large scale multiple kernel learning while classical kernel based learning algorithms are based on a single kernel in practice it is often desirable to use multiple kernels lanckriet et al 2004 considered conic combinations of kernel matrices for classification leading to a convex quadratically constrained quadratic program we show that it can be rewritten as a semi infinite linear program that can be efficiently solved by recycling the standard svm implementations moreover we generalize the formulation and our method to a larger class of problems including regression and one class classification experimental results show that the proposed algorithm works for hundred thousands of examples or hundreds of kernels to be combined and helps for automatic model selection improving the interpretability of the learning result in a second part we discuss general speed up mechanism for svms especially when used with sparse feature maps as appear for string kernels allowing us to train a string kernel svm on a 10 million real world splice data set from computational biology we integrated multiple kernel learning in our machine learning toolbox shogun for which the source code is publicly available at http www fml tuebingen mpg de raetsch projects shogun

manifold constrained coding and sparse representation for human action recognition due to its various applications human action recognition has been widely studied and achieved tremendous progress however how to learn an accurate and discriminative behavior representation based on the extracted features remains as a challenging problem in this paper we present an effective coding scheme that can discover the manifold structure of the learned features with an l 2 norm regularization coupled with a local constraint the proposed coding scheme which has an analytical solution can learn an accurate compact and yet discriminative behavior representation after the behavior representations are obtained the action recognition problem is formulated as a sparse linear representation of an overcomplete dictionary constructed by labeled behavior representations the same manifold l 2 norm regularization is also employed in this stage the reconstruction error associated with each class is used for classification experimental results demonstrate the effectiveness of the proposed approach on several public datasets including various physical actions and facial expressions

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

unsupervised learning of human action categories using spatial temporal words we present a novel unsupervised learning method for human action categories a video sequence is represented as a collection of spatial temporal words by extracting space time interest points the algorithm automatically learns the probability distributions of the spatial temporal words and the intermediate topics corresponding to human action categories this is achieved by using latent topic models such as the probabilistic latent semantic analysis plsa model and latent dirichlet allocation lda our approach can handle noisy feature points arisen from dynamic background and moving cameras due to the application of the probabilistic models given a novel video sequence the algorithm can categorize and localize the human action s contained in the video we test our algorithm on three challenging datasets the kth human motion dataset the weizmann human action dataset and a recent dataset of figure skating actions our results reflect the promise of such a simple approach in addition our algorithm can recognize and localize multiple actions in long and complex video sequences containing multiple motions

goodness of fit and related inference processes for quantile regression abstract we introduce a goodness of fit process for quantile regression analogous to the conventional r2 statistic of least squares regression several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated the asymptotic behavior of the inference processes is shown to be closely related to earlier p sample goodness of fit theory involving bessel processes the approach is illustrated with some hypothetical examples an application to recent empirical models of international economic growth and some monte carlo evidence

statistical methods for eliciting probability distributions elicitation is a key task for subjectivist bayesians although skeptics hold that elicitation cannot or perhaps should not be done in practice it brings statisticians closer to their clients and subject matter expert colleagues this article reviews the state of the art reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively and how they respond to questions about that information in a discussion of the elicitation process the first issue to address is what it means for an elicitation to be successful that is what criteria should be used our answer is that a successful elicitation faithfully represents the opinion of the person being elicited it is not necessarily true in some objectivistic sense and cannot be judged in that way we see that elicitation as simply part of the process of statistical modeling indeed in a hierarchical model at which point the likelihood ends and the pr

modeling tangential vector fields on a sphere abstractphysical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences these naturally occurring vector fields are often subject to physical constraints such as being curl free or divergence free we start with constructing parametric models for curl free and divergence free vector fields that are tangential to the unit sphere through applying the surface gradient or the surface curl operator to a scalar random potential field on the unit sphere using the helmholtz hodge decomposition we then construct a class of simple but flexible parametric models for general tangential vector fields which are represented as a sum of a curl free and a divergence free components we propose a likelihood based parameter estimation procedure and show that fast computation is possible even for large data sets when the observations are on a regular latitude longitude grid characteristics and practical utility of the proposed methodology are illustrated th

