Showing papers on "Parametric model published in 2015"

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Abstract: Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for wh...

Determinantal point process models and statistical inference

Abstract: Summary Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern data sets where nearby points repel each other. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric models, where the likelihood and moment expressions can be easily evaluated and realizations can be quickly simulated. We discuss how statistical inference is conducted by using the likelihood or moment properties of DPP models, and we provide freely available software for simulation and statistical inference.

Variable importance in regression models

Abstract: Regression analysis is one of the most-used statistical methods. Often part of the research question is the identification of the most important regressors or an importance ranking of the regressors. Most regression models are not specifically suited for answering the variable importance question, so that many different proposals have been made. This article reviews in detail the various variable importance metrics for the linear model, particularly emphasizing variance decomposition metrics. All linear model metrics are illustrated by an example analysis. For nonlinear parametric models, several principles from linear models have been adapted, and machine-learning methods have their own set of variable importance methods. These are also briefly covered. Although there are many variable importance metrics, there is still no convincing theoretical basis for them, and they all have a heuristic touch. Nevertheless, some metrics are considered useful for a crude assessment in the absence of a good subject matter theory. WIREs Comput Stat 2015, 7:137-152. doi: 10.1002/wics.1346

Dense, accurate optical flow estimation with piecewise parametric model

Abstract: This paper proposes a simple method for estimating dense and accurate optical flow field. It revitalizes an early idea of piecewise parametric flow model. A key innovation is that, we fit a flow field piecewise to a variety of parametric models, where the domain of each piece (i.e., each piece's shape, position and size) is determined adaptively, while at the same time maintaining a global inter-piece flow continuity constraint. We achieve this by a multi-model fitting scheme via energy minimization. Our energy takes into account both the piecewise constant model assumption and the flow field continuity constraint, enabling the proposed method to effectively handle both homogeneous motions and complex motions. The experiments on three public optical flow benchmarks (KITTI, MPI Sintel, and Middlebury) show the superiority of our method compared with the state of the art: it achieves top-tier performances on all the three benchmarks.

GalPaK3D: A BAYESIAN PARAMETRIC TOOL FOR EXTRACTING MORPHOKINEMATICS OF GALAXIES FROM 3D DATA

Abstract: We present a method to constrain galaxy parameters directly from three-dimensional data cubes. The algorithm compares directly the data with a parametric model mapped in coordinates. It uses the spectral line-spread function and the spatial point-spread function (PSF) to generate a three-dimensional kernel whose characteristics are instrument specific or user generated. The algorithm returns the intrinsic modeled properties along with both an “intrinsic” model data cube and the modeled galaxy convolved with the 3D kernel. The algorithm uses a Markov Chain Monte Carlo approach with a nontraditional proposal distribution in order to efficiently probe the parameter space. We demonstrate the robustness of the algorithm using 1728 mock galaxies and galaxies generated from hydrodynamical simulations in various seeing conditions from 0.″6 to 1.″2. We find that the algorithm can recover the morphological parameters (inclination, position angle) to within 10% and the kinematic parameters (maximum rotation velocity) to within 20%, irrespectively of the PSF in seeing (up to 1.″2) provided that the maximum signal-to-noise ratio (S/N) is greater than ∼3 pixel−1 and that the ratio of galaxy half-light radius to seeing radius is greater than about 1.5. One can use such an algorithm to constrain simultaneously the kinematics and morphological parameters of (nonmerging) galaxies observed in nonoptimal seeing conditions. The algorithm can also be used on adaptive optics data or on high-quality, high-S/N data to look for nonaxisymmetric structures in the residuals.

