Consistent estimation of shape parameters in statistical shape model by symmetric EM algorithm

In order to fit an unseen surface using statistical shape model (SSM), a correspondence between the unseen surface and the model needs to be established, before the shape parameters can be estimated based on this correspondence. The correspondence and parameter estimation problem can be modeled probabilistically by a Gaussian mixture model (GMM), and solved by expectation-maximization iterative closest points (EM-ICP) algorithm. In this paper, we propose to exploit the linearity of the principal component analysis (PCA) based SSM, and estimate the parameters for the unseen shape surface under the EM-ICP framework. The symmetric data terms are devised to enforce the mutual consistency between the model reconstruction and the shape surface. The a priori shape information encoded in the SSM is also included as regularization. The estimation method is applied to the shape modeling of the hippocampus using a hippocampal SSM

Uncovering Causality from Multivariate Hawkes Integrated Cumulants

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the third-order integrated cumulants of the process. We show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database

Estimation of latent variable models for ordinal data via fully exponential Laplace approximation

Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function can arise since analytical solutions do not exist. Numerical approximations, like the widely used Gauss Hermite (GH) quadrature, are generally applied to solve these problems. However, GH becomes unfeasible as the number of latent variables increases. Thus, alternative solutions have to be found. In this paper, we propose an extended version of the Laplace method for approximating the integrals, known as fully exponential Laplace approximation. It is computational feasible also in presence of many latent variables, and it is more accurate than the classical Laplace method

Linear Mixed Models with Marginally Symmetric Nonparametric Random Effects

Linear mixed models (LMMs) are used as an important tool in the data analysis of repeated measures and longitudinal studies. The most common form of LMMs utilize a normal distribution to model the random effects. Such assumptions can often lead to misspecification errors when the random effects are not normal. One approach to remedy the misspecification errors is to utilize a point-mass distribution to model the random effects; this is known as the nonparametric maximum likelihood-fitted (NPML) model. The NPML model is flexible but requires a large number of parameters to characterize the random-effects distribution. It is often natural to assume that the random-effects distribution be at least marginally symmetric. The marginally symmetric NPML (MSNPML) random-effects model is introduced, which assumes a marginally symmetric point-mass distribution for the random effects. Under the symmetry assumption, the MSNPML model utilizes half the number of parameters to characterize the same number of point masses as the NPML model; thus the model confers an advantage in economy and parsimony. An EM-type algorithm is presented for the maximum likelihood (ML) estimation of LMMs with MSNPML random effects; the algorithm is shown to monotonically increase the log-likelihood and is proven to be convergent to a stationary point of the log-likelihood function in the case of convergence. Furthermore, it is shown that the ML estimator is consistent and asymptotically normal under certain conditions, and the estimation of quantities such as the random-effects covariance matrix and individual a posteriori expectations is demonstrated