actions as space time shapes human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion we regard human actions as three dimensional shapes induced by the silhouettes in the space time volume we adopt a recent approach 14 for analyzing 2d shapes and generalize it to deal with volumetric space time action shapes our method utilizes properties of the solution to the poisson equation to extract space time features such as local space time saliency action dynamics shape structure and orientation we show that these features are useful for action recognition detection and clustering the method is fast does not require video alignment and is applicable in but not limited to many scenarios where the background is known moreover we demonstrate the robustness of our method to partial occlusions nonrigid deformations significant changes in scale and viewpoint high irregularities in the performance of an action and low quality video

rates of convergence for minimum contrast estimators we shall present here a general study of minimum contrast estimators in a nonparametric setting although our results are also valid in the classical parametric case for independent observations these estimators include many of the most popular estimators in various situations such as maximum likelihood estimators least squares and other estimators of the regression function estimators for mixture models or deconvolution the main theorem relates the rate of convergence of those estimators to the entropy structure of the space of parameters optimal rates depending on entropy conditions are already known at least for some of the models involved and they agree with what we get for minimum contrast estimators as long as the entropy counts are not too large but under some circumstances large entropies or changes in the entropy structure due to local perturbations the resulting the rates are only suboptimal counterexamples are constructed which show that the phenomenon is real for non parametric maximum likelihood or regression this proves that under purely metric assumptions our theorem is optimal and that minimum contrast estimators happen to be suboptimal

bayesian calibration of inexact computer models bayesian calibration is used to study computer models in the presence of both a calibration parameter and model bias the parameter in the predominant methodology is left undefined this results in an issue where the posterior of the parameter is suboptimally broad there has been no generally accepted alternatives to date this article proposes using bayesian calibration where the prior distribution on the bias is orthogonal to the gradient of the computer model problems associated with bayesian calibration are shown to be mitigated through analytic results in addition to examples supplementary materials for this article are available online

powering up with space time wind forecasting the technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality high quality short term forecasts of wind speed are vital to making this a more reliable energy source gneiting et al 2006 have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information the forecasts produced by this model are accurate and subject to accuracy the predictive distribution is sharp that is highly concentrated around its center however this model is split into nonunique regimes based on the wind direction at an offsite location this paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model it is robust in many experiments such as predicting wind at other locations we compare this with the more common approach of modeling wind speeds and directions in the cartesian space and use a skew t distribution for the errors the quality of t

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

general notions of statistical depth function statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data here we introduce several general structures for depth functions classify many existing examples as special cases and establish results on the possession or lack thereof of four key properties desirable for depth functions in general roughly speaking these properties may be described as affine invariance maximality at center monotonicity relative to deepest point and vanishing at infinity this provides a more systematic basis for selection of a depth function in particular from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors

prediction via orthogonalized model mixing abstract we introduce an approach and algorithms for model mixing in large prediction problems with correlated predictors we focus on the choice of predictors in linear models and mix over possible subsets of candidate predictors our approach is based on expressing the space of models in terms of an orthogonalization of the design matrix advantages are both statistical and computational statistically orthogonalization often leads to a reduction in the number of competing models by eliminating correlations computationally large model spaces cannot be enumerated recent approaches are based on sampling models with high posterior probability via markov chains based on orthogonalization of the space of candidate predictors we can approximate the posterior probabilities of models by products of predictor specific terms this leads to an importance sampling function for sampling directly from the joint distribution over the model space without resorting to markov chains compared to the latter ortho

multivariate type g matern stochastic partial differential equation random fields for many applications with multivariate data random field models capturing departures from gaussianity within realizations are appropriate for this reason we formulate a new class of multivariate non gaussian models based on systems of stochastic partial differential equations with additive type g noise whose marginal covariance functions are of matern type we consider four increasingly flexible constructions of the noise where the first two are similar to existing copula based models in contrast with these the last two constructions can model non gaussian spatial data without replicates computationally efficient methods for likelihood based parameter estimation and probabilistic prediction are proposed and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications less

