Low-dimensional Parameter Research Articles

Pulse shape optimization for electron-positron production in rotating fields

We optimize the pulse shape and polarization of time-dependent electric fields to maximize the production of electron-positron pairs via strong field quantum electrodynamics processes. The pulse is parametrized in Fourier space by a B-spline polynomial basis, which results in a relatively low-dimensional parameter space while still allowing for a large number of electric field modes. The optimization is performed by using a parallel implementation of the differential evolution, one of the most efficient metaheuristic algorithms. The computational performance of the numerical method and the results on pair production are compared with a local multistart optimization algorithm. These techniques allow us to determine the pulse shape and field polarization that maximize the number of produced pairs in computationally accessible regimes.

A Human Body Gait Recognition System Based on Fourier Transform and Quartile Difference Extraction

A research method of gait recognition based on feature combination is proposed, which includes the wavelet transform (WT), Fourier transform (FT) and the quartile difference, to explore the gait recognition system in Internet of things human body sensor based on smart phone. It can extract the low-dimensional gait parameters of the acceleration signal, and these gait parameters can reflect the movement characteristics. Then, they are combined into feature vector to identify by a pattern recognition algorithm.Finally, the experimental verification is carried out in the experimental system. The results show thatthis gait recognition method simplifies the processing flow to a certain extent, and improves the recognition accuracy. In conclusion, the algorithm has a good effect, and can identify the gait behavior with high precision.

ThrEEBoost: Thresholded Boosting for Variable Selection and Prediction via Estimating Equations

ABSTRACTMost variable selection techniques for high-dimensional models are designed to be used in settings, where observations are independent and completely observed. At the same time, there is a rich literature on approaches to estimation of low-dimensional parameters in the presence of correlation, missingness, measurement error, selection bias, and other characteristics of real data. In this article, we present ThrEEBoost (Thresholded EEBoost), a general-purpose variable selection technique which can accommodate such problem characteristics by replacing the gradient of the loss by an estimating function. ThrEEBoost generalizes the previously proposed EEBoost algorithm (Wolfson 2011) by allowing the number of regression coefficients updated at each step to be controlled by a thresholding parameter. Different thresholding parameter values yield different variable selection paths, greatly diversifying the set of models that can be explored; the optimal degree of thresholding can be chosen by cross-validation. ThrEEBoost was evaluated using simulation studies to assess the effects of different threshold values on prediction error, sensitivity, specificity, and the number of iterations to identify minimum prediction error under both sparse and nonsparse true models with correlated continuous outcomes. We show that when the true model is sparse, ThrEEBoost achieves similar prediction error to EEBoost while requiring fewer iterations to locate the set of coefficients yielding the minimum error. When the true model is less sparse, ThrEEBoost has lower prediction error than EEBoost and also finds the point yielding the minimum error more quickly. The technique is illustrated by applying it to the problem of identifying predictors of weight change in a longitudinal nutrition study. Supplementary materials are available online.

Progressive Minimal Path Method for Segmentation of 2D and 3D Line Structures.

We propose a novel minimal path method for the segmentation of 2D and 3D line structures. Minimal path methods perform propagation of a wavefront emanating from a start point at a speed derived from image features, followed by path extraction using backtracing. Usually, the computation of the speed and the propagation of the wave are two separate steps, and point features are used to compute a static speed. We introduce a new continuous minimal path method which steers the wave propagation progressively using dynamic speed based on path features. We present three instances of our method, using an appearance feature of the path, a geometric feature based on the curvature of the path, and a joint appearance and geometric feature based on the tangent of the wavefront. These features have not been used in previous continuous minimal path methods. We compute the features dynamically during the wave propagation, and also efficiently using a fast numerical scheme and a low-dimensional parameter space. Our method does not suffer from discretization or metrication errors. We performed qualitative and quantitative evaluations using 2D and 3D images from different application areas.

Generalized Pareto Processes and Liquidity

Motivated by the modeling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a modified ARGP (MARGP) and a thresholded ARGP (TARGP). These models are able to capture key data features apparent in fund liquidity data and reflect the underlying phenomena via easily interpreted, low-dimensional model parameters. We establish stationarity and ergodicity, provide a link to the class of shot-noise processes, and determine the associated interarrival distributions for exceedances. Moreover, we provide estimators for all relevant model parameters and establish consistency and asymptotic normality for all estimators (except the threshold parameter, which as usual must be dealt with separately). Finally, we illustrate our approach using real-world fund redemption data, and we discuss the goodness-of-fit of the estimated models.