GalPak3D: A Bayesian parametric tool for extracting morpho-kinematics of galaxies from 3D data

Abstract: We present a method to constrain galaxy parameters directly from three-dimensional data cubes. The algorithm compares directly the data with a parametric model mapped in $x,y,\lambda$ coordinates. It uses the spectral lines-spread function (LSF) and the spatial point-spread function (PSF) to generate a three-dimensional kernel whose characteristics are instrument specific or user generated. The algorithm returns the intrinsic modeled properties along with both an `intrinsic' model data cube and the modeled galaxy convolved with the 3D-kernel. The algorithm uses a Markov Chain Monte Carlo (MCMC) approach with a nontraditional proposal distribution in order to efficiently probe the parameter space. We demonstrate the robustness of the algorithm using 1728 mock galaxies and galaxies generated from hydrodynamical simulations in various seeing conditions from 0.6" to 1.2". We find that the algorithm can recover the morphological parameters (inclination, position angle) to within 10% and the kinematic parameters (maximum rotation velocity) to within 20%, irrespectively of the PSF in seeing (up to 1.2") provided that the maximum signal-to-noise ratio (SNR) is greater than $\sim3$ pixel$^{-1}$ and that the ratio of the galaxy half-light radius to seeing radius is greater than about 1.5. One can use such an algorithm to constrain simultaneously the kinematics and morphological parameters of (nonmerging) galaxies observed in nonoptimal seeing conditions. The algorithm can also be used on adaptive-optics (AO) data or on high-quality, high-SNR data to look for nonaxisymmetric structures in the residuals.

Camera model identification framework using an ensemble of demosaicing features

Abstract: Existing approaches to camera model identification frequently operate by building a parametric model of a camera component, then using an estimate of these model parameters to identify the source camera model Since many components in a camera's processing pipeline are both complex and nonlinear, it is often very difficult to build these parametric models or improve their accuracy In this paper, we propose a new framework for identifying the model of an image's source camera Our framework builds a rich model of a camera's demosaicing algorithm inspired by Fridrich et al's recent work on rich models for steganalysis We present experimental results showing that our framework can identify the correct make and model of an image's source camera with an average accuracy of 992%

Validation of direct normal irradiance predictions under arid conditions: A review of radiative models and their turbidity-dependent performance

Abstract: In this study, a detailed review of the performance of 24 radiative models from the literature is presented. These models are used to predict the clear-sky surface direct normal irradiance (DNI) at a 1-min time resolution. Coincident radiometric and sunphotometric databases of the highest possible quality, and recorded at seven stations located in arid environments, are used for this analysis. At most sites, an extremely large range of aerosol loading conditions and high variability in their characteristics are noticed. At one site (Solar Village), DNI was measured routinely with an active cavity radiometer with very low uncertainty compared to field pyrheliometers, which makes its dataset exceptional. The reviewed models are categorized into 5 classes, depending on the number of aerosol-related inputs they require. One of the models (RRTMG) is considerably more sophisticated (and thus less computationally efficient) than the other models—which are all of the parametric type currently in use in solar applications, and specifically devised for cloudless conditions. RRTMG is more versatile and is selected here for benchmarking purposes. The results show good consistency between the different stations, with generally higher prediction uncertainties at sites experiencing larger mean aerosol optical depth (AOD). Disaggregation of the performance results as a function of two aerosol optical characteristics (AOD at 1 µm, β , and Angstrom exponent, α ) shows that the simplest parametric models׳ performance decreases when subjected to turbidity conditions outside of what is “normal” or “typical” under temperate climates. Only a few parametric models perform well under all conditions and at all stations: REST2, CPCR2, MMAC, and METSTAT, in decreasing order of performance. The Ineichen and Hoyt models perform adequately at low AODs, but diverge beyond a specific limit. REST2 is the only parametric model that performs similarly to the RRTMG benchmark under all AOD regimes observed here—and even sometimes better. The inspection of the models׳ performance when considering the simultaneous effects of both β and α reveals a clear pattern in the models׳ error, which is influenced by the frequency distribution of α values. This suggests most models may have difficulty in correctly capturing the effect of α , and/or that observational and instrumental issues at high AOD values may also enhance the apparent model prediction errors. A study of the specific sensitivity of DNI on AOD confirmed previous findings. It is concluded that, assuming a “perfect” model, DNI can be modeled within 5% accuracy only if β is known to within ≈0.02.

Ensemble learning of inverse probability weights for marginal structural modeling in large observational datasets.