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

a general method for comparing probability assessors a probability assessor or forecaster is a person who assigns subjective probabilities to events which will eventually occur or not occur in this paper a general method for comparing forecasters after a finite number of trials is introduced the general method is proven to include calculating all proper scoring rules as special cases it also includes comparison of forecasters in all simple two decision problems as special cases the relationship between the general method and calibration is also explored the general method is also translated into a method for deciding who will give better forecasts in the future

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

time varying combinations of predictive densities using nonlinear filtering abstract we propose a bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights several specifications of multivariate time varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms in the proposed approach the model set can be incomplete meaning that all models can be individually misspecified a sequential monte carlo method is proposed to approximate the filtering and predictive densities the combination approach is assessed using statistical and utility based performance measures for evaluating density forecasts of simulated data us macroeconomic time series and surveys of stock market prices simulation results indicate that for a set of linear autoregressive models the combination strategy is successful in selecting with probability close to one the true model when the model set is complete and it is able to detect parameter instability when the model set includes the true model that has generated subsamples of data also substantial uncertainty appears in the weights when predictors are similar residual uncertainty reduces when the model set is complete and learning reduces this uncertainty for the macro series we find that incompleteness of the models is relatively large in the 1970 s the beginning of the 1980 s and during the recent financial crisis and lower during the great moderation the predicted probabilities of recession accurately compare with the nber business cycle dating model weights have substantial uncertainty attached with respect to returns of the s p 500 series we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 1990 s and switches to giving more weight to the professional forecasts over time information on the complete predictive distribution and not just on some moments turns out to be very important above all during turbulent times such as the recent financial crisis more generally the proposed distributional state space representation offers great flexibility in combining densities

statistical correction of a deterministic numerical weather prediction model the forecasting skill of meteorologists is determined largely by their ability to interpret output from deterministic numerical weather prediction nwp models in the light of local conditions biases in the deterministic model may arise for many reasons including the inability to account for physical processes at a scale smaller than the grid used in the numerical solution of the model equations a statistical method for correction and interpretation of nwp model output is the model output statistics technique mos where regression analysis is used to relate observations and nwp model predictions we describe a bayesian hierarchical approach to mos that was motivated by the need to develop sensible statistical corrections for recently opened stations with a short historical data record the strength of the bayesian hierarchical formulation is its ability to combine information from stations with short and long observational records in a sensible way markov chain monte carlo methods are used for compu

making and evaluating point forecasts typically point forecasting methods are compared and assessed by means of an error measure or scoring function with the absolute error and the squared error being key examples the individual scores are averaged over forecast cases to result in a summary measure of the predictive performance such as the mean absolute error or the mean squared error i demonstrate that this common practice can lead to grossly misguided inferences unless the scoring function and the forecasting task are carefully matched effective point forecasting requires that the scoring function be specified ex ante or that the forecaster receives a directive in the form of a statistical functional such as the mean or a quantile of the predictive distribution if the scoring function is specified ex ante the forecaster can issue the optimal point forecast namely the bayes rule if the forecaster receives a directive in the form of a functional it is critical that the scoring function be consistent for it in the sense that t

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

the intrinsic bayes factor for model selection and prediction abstract in the bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions it is typically not possible to utilize standard noninformative or default prior distributions this has led bayesians to use conventional proper prior distributions or crude approximations to bayes factors in this article we introduce a new criterion called the intrinsic bayes factor which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual bayes factors the criterion can be used for nested or nonnested models and for multiple model comparison and prediction from another perspective the development suggests a general definition of a reference prior for model comparison

comparison of alternative functional forms in production abstract in this paper a bayesian approach to choosing between two non nested multivariate regression systems is developed the bayesian approach involves the calculation of the posterior probabilities of alternative hypotheses and formation of a posterior odds ratio specific results are obtained for the comparison of a multivariate regression and seemingly unrelated regression model these odds ratio results are applied to the choice between translog and fourier flexible form cost share equation systems when calculated for aggregate u s manufacturing cost data the odds ratios favor the fourier flexible form over the translog form even in small samples the fourier series expansion appears to be an effective approximation technique

