used for illustration

the effect of source amplitude and phase in matched field source localization traditional matched field processing is typically employed for localization of a source with unknown amplitude and phase at transmission the spectral information of the source is estimated via maximum likelihood and is used for localization with the bartlett processor maximum a posteriori estimation of the spectrum of the source is here proposed along with the estimation of source location and noise variance where the joint posterior probability distribution of all parameters is computed with gibbs sampling it is shown that the proposed method has a higher probability of correct localization than the traditional approach

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

maximizing a class of submodular utility functions given a finite ground set n and a value vector a in mathbb r n we consider optimization problems involving maximization of a submodular set utility function of the form h s f left sum i in s a i right s subseteq n where f is a strictly concave increasing differentiable function this utility function appears frequently in combinatorial optimization problems when modeling risk aversion and decreasing marginal preferences for instance in risk averse capital budgeting under uncertainty competitive facility location and combinatorial auctions these problems can be formulated as linear mixed 0 1 programs however the standard formulation of these problems using submodular inequalities is ineffective for their solution except for very small instances in this paper we perform a polyhedral analysis of a relevant mixed integer set and by exploiting the structure of the utility function h strengthen the standard submodular formulation significantly we show the lifting problem of the submodular inequalities to be a submodular maximization problem with a special structure solvable by a greedy algorithm which leads to an easily computable strengthening by subadditive lifting of the inequalities computational experiments on expected utility maximization in capital budgeting show the effectiveness of the new formulation

model evaluation and multiple strategies in cognitive diagnosis an analysis of fraction subtraction data this paper studies three models for cognitive diagnosis each illustrated with an application to fraction subtraction data the objective of each of these models is to classify examinees according to their mastery of skills assumed to be required for fraction subtraction we consider the dina model the nida model and a new model that extends the dina model to allow for multiple strategies of problem solving for each of these models the joint distribution of the indicators of skill mastery is modeled using a single continuous higher order latent trait to explain the dependence in the mastery of distinct skills this approach stems from viewing the skills as the specific states of knowledge required for exam performance and viewing these skills as arising from a broadly defined latent trait resembling the of item response models we discuss several techniques for comparing models and assessing goodness of fit we then implement these methods using the fraction subtraction data with the aim of selecting the best of the three models for this application we employ markov chain monte carlo algorithms to fit the models and we present simulation results to examine the performance of these algorithms

information theoretic active polygons for unsupervised texture segmentation curve evolution models used in image segmentation and based on image region information usually utilize simple statistics such as means and variances hence can not account for higher order nature of the textural characteristics of image regions in addition the object delineation by active contour methods results in a contour representation which still requires a substantial amount of data to be stored for subsequent multimedia applications such as visual information retrieval from databases polygonal approximations of the extracted continuous curves are required to reduce the amount of data since polygons are powerful approximators of shapes for use in later recognition stages such as shape matching and coding the key contribution of this paper is the development of a new active contour model which nicely ties the desirable polygonal representation of an object directly to the image segmentation process this model can robustly capture texture boundaries by way of higher order statistics of the data and using an information theoretic measure and with its nature of the ordinary differential equations this new variational texture segmentation model is unsupervised since no prior knowledge on the textural properties of image regions is used another contribution in this sequel is a new polygon regularizer algorithm which uses electrostatics principles this is a global regularizer and is more consistent than a local polygon regularization in preserving local features such as corners