Abstract: Inverse probability weights used to fit marginal structural models are typically estimated using logistic regression. However, a data-adaptive procedure may be able to better exploit information available in measured covariates. By combining predictions from multiple algorithms, ensemble learning offers an alternative to logistic regression modeling to further reduce bias in estimated marginal structural model parameters. We describe the application of two ensemble learning approaches to estimating stabilized weights: super learning (SL), an ensemble machine learning approach that relies on V-fold cross validation, and an ensemble learner (EL) that creates a single partition of the data into training and validation sets. Longitudinal data from two multicenter cohort studies in Spain (CoRIS and CoRIS-MD) were analyzed to estimate the mortality hazard ratio for initiation versus no initiation of combined antiretroviral therapy among HIV positive subjects. Both ensemble approaches produced hazard ratio estimates further away from the null, and with tighter confidence intervals, than logistic regression modeling. Computation time for EL was less than half that of SL. We conclude that ensemble learning using a library of diverse candidate algorithms offers an alternative to parametric modeling of inverse probability weights when fitting marginal structural models. With large datasets, EL provides a rich search over the solution space in less time than SL with comparable results.

Integrating parametric and non-parametric models for scene labeling

Abstract: We adopt Convolutional Neural Networks (CNN) as our parametric model to learn discriminative features and classifiers for local patch classification. As visually similar pixels are indistinguishable from local context, we alleviate such ambiguity by introducing a global scene constraint. We estimate the global potential in a non-parametric framework. Furthermore, a large margin based CNN metric learning method is proposed for better global potential estimation. The final pixel class prediction is performed by integrating local and global beliefs. Even without any post-processing, we achieve state-of-the-art performance on SiftFlow and competitive results on Stanford Background benchmark.

A new generalized Weibull family of distributions: mathematical properties and applications

Abstract: We propose a generalized Weibull family of distributions with two extra positive parameters to extend the normal, gamma, Gumbel and inverse Gausssian distributions, among several other well-known distributions. We provide a comprehensive treatment of its general mathematical properties including quantile and generating functions, ordinary and incomplete moments and other properties. We introduce the log-generalized Weibull-log-logistic, this is new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We discuss estimation of the model parameters by maximum likelihood and provide two applications to real data.

SimSeq: a nonparametric approach to simulation of RNA-sequence datasets

Abstract: Motivation: RNA sequencing analysis methods are often derived by relying on hypothetical parametric models for read counts that are not likely to be precisely satisfied in practice. Methods are often tested by analyzing data that have been simulated according to the assumed model. This testing strategy can result in an overly optimistic view of the performance of an RNA-seq analysis method. Results: We develop a data-based simulation algorithm for RNA-seq data. The vector of read counts simulated for a given experimental unit has a joint distribution that closely matches the distribution of a source RNA-seq dataset provided by the user. We conduct simulation experiments based on the negative binomial distribution and our proposed nonparametric simulation algorithm. We compare performance between the two simulation experiments over a small subset of statistical methods for RNA-seq analysis available in the literature. We use as a benchmark the ability of a method to control the false discovery rate. Not surprisingly, methods based on parametric modeling assumptions seem to perform better with respect to false discovery rate control when data are simulated from parametric models rather than using our more realistic nonparametric simulation strategy. Availability and implementation: The nonparametric simulation algorithm developed in this article is implemented in the R package SimSeq, which is freely available under the GNU General Public License (version 2 or later) from the Comprehensive R Archive Network (http://cran.rproject.org/). Contact: sgbenidt@gmail.com Supplementary information: Supplementary data are available at Bioinformatics online.

Graphical LASSO based Model Selection for Time Series

Abstract: We propose a novel graphical model selection scheme for high-dimensional stationary time series or discrete time processes. The method is based on a natural generalization of the graphical LASSO algorithm, introduced originally for the case of i.i.d. samples, and estimates the conditional independence graph of a time series from a finite length observation. The graphical LASSO for time series is defined as the solution of an ${\ell _1}$ -regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers. Our approach is nonparametric as we do not assume a finite dimensional parametric model, but only require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails. Numerical experiments demonstrate the ability of our method to recover the correct conditional independence graph from a limited amount of samples.