human activity recognition using multi features and multiple kernel learning this paper presents two sets of features shape representation and kinematic structure for human activity recognition using a sequence of rgb d images the shape features are extracted using the depth information in the frequency domain via spherical harmonics representation the other features include the motion of the 3d joint positions i e the end points of the distal limb segments in the human body both sets of features are fused using the multiple kernel learning mkl technique at the kernel level for human activity recognition our experiments on three publicly available datasets demonstrate that the proposed features are robust for human activity recognition and particularly when there are similarities among the actions

weather forecasting for weather derivatives we take a simple time series approach to modeling and forecasting daily average temperature in u s cities and we inquire systematically as to whether it may prove useful from the vantage point of participants in the weather derivatives market the answer is perhaps surprisingly yes time series modeling reveals conditional mean dynamics and crucially strong conditional variance dynamics in daily average temperature and it reveals sharp differences between the distribution of temperature and the distribution of temperature surprises as we argue it also holds promise for producing the long horizon predictive densities crucial for pricing weather derivatives so that additional inquiry into time series weather forecasting methods will likely prove useful in weather derivatives contexts

a valid matern class of cross covariance functions for multivariate random fields with any number of components we introduce a valid parametric family of cross covariance functions for multivariate spatial random fields where each component has a covariance function from a well celebrated matern class unlike previous attempts our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components we present the conditions on the parameter space that result in valid models with varying degrees of complexity we discuss practical implementations including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency we perform various monte carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging the application of the proposed multivariate matern model is illustrated on two meteorological datasets temperature pressure over the pacific northwest bivariate and wind temperature pressure in oklahoma trivariate in the latter case our flexi

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

model selection when there is minimal prior information a number of authors argue that a bayesian posterior odds criterion is appropriate for model selection 2 this paper considers how to derive this criterion when there is minimal prior information we propose minimizing measures of prior information relative to the models in question rather than relative to the parameters of the particular models in so doing we obtain an expression for the odds that is invariant to the parameterization of the particular models and overcomes certain well known finite sample limiting problems we illustrate this procedure using two popular measures of information derived from the well known shannon 26 measure by minimizing these measures with the sample size held fixed we obtain the same model selection criterion that schwarz 25 derived asymptotically for large sample sizes this expression has a number of desirable properties and is computationally no more

the ecme algorithm a simple extension of em and ecm with faster monotone convergence a generalisation of the ecm algorithm meng rubin 1993 which is itselfan extension of the em algorithm dempster laird rubin 1977 can be obtained by replacing some cm steps of ecm which maximise the constrained expected complete data loglikelihood function with steps that maximise the correspondingly constrained actual likelihood function this algorithm which we call ecme algorithm for expectation conditional maximisation either shares with both em and ecm their stable monotone convergence and basic simplicity of implementation relative to competing faster converging methods moreover ecme can have a substantially faster convergence rate than either em or ecm measured using either the number of iterations or actual computer time

a reference bayesian test for nested hypotheses and its relationship to the schwarz criterion abstract to compute a bayes factor for testing h 0 0 in the presence of a nuisance parameter priors under the null and alternative hypotheses must be chosen as in bayesian estimation an important problem has been to define automatic or reference methods for determining priors based only on the structure of the model in this article we apply the heuristic device of taking the amount of information in the prior on equal to the amount of information in a single observation then after transforming to be null orthogonal to we take the marginal priors on to be equal under the null and alternative hypotheses doing so and taking the prior on to be normal we find that the log of the bayes factor may be approximated by the schwarz criterion with an error of order o p n rather than the usual error of order o p 1 this result suggests the schwarz criterion should provide sensible approximate solutions to bayesian testing problems at least when the hypotheses are nested when

on a notion of data depth based on random simplices for a distribution f on mathbb r p and a point x in mathbb r p the simplical depth d x is introduced which is the probability that the point x is contained inside a random simplex whose vertices are p 1 independent observations from f mathematically and heuristically it is argued that d x indeed can be viewed as a measure of depth of the point x with respect to f an empirical version of d cdot gives rise to a natural ordering of the data points from the center outward the ordering thus obtained leads to the introduction of multivariate generalizations of the univariate sample median and l statistics this generalized sample median and l statistics are affine equivariant

