The Poisson transform for unnormalised statistical models

Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Here we show that inferring the parameters of a unnormalised model on a space $\Omega$ can be mapped onto an equivalent problem of estimating the intensity of a Poisson point process on $\Omega$. The unnormalised statistical model now specifies an intensity function that does not need to be normalised. Effectively, the normalisation constant may now be inferred as just another parameter, at no loss of information. The result can be extended to cover non-IID models, which includes for example unnormalised models for sequences of graphs (dynamical graphs), or for sequences of binary vectors. As a consequence, we prove that unnormalised parameteric inference in non-IID models can be turned into a semi-parametric estimation problem. Moreover, we show that the noise-contrastive divergence of Gutmann & Hyv\"arinen (2012) can be understood as an approximation of the Poisson transform, and extended to non-IID settings. We use our results to fit spatial Markov chain models of eye movements, where the Poisson transform allows us to turn a highly non-standard model into vanilla semi-parametric logistic regression

Limbus misrepresentation in parametric eye models

PurposeTo assess the axial, radial and tangential limbus position misrepresentation when parametric models are used to represent the cornea and the sclera.MethodsThis retrospective study included 135 subjects aged 22 to 65 years (36.5 mean ±9.8 STD), 71 females and 64 males. Topography measurements were taken using an Eye Surface Profiler topographer and processed by a custom-built MATLAB code. Eye surfaces were freed from edge-effect artefacts and fitted to spherical, conic and biconic models.ResultsWhen comparing the radial position of the limbus, average errors of -0.83±0.19mm, -0.76±0.20mm and -0.69±0.20mm were observed within the right eye population for the spherical, conic and biconic models fitted up to 5mm. For the same fitting radius, the average fitting errors were -0.86±0.23mm, -0.78±0.23mm and -0.73±0.23mm for the spherical, conic and biconic models respectively within the left eye population. For the whole cornea fit, the average errors were -0.27±0.12mm and -0.28±0.13mm for the spherical models, -0.02±0.29mm and -0.05±0.27mm for the conic models, and -0.22±0.16mm and 0.24±0.17mm for the biconic models in the right and left eye populations respectively.ConclusionsThrough the use of spherical, conic and biconic parametric modelling methods, the eye's limbus is being mislocated. Additionally, it is evident that the magnitude of fitting error associated with the sclera may be propagating through the other components of the eye. This suggests that a corneal nonparametric model may be necessary to improve the representation of the limbus

Linkage analysis of high myopia susceptibility locus in 26 families

Purpose: We conducted a linkage analysis in high myopia families to replicate suggestive results from chromosome 7q36 using a model of autosomal dominant inheritance and genetic heterogeneity. We also performed a genome-wide scan to identify novel loci. Methods: Twenty-six families, with at least two high-myopic subjects (ie. refractive value in the less affected eye of -5 diopters) in each family, were included. Phenotypic examination included standard autorefractometry, ultrasonographic eye length measurement, and clinical confirmation of the non-syndromic character of the refractive disorder. Nine families were collected de novo including 136 available members of whom 34 were highly myopic subjects. Twenty new subjects were added in 5 of the 17 remaining families. A total of 233 subjects were submitted to a genome scan using ABI linkage mapping set LMSv2-MD-10, additional markers in all regions where preliminary LOD scores were greater than 1.5 were used. Multipoint parametric and non-parametric analyses were conducted with the software packages Genehunter 2.0 and Merlin 1.0.1. Two autosomal recessive, two autosomal dominant, and four autosomal additive models were used in the parametric linkage analyses. Results: No linkage was found using the subset of nine newly collected families. Study of the entire population of 26 families with a parametric model did not yield a significant LOD score (>3), even for the previously suggestive locus on 7q36. A non-parametric model demonstrated significant linkage to chromosome 7p15 in the entire population (Z-NPL=4.07, p=0.00002). The interval is 7.81 centiMorgans (cM) between markers D7S2458 and D7S2515. Conclusions: The significant interval reported here needs confirmation in other cohorts. Among possible susceptibility genes in the interval, certain candidates are likely to be involved in eye growth and development

PRIMAL-GMM: PaRametrIc MAnifold Learning of Gaussian Mixture Models.

We propose a ParametRIc MAnifold Learning (PRIMAL) algorithm for Gaussian mixtures models (GMM), assuming that GMMs lie on or near to a manifold of probability distributions that is generated from a low-dimensional hierarchical latent space through parametric mappings. Inspired by principal component analysis (PCA), the generative processes for priors, means and covariance matrices are modeled by their respective latent space and parametric mapping. Then, the dependencies between latent spaces are captured by a hierarchical latent space by a linear or kernelized mapping. The function parameters and hierarchical latent space are learned by minimizing the reconstruction error between ground-truth GMMs and manifold-generated GMMs, measured by Kullback-Leibler Divergence (KLD). Variational approximation is employed to handle the intractable KLD between GMMs and a variational EM algorithm is derived to optimize the objective function. Experiments on synthetic data, flow cytometry analysis, eye-fixation analysis and topic models show that PRIMAL learns a continuous and interpretable manifold of GMM distributions and achieves a minimum reconstruction error

Parametric Macromodels of Differential Drivers with Pre-Emphasis

This paper discusses the extraction of behavioral models of differential drivers with pre-emphasis for the assessment of signal integrity and electromagnetic compatibility effects in multigigabit data transmission systems. A suitable model structure is derived and the procedure for its estimation from port transient waveforms is illustrated. The proposed methodology is an extension of the macromodeling based on parametric relations applied to plain differential drivers. The obtained models preserve the accuracy and efficiency strengths of behavioral parametric macromodels for conventional devices. A realistic application example involving a high-speed communication path and a 3.125 Gb/s commercial driver model with pre-emphasis is presente

The Decision Value Computations in the vmPFC and Striatum Use a Relative Value Code That is Guided by Visual Attention

There is a growing consensus in behavioral neuroscience that the brain makes simple choices by first assigning a value to the options under consideration and then comparing them. Two important open questions are whether the brain encodes absolute or relative value signals, and what role attention might play in these computations.Weinvestigated these questions using a human fMRI experiment with a binary choice task in which the fixations to both stimuli were exogenously manipulated to control for the role of visual attention in the valuation computation. We found that the ventromedial prefrontal cortex and the ventral striatum encoded fixation-dependent relative value signals: activity in these areas correlated with the difference in value between the attended and the unattended items. These attention-modulated relative value signals might serve as the input of a comparator system that is used to make a choice

HeadOn: Real-time Reenactment of Human Portrait Videos

We propose HeadOn, the first real-time source-to-target reenactment approach for complete human portrait videos that enables transfer of torso and head motion, face expression, and eye gaze. Given a short RGB-D video of the target actor, we automatically construct a personalized geometry proxy that embeds a parametric head, eye, and kinematic torso model. A novel real-time reenactment algorithm employs this proxy to photo-realistically map the captured motion from the source actor to the target actor. On top of the coarse geometric proxy, we propose a video-based rendering technique that composites the modified target portrait video via view- and pose-dependent texturing, and creates photo-realistic imagery of the target actor under novel torso and head poses, facial expressions, and gaze directions. To this end, we propose a robust tracking of the face and torso of the source actor. We extensively evaluate our approach and show significant improvements in enabling much greater flexibility in creating realistic reenacted output videos.Comment: Video: https://www.youtube.com/watch?v=7Dg49wv2c_g Presented at Siggraph'1