GcsDecolor: Gradient Correlation Similarity for Efficient Contrast Preserving Decolorization

Abstract: This paper presents a novel gradient correlation similarity (Gcs) measure-based decolorization model for faithfully preserving the appearance of the original color image. Contrary to the conventional data-fidelity term consisting of gradient error-norm-based measures, the newly defined Gcs measure calculates the summation of the gradient correlation between each channel of the color image and the transformed grayscale image. Two efficient algorithms are developed to solve the proposed model. On one hand, due to the highly nonlinear nature of Gcs measure, a solver consisting of the augmented Lagrangian and alternating direction method is adopted to deal with its approximated linear parametric model. The presented algorithm exhibits excellent iterative convergence and attains superior performance. On the other hand, a discrete searching solver is proposed by determining the solution with the minimum function value from the linear parametric model-induced candidate images. The non-iterative solver has advantages in simplicity and speed with only several simple arithmetic operations, leading to real-time computational speed. In addition, it is very robust with respect to the parameter and candidates. Extensive experiments under a variety of test images and a comprehensive evaluation against existing state-of-the-art methods consistently demonstrate the potential of the proposed model and algorithms.

Fab forms: customizable objects for fabrication with validity and geometry caching

Abstract: We address the problem of allowing casual users to customize parametric models while maintaining their valid state as 3D-printable functional objects. We define Fab Form as any design representation that lends itself to interactive customization by a novice user, while remaining valid and manufacturable. We propose a method to achieve these Fab Form requirements for general parametric designs tagged with a general set of automated validity tests and a small number of parameters exposed to the casual user. Our solution separates Fab Form evaluation into a precomputation stage and a runtime stage. Parts of the geometry and design validity (such as manufacturability) are evaluated and stored in the precomputation stage by adaptively sampling the design space. At runtime the remainder of the evaluation is performed. This allows interactive navigation in the valid regions of the design space using an automatically generated Web user interface (UI). We evaluate our approach by converting several parametric models into corresponding Fab Forms.

Sector-Based Parametric Sound Field Reproduction in the Spherical Harmonic Domain

Abstract: This papers presents a parametric method for perceptual sound field recording and reproduction from a small-sized microphone array to arbitrary loudspeaker layouts. The applied parametric model has been found to be effective and well-correlated with perceptual attributes in the context of directional audio coding, and here it is generalized and extended to higher orders of spherical harmonic signals. Higher order recordings are used for estimation of the model parameters inside angular sectors that provide increased separation between simultaneous sources and reverberation. The perceptual synthesis according to the combined properties of these sector parameters is achieved with an adaptive least-squares mixing technique. Furthermore, considerations regarding practical microphone arrays are presented and a frequency-dependent scheme is proposed. A realization of the system is described for an existing spherical microphone array and for a target loudspeaker setup similar to NHK 22.2. It is demonstrated through listening tests that, compared to a reference scene, the perceived difference is greatly reduced with the proposed higher order analysis model. The results further indicate that, on the same task, the method outperforms linear reproduction with the same recordings available.

A nonlinear parametric model reduction method for efficient gear contact simulations

Abstract: Summary A novel nonlinear parametric model order reduction technique for the solution of contact problems in flexible multibody dynamics is presented. These problems are characterized by significant variations in the location and size of the contact area and typically require high-dimensional finite element models having multiple inputs and outputs to be solved. The presented technique draws from the fields of nonlinear and parametric model reduction to construct a reduced-order model whose dimensions are insensitive to the dimensions of the full-order model. The solution of interest is approximated in a lower-dimensional subspace spanned by a constant set of eigenvectors augmented with a parameter-dependent set of global contact shapes. The latter represent deformation patterns of the interacting bodies obtained from a series of static contact analyses. The set of global contact shapes is parameterized with respect to the system configuration and therefore continuously varies in time. An energy-consistent formulation is assured by explicitly taking into account the dynamic parameter variability in the derivation of the equations of motion. The performance of the novel technique is demonstrated by simulating a dynamic gear contact problem and comparing results against traditional model reduction techniques as well as commercial nonlinear finite element software. Copyright © 2014 John Wiley & Sons, Ltd.