variable selection and function estimation in additive nonparametric regression using a data based prior abstract a hierarchical bayesian approach is proposed for variable selection and function estimation in additive nonparametric gaussian regression models and additive nonparametric binary regression models the prior for each component function is an integrated wiener process resulting in a posterior mean estimate that is a cubic smoothing spline each of the explanatory variables is allowed to be in or out of the model and the regression functions are estimated by model averaging to allow variable selection and model averaging data based priors are used for the smoothing parameter and the slope at 0 of each component function a two step markov chain monte carlo method is used to efficiently obtain the data based prior and to carry out variable selection and function estimation it is shown by simulation that significant improvements in the function estimators can be obtained over an approach that estimates all the unknown functions simultaneously the methodology is illustrated for a binary regressio

probabilistic wind speed forecasting using ensembles and bayesian model averaging the current weather forecasting paradigm is deterministic based on numerical models multiple estimates of the current state of the atmosphere are used to generate an ensemble of deterministic predictions ensemble forecasts while providing information on forecast uncertainty are often uncalibrated bayesian model averaging bma is a statistical ensemble postprocessing method that creates calibrated predictive probability density functions pdfs probabilistic wind forecasting offers two challenges a skewed distribution and observations that are coarsely discretized we extend bma to wind speed taking account of these challenges this method provides calibrated and sharp probabilistic forecasts comparisons are made between several formulations

asymptotic data analysis on manifolds given an m dimensional compact submanifold m of euclidean space r s the concept of mean location of a distribution related to mean or expected vector is generalized to more general r s valued functionals including median location which is derived from the spatial median the asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated convergence properties are studied in relation to the behavior of the underlying distributions with respect to the cutlocus an application is given in the context of independent but not identically distributed samples in particular to a multisample setup

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

strict definiteness of integrals via complete monotonicity of derivatives let k be a nonnegative integer and let 0 r be a c function with k k completely monotone and not constant if 6 0 is a signed measure on any euclidean space rd with vanishing moments up to order k 1 then the integral rd rd x y 2 d x d y is strictly positive whenever it exists for general d no larger class of continuous functions seems to admit the same conclusion examples and applications are indicated a section on bilinear integrability might be of independent interest

a predictive approach to the bayesian design problem with application to normal regression models a predictive decision theoretic approach is developed for the bayesian design problem the loss functions used are fair bayes or proper scoring rules and are quadratic measures of distance between probability measures optimal bayesian designs are those which minimise the preposterior risk for the decision problem such designs typically depend on both the prior distribution and the loss function the results are applied to certain normal regression models where explicit optimal designs are constructed

game theory maximum entropy minimum discrepancy and robust bayesian decision theory we describe and develop a close relationship between two problems that have customarily been regarded as distinct that of maximizing entropy and that of minimizing worst case expected loss using a formulation grounded in the equilibrium theory of zero sum games between decision maker and nature these two problems are shown to be dual to each other the solution to each providing that to the other although topsoe described this connection for the shannon entropy over 20 years ago it does not appear to be widely known even in that important special case we here generalize this theory to apply to arbitrary decision problems and loss functions we indicate how an appropriate generalized definition of entropy can be associated with such a problem and we show that subject to certain regularity conditions the above mentioned duality continues to apply in this extended context this simultaneously provides a possible rationale for maximizing entropy and a tool for finding robust bayes acts we also describe the essential identity between the problem of maximizing entropy and that of minimizing a related discrepancy or divergence between distributions this leads to an extension to arbitrary discrepancies of a well known minimax theorem for the case of kullback leibler divergence the redundancy capacity theorem of information theory for the important case of families of distributions having certain mean values specified we develop simple sufficient conditions and methods for identifying the desired solutions we use this theory to introduce a new concept of generalized exponential family linked to the specific decision problem under consideration and we demonstrate that this shares many of the properties of standard exponential families finally we show that the existence of an equilibrium in our game can be rephrased in terms of a pythagorean property of the related divergence thus generalizing previously announced results for kullback leibler and bregman divergences