Factorized Hidden Layer Adaptation for Deep Neural Network Based Acoustic Modeling

In this paper, we propose the factorized hidden layer (FHL) approach to adapt the deep neural network (DNN) acoustic models for automatic speech recognition (ASR). FHL aims at modeling speaker dependent (SD) hidden layers by representing an SD affine transformation as a linear combination of bases. The combination weights are low-dimensional speaker parameters that can be initialized using speaker representations like i-vectors and then reliably refined in an unsupervised adaptation fashion. Therefore, our method provides an efficient way to perform both adaptive training and (test-time) adaptation. Experimental results have shown that the FHL adaptation improves the ASR performance significantly, compared to the standard DNN models, as well as other state-of-the-art DNN adaptation approaches, such as training with the speaker-normalized CMLLR features, speaker-aware training using i-vector and learning hidden unit contributions (LHUC). For Aurora 4, FHL achieves 3.8% and 2.3% absolute improvements over the standard DNNs trained on the LDA + STC and CMLLR features, respectively. It also achieves 1.7% absolute performance improvement over a system that combines the i-vector adaptive training with LHUC adaptation. For the AMI dataset, FHL achieved 1.4% and 1.9% absolute improvements over the sequence-trained CMLLR baseline systems, for the IHM and SDM tasks, respectively.

A marginalized multilevel model for bivariate longitudinal binary data

This study considers analysis of bivariate longitudinal binary data. We propose a model based on marginalized multilevel model framework. The proposed model consists of two levels such that the first level associates the marginal mean of responses with covariates through a logistic regression model and the second level includes subject/time specific random intercepts within a probit regression model. The covariance matrix of multiple correlated time-specific random intercepts for each subject is assumed to represent the within-subject association. The subject-specific random effects covariance matrix is further decomposed into its dependence and variance components through modified Cholesky decomposition method and then the unconstrained version of resulting parameters are modelled in terms of covariates with low-dimensional regression parameters. This provides better explanations related to dependence and variance parameters and a reduction in the number of parameters to be estimated in random effects covariance matrix to avoid possible identifiability problems. Marginal correlations between responses of subjects and within the responses of a subject are derived through a Taylor series-based approximation. Data cloning computational algorithm is used to compute the maximum likelihood estimates and standard errors of the parameters in the proposed model. The validity of the proposed model is assessed through a Monte Carlo simulation study, and results are observed to be at acceptable level. Lastly, the proposed model is illustrated through Mother’s Stress and Children’s Morbidity study data, where both population-averaged and subject-specific interpretations are drawn through Emprical Bayes estimation of random effects.

Stochastic hyperelastic constitutive laws and identification procedure for soft biological tissues with intrinsic variability

In this work, we address the constitutive modeling, in a probabilistic framework, of the hyperelastic response of soft biological tissues. The aim is on the one hand to mimic the mean behavior and variability that are typically encountered in the experimental characterization of such materials, and on the other hand to derive mathematical models that are almost surely consistent with the theory of nonlinear elasticity. Towards this goal, we invoke information theory and discuss a stochastic model relying on a low-dimensional parametrization. We subsequently propose a two-step methodology allowing for the calibration of the model using standard data, such as mean and standard deviation values along a given loading path. The framework is finally applied and benchmarked on three experimental databases proposed elsewhere in the literature. It is shown that the stochastic model allows experiments to be accurately reproduced, regardless of the tissue under consideration.

Honest confidence regions and optimality in high-dimensional precision matrix estimation

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters p can be much larger than the sample size. We show that the novel estimator achieves minimax rates in supremum norm and the low-dimensional components of the estimator have a Gaussian limiting distribution. These results hold uniformly over the class of precision matrices with row sparsity of small order $$\sqrt{n}/\log p$$ and spectrum uniformly bounded, under a sub-Gaussian tail assumption on the margins of the true underlying distribution. Consequently, our results lead to uniformly valid confidence regions for low-dimensional parameters of the precision matrix. Thresholding the estimator leads to variable selection without imposing irrepresentability conditions. The performance of the method is demonstrated in a simulation study and on real data.

Data-driven forward model inference for EEG brain imaging

Electroencephalography (EEG) is a flexible and accessible tool with excellent temporal resolution but with a spatial resolution hampered by volume conduction. Reconstruction of the cortical sources of measured EEG activity partly alleviates this problem and effectively turns EEG into a brain imaging device. The quality of the source reconstruction depends on the forward model which details head geometry and conductivities of different head compartments. These person-specific factors are complex to determine, requiring detailed knowledge of the subject's anatomy and physiology. In this proof-of-concept study, we show that, even when anatomical knowledge is unavailable, a suitable forward model can be estimated directly from the EEG. We propose a data-driven approach that provides a low-dimensional parametrization of head geometry and compartment conductivities, built using a corpus of forward models. Combined with only a recorded EEG signal, we are able to estimate both the brain sources and a person-specific forward model by optimizing this parametrization. We thus not only solve an inverse problem, but also optimize over its specification. Our work demonstrates that personalized EEG brain imaging is possible, even when the head geometry and conductivities are unknown.