Theories and models of parametric design thinking

Abstract: Due to significant recent design-related technological developments, design theories and processes are undergoing re-formulation and an epistemological shift. The tools and practices of parametric design are beginning to impact new forms of Parametric Design Thinking (PDT). The present work is motivated by the need to explore and formulate the body of theoretical concepts of parametric design. It is built around the intersection of three areas of knowledge: cognitive models of design, digital models of design, and parametric tools and scripts. The work identifies forms of cognitive mechanisms in parametric design; types of logical flow of information that can be applied in digital processes for performance-based design; generative design and form finding. It explores the impact of parametric models and tools upon styles of design thinking from conception to production. These are presented as a body of knowledge in the search for thinking and process models of PDT in design.

On parametric estimation

Abstract: In this paper we are focused on parametric modeling. To estimate the distribution of the population under study we use the point estimate. For the unknown parameter a of the uniform (continue) distribution U(0, a ) we present a better estimator than the sample mean. It will provide a basis for developing efficient estimators when faced with similar problems.

Extrapolation of MIMO Mobile-to-Mobile Wireless Channels Using Parametric-Model-Based Prediction

Abstract: This paper investigates the prediction of multiple-input–multiple-output (MIMO) narrow-band multipath fading channels for mobile-to-mobile (M-to-M) wireless communication systems. Using a statistical model for M-to-M communication in urban and suburban environments, we derive a parameterized double directional model and utilize a multidimensional extension of the ESPRIT algorithm to jointly estimate the angles of departure (AoD), angles of arrival (AoA), and effective Doppler frequencies. A simple method is also proposed for mobile velocity estimation. The parameter estimates are then used to forecast the M-to-M channel. The bound on the prediction error is derived using a vector formulation of the Cramer–Rao lower bound (CRLB). Simulations are used to evaluate the performance of the prediction scheme and to compare it to the derived error bound.

MuProp: Unbiased Backpropagation for Stochastic Neural Networks

Abstract: Deep neural networks are powerful parametric models that can be trained efficiently using the backpropagation algorithm. Stochastic neural networks combine the power of large parametric functions with that of graphical models, which makes it possible to learn very complex distributions. However, as backpropagation is not directly applicable to stochastic networks that include discrete sampling operations within their computational graph, training such networks remains difficult. We present MuProp, an unbiased gradient estimator for stochastic networks, designed to make this task easier. MuProp improves on the likelihood-ratio estimator by reducing its variance using a control variate based on the first-order Taylor expansion of a mean-field network. Crucially, unlike prior attempts at using backpropagation for training stochastic networks, the resulting estimator is unbiased and well behaved. Our experiments on structured output prediction and discrete latent variable modeling demonstrate that MuProp yields consistently good performance across a range of difficult tasks.

Spectrally regularized surfaces

Abstract: Priors play an essential role in Bayesian theory, and they are frequently center stage in scientific inference. In image processing, geometric priors became very popular in the past decades because of their physical explanation. They usually favor sparsity in the result in order to remove the noise. However, the sparsity might not only remove the noise, but also the details of the surface. In this thesis, we argue what priors should be imposed for certain types of surfaces and how they can be imposed efficiently in a variational framework. We show that spectral priors can preserve the details while removing noise efficiently. These priors lead to spectral regularizations that are more general than geometric ones, but more specific than entropy regularizations. In order to infer the distribution of a certain geometric property, such as curvature, over a surface from a finite number of discrete samples observed from that surface, we either need a regularizationfree method for surface reconstruction or directly infer the property from the samples. We first show a novel method that can reconstruct a closed surface from a finite point cloud without any regularization. Thanks to the regularization-freeness, we can directly extract prior information from the reconstructed surfaces. Directly learning from the samples, we investigate the gradient distribution of digital natural-scene images. We provide two parametric models for this distribution and analyze their properties, such as fitting accuracy, sparsity, entropy, and computational efficiency. In order to impose these priors in an application, we present a generic variational model with spectral regularization. We discuss several special cases of this model that recover to well-known models in the field. We analyze the role of regularization coefficient and how it is related to the convexity of the model. We illustrate several applications of this model with gradient distribution priors in image processing problems, including image enhancement, denoising, blind deconvolution, and scatter light removal. Considering second-order derivatives, we first show an efficient filter that can minimize total Gaussian curvature over a surface. Based on the same theory, we then extend this to filters for minimizing mean curvature and total variation. We finally extend these curvature filters to spectral regularization. We close by discussing the advantages and disadvantages of spectrally regularized surfaces and discussing possible future work.