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

effective scoring rules for probabilistic forecasts this paper studies the use of a scoring rule for the elicitation of forecasts in the form of probability distributions and for the subsequent evaluation of such forecasts given a metric distance function on a space of probability distributions a scoring rule is said to be effective if the forecaster s expected score is a strictly decreasing function of the distance between the elicited and true distributions two simple well known rules the spherical and the quadratic are shown to be effective with respect to suitable metrics examples and a practical application in foreign exchange rate forecasting are also provided

accurate 3d action recognition using learning on the grassmann manifold in this paper we address the problem of modeling and analyzing human motion by focusing on 3d body skeletons particularly our intent is to represent skeletal motion in a geometric and efficient way leading to an accurate action recognition system here an action is represented by a dynamical system whose observability matrix is characterized as an element of a grassmann manifold to formulate our learning algorithm we propose two distinct ideas 1 in the first one we perform classification using a truncated wrapped gaussian model one for each class in its own tangent space 2 in the second one we propose a novel learning algorithm that uses a vector representation formed by concatenating local coordinates in tangent spaces associated with different classes and training a linear svm we evaluate our approaches on three public 3d action datasets msr action 3d ut kinect and ucf kinect datasets these datasets represent different kinds of challenges and together help provide an exhaustive evaluation the results show that our approaches either match or exceed state of the art performance reaching 91 21 on msr action 3d 97 91 on ucf kinect and 88 5 on ut kinect finally we evaluate the latency i e the ability to recognize an action before its termination of our approach and demonstrate improvements relative to other published approaches highlightsa human action recognition approach which represents skeletal sequence as point on the grassmann manifold a new learning algorithm is introduced for learning human actions experiments are performed on three public datasets promising success rates are achieved showing accuracy and better latency performances

evaluating probabilities asymmetric scoring rules proper scoring rules are over evaluation measures that reward accurate probabilities specific rules encountered in the literature and used in practice are invariably symmetric in the sense that the expected score for a perfectly calibrated probability assessor or model generating probabilities is minimized at a probability of one half a family of asymmetric scoring rules that provide better measures of the degree of skill inherent in the probabilities and render scores that are more comparable in different situations is developed here one member of this family a quadratic asymmetric rule is applied to evaluate an extensive set of precipitation probability forecasts from the u s national weather service connections to previous characterizations of proper scoring rules are investigated and some relevant issues pertaining to the design of specific asymmetric rules for particular inferential and decision making problems are discussed briefly

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

should scoring rules be effective a scoring rule is a reward function for eliciting or evaluating forecasts expressed as discrete or continuous probability distributions a rule is strictly proper if it encourages the forecaster to state his true subjective probabilities and effective if it is associated with a metric on the set of probability distributions recently the property of effectiveness which is stronger than strict properness has been proposed as a desideratum for scoring rules for continuous forecasts for reasons of monotonicity in keeping the forecaster close to his true probabilities since in practice the forecast must be chosen from a low dimensional set of admissible distributions it is shown in this paper that what effectiveness implies beyond strict properness is not a monotonicity property but a transitivity property which is difficult to justify behaviorally the logarithmic scoring rule is shown to violate the transitivity property and hence is not effective the l1 and l metrics are shown to allow no effective scoring rules some potential difficulties in interpreting admissible forecasts are also discussed

discrimination slope and integrated discrimination improvement properties relationships and impact of calibration discrimination slope defined as the slope of a linear regression of predicted probabilities of event derived from a prognostic model on the binary event status has recently gained popularity as a measure of model performance it is as a building block for the integrated discrimination improvement that equals the difference in discrimination slopes between the two models being compared several authors have pointed out that it does not make sense to apply the integrated discrimination improvement and discrimination slope when working with mis calibrated models whereas others have raised concerns about the ability of improving discrimination slope without adding new information in this paper we show that under certain assumptions the discrimination slope is asymptotically related to two other r squared measures one of which is a rescaled version of the brier score known to be proper furthermore we illustrate how a simple recalibration makes the slope equal to the rescaled brier r squared metric we also show that the discrimination slope can be interpreted as a measure of reduction in expected regret for the gini brier regret function using theoretical and practical examples we illustrate how all of these metrics are affected by different levels of model mis calibration in particular we demonstrate that simple recalibration ascertaining calibration in the large and calibration slope equal to 1 are not sufficient to correct for some forms of mis calibration we conclude that r squared metrics including the discrimination slope offer an attractive choice for quantifying model performance as long as one accounts for their sensitivity to model calibration copyright 2016 john wiley sons ltd

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

uniqueness of the spatial median on montre que si une mesure de probabilite sur un espace euclidien n est pas concentree sur une droite alors sa mediane spatiale est unique

spatial bayesian variable selection with application to functional magnetic resonance imaging we propose a procedure to undertake bayesian variable selection and model averaging for a series of regressions located on a lattice for those regressors that are in common in the regressions we consider using an ising prior to smooth spatially the indicator variables representing whether or not the variable is zero or nonzero in each regression this smooths spatially the probabilities that each independent variable is nonzero in each regression and indirectly smooths spatially the regression coefficients we discuss how single site sampling schemes can be used to evaluate the joint posterior distribution the approach is applied to the problem of functional magnetic resonance imaging in medical statistics where massive datasets arise that require prompt processing here the ising prior with a three dimensional neighborhood structure is used to smooth spatially activation maps from regression models of blood oxygenation the ising prior also has the advantage of allowing incorporation of anatomic prio

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

fusing appearance and distribution information of interest points for action recognition most of the existing action recognition methods represent actions as bags of space time interest points specifically space time interest points are detected from the video and described using appearance based descriptors each descriptor is then classified as a video word and a histogram of these video words is used for recognition these methods therefore rely solely on the discriminative power of individual local space time descriptors whilst ignoring the potentially useful information about the global spatio temporal distribution of interest points in this paper we propose a novel action representation method which differs significantly from the existing interest point based representation in that only the global distribution information of interest points is exploited in particular holistic features from clouds of interest points accumulated over multiple temporal scales are extracted since the proposed spatio temporal distribution representation contains different but complementary information to the conventional bag of words representation we formulate a feature fusion method based on multiple kernel learning experiments using the kth and weizmann datasets demonstrate that our approach outperforms most existing methods in particular under occlusion and changes in view angle clothing and carrying condition

penalty based aggregation of multidimensional data abstract research in aggregation theory is nowadays still mostly focused on algorithms to summarize tuples consisting of observations in some real interval or of diverse general ordered structures of course in practice of information processing many other data types between these two extreme cases are worth inspecting this contribution deals with the aggregation of lists of data points in r d for arbitrary d 1 even though particular functions aiming to summarize multidimensional data have been discussed by researchers in data analysis computational statistics and geometry there is clearly a need to provide a comprehensive and unified model in which their properties like equivariances to geometric transformations internality and monotonicity may be studied at an appropriate level of generality the proposed penalty based approach serves as a common framework for all idempotent information aggregation methods including componentwise functions pairwise distance minimizers and data depth based medians it also allows for deriving many new practically useful tools

on m estimators and normal quantiles this paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles our estimators are linear combinations of m estimators their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators compared with empirical quantiles the new estimators offer considerable reduction of variance at near normal probability distributions

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

comparing spatial predictions under a general loss function we develop a hypothesis test to determine whether a significant difference in the spatial predictions produced by two competing models exists on average across the entire spatial domain of interest the null hypothesis is that of no difference and a spatial loss differential is created based on the observed data the two sets of predictions and the loss function chosen by the researcher the test assumes only isotropy and short range spatial dependence of the loss differential but does allow it to be non gaussian non zero mean and spatially correlated constant and nonconstant spatial trends in the loss differential are treated in two separate cases monte carlo simulations illustrate the size and power properties of this test and an example based on daily average wind speeds in oklahoma is used for illustration supplemental results are available online

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

convergence of markovian stochastic approximation with discontinuous dynamics this paper is devoted to the convergence analysis of stochastic approximation algorithms of the form theta n 1 theta n gamma n 1 h theta n x n 1 where left theta n n in mathbb n right is an mathbb r d valued sequence left gamma n n in mathbb n right is a deterministic stepsize sequence and left x n n in mathbb n right is a controlled markov chain we study the convergence under weak assumptions on smoothness in theta of the function theta mapsto h theta x it is usually assumed that this function is continuous for any x in this work we relax this condition our results are illustrated by considering stochastic approximation algorithms for adaptive quantile estimation and a penalized version of the vector quantization

m estimation convexity and quantiles the paper develops a class of extensions of the univariate quantile function to the multivariate case m quantiles related in a certain way to m parameters of a probability distribution and their m estimators the spatial geometric quantiles recently introduced by koltchinskii and dudley and by chaudhuri as well as the regression quantiles of koenker and basset are the examples of the m quantile function discussed in the paper we study the main properties of m quantiles and develop the asymptotic theory of empirical m quantiles we use m quantiles to extend l parameters and l estimators to the multivariate case to introduce a bootstrap test for spherical symmetry of a multivariate distribution and to extend the notion of regression quantiles to multiresponse linear regression models

coherent dispersion criteria for optimal experimental design we characterize those coherent design criteria which depend only on the dispersion matrix assumed proper and nonsingular of the state of nature which may be a parameter vector or a set of future observables and describe the associated decision problems connections are established with the classical approach to optimal design theory for the normal linear model based on concave functions of the information matrix implications of the theory for more general models are also considered

learning and matching of dynamic shape manifolds for human action recognition in this paper we learn explicit representations for dynamic shape manifolds of moving humans for the task of action recognition we exploit locality preserving projections lpp for dimensionality reduction leading to a low dimensional embedding of human movements given a sequence of moving silhouettes associated to an action video by lpp we project them into a low dimensional space to characterize the spatiotemporal property of the action as well as to preserve much of the geometric structure to match the embedded action trajectories the median hausdorff distance or normalized spatiotemporal correlation is used for similarity measures action classification is then achieved in a nearest neighbor framework to evaluate the proposed method extensive experiments have been carried out on a recent dataset including ten actions performed by nine different subjects the experimental results show that the proposed method is able to not only recognize human actions effectively but also considerably tolerate some challenging conditions e g partial occlusion low quality videos changes in viewpoints scales and clothes within class variations caused by different subjects with different physical build styles of motion etc

probabilistic forecasts calibration and sharpness summary probabilistic forecasts of continuous variables take the form of predictive densities or predictive cumulative distribution functions we propose a diagnostic approach to the evaluation of predictive performance that is based on the paradigm of maximizing the sharpness of the predictive distributions subject to calibration calibration refers to the statistical consistency between the distributional forecasts and the observations and is a joint property of the predictions and the events that materialize sharpness refers to the concentration of the predictive distributions and is a property of the forecasts only a simple theoretical framework allows us to distinguish between probabilistic calibration exceedance calibration and marginal calibration we propose and study tools for checking calibration and sharpness among them the probability integral transform histogram marginal calibration plots the sharpness diagram and proper scoring rules the diagnostic approach is illustrated by an assessment and ranking of probabilistic forecasts of wind speed at the stateline wind energy centre in the us pacific northwest in combination with cross validation or in the time series context our proposal provides very general nonparametric alternatives to the use of information criteria for model diagnostics and model selection

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series

the predictive utility of generalized expected utility theories many alternative theories have been proposed to explain violations of expected utility eu theory observed in experiments several recent studies test some of these alternative theories against each other formal tests used to judge the theories usually count the number of responses consistent with the theory ignoring systematic variation in responses that are inconsistent we develop a maximum likelihood estimation method which uses all the information in the data creates test statistics that can be aggregated across studies and enables one to judge the predictive utility the fit and parsimony of utility theories analyses of 23 data sets using several thousand choices suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit the menu is mixed fanning prospect theory eu and expected value which theories are best is highly sensitive to whether gambles in a pair have the same support eu fits better or not eu fits poorly our method may have application to other domains in which various theories predict different subsets of choices e g refinements of nash equilibrium in noncooperative games

testing forecast optimality under unknown loss empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function in this article we establish new testable properties that hold when the forecaster s loss function is unknown but testable restrictions can be imposed on the data generating process trading off conditions on the data generating process against conditions on the loss function we propose flexible estimation of the forecaster s loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable we apply our results to the problem of evaluating the federal reserve s forecasts of output growth forecast optimality is rejected if the fed s loss depends only on the forecast error however the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the fed than underpredictions particularly during per