A technique for the classification of tissues by combining mechanics based models with Bayesian inference

This paper deals with a key issue in diagnostics and classification of tissue: given a few samples of tissue which are known to belong to certain categories (such as “healthy” and “diseased”) how to categorize a new sample? This is a well known and analyzed problem and very powerful purely data driven approaches have been developed. However, in situations with limited experimental data with a large spread that is typical of biomaterials, a purely data driven approach to classifying the samples is inadequate, since it can suffer from serious bias due to scant data. Here we propose an approach that uses our understanding of the mechanics of the behavior of tissues to transform the problem from the high dimensional space of raw data to a probability distribution on a low dimensional parameter space and then use a Bayesian technique for the classification based on the parameters. A key point in the paper is that the mapping from the raw data to the parameters is not a deterministic mapping (as would be obtained from a lest squares or maximum likelihood approach) but a probabilistic one based on Bayes rule. To apply this rule, there is a need for hypothesis on the prior probability distributions of the parameters themselves and a way to systematically update the hypothesis as more data is obtained. Such a framework should be able to (1) capture prior knowledge that we have about the parameters (such as for example minimum and maximum values for the parameters, likely mean values etc.) ; (2) provide a means for incorporating the knowledge gained from experiments and (3) gradually evolve towards a purely data driven approach as large amounts of data become available.We utilize a “max-ent” approach to the prior distribution: i.e. we select a distribution that incorporates any available statistical information about the data while being maximally indifferent to all other information. this probability distribution is updated by Bayesian inference where the posterior distributions are obtained by a Markov Chain Monte Carlo (MCMC) sampling method combined with a continuum mechanics based exact solution of a boundary value problem. We illustrate this approach by considering the “soft” classification (i.e we computer the probability of belonging to a class or category) of nominally similar sheep arteries (from two different sheep) based on the probability distribution of the parameters corresponding to each class This is an alternative to a logistic regression type approach in situations where there is high uncertainty or limited data distribution.

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting--both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

Spectral gap optimization of order parameters for sampling complex molecular systems

In modern-day simulations of many-body systems, much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CVs) or reaction coordinates. A vast array of enhanced-sampling methods are based on the identification and biasing of these low-dimensional order parameters, whose fluctuations are important in driving rare events of interest. Here, we describe a new algorithm for finding optimal low-dimensional CVs for use in enhanced-sampling biasing methods like umbrella sampling, metadynamics, and related methods, when limited prior static and dynamic information is known about the system, and a much larger set of candidate CVs is specified. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV. The algorithm is called spectral gap optimization of order parameters (SGOOP). Through multiple practical examples, we show how this postprocessing procedure can lead to optimization of CV and several orders of magnitude improvement in the convergence of the free energy calculated through metadynamics, essentially giving the ability to extract useful information even from unsuccessful metadynamics runs.

New Controls for Combining Images in Correspondence.

When interpolating images, for instance in the context of morphing, there are myriad approaches for defining correspondence maps that align structurally similar elements. However, the actual interpolation usually involves simple functions for both geometric paths and color blending. In this paper we explore new types of controls for combining two images related by a correspondence map. Our insight is to apply recent edge-aware decomposition techniques, not just to the image content but to the map itself. Our framework establishes an intuitive low-dimensional parameter space for merging the shape and color from the two source images at both low and high frequencies. A gallery-based user interface enables interactive traversal of this rich space, to either define a morph path or synthesize new hybrid images. Extrapolation of the shape parameters achieves compelling effects. Finally we demonstrate an extension of the framework to videos.

Kinematic gait synthesis for snake robots

Snake robots are highly articulated mechanisms that can perform a variety of motions that conventional robots cannot. Despite many demonstrated successes of snake robots, these mechanisms have not been able to achieve the agility displayed by their biological counterparts. We suggest that studying how biological snakes coordinate whole-body motion to achieve agile behaviors can help improve the performance of snake robots. The foundation of this work is based on the hypothesis that, for snake locomotion that is approximately kinematic, replaying parameterized shape trajectory data collected from biological snakes can generate equivalent motions in snake robots. To test this hypothesis, we collected shape trajectory data from sidewinder rattlesnakes executing a variety of different behaviors. We then analyze the shape trajectory data in a concise and meaningful way by using a new algorithm, called conditioned basis array factorization, which projects high-dimensional data arrays onto a low-dimensional representation. The low-dimensional representation of the recorded snake motion is able to reproduce the essential features of the recorded biological snake motion on a snake robot, leading to improved agility and maneuverability, confirming our hypothesis. This parameterized representation allows us to search the low-dimensional parameter space to generate behaviors that further improve the performance of snake robots.

Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach

We present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter in the presence of a very high-dimensional nuisance parameter that is estimated using selection or regularization methods. Our analysis provides a set of high-level conditions under which inference for the low-dimensional parameter based on testing or point estimation methods will be regular despite selection or regularization biases occurring in the estimation of the high-dimensional nuisance parameter. A key element is the use of so-called immunized or orthogonal estimating equations that are locally insensitive to small mistakes in the estimation of the high-dimensional nuisance parameter. As an illustration, we analyze affine-quadratic models and specialize these results to a linear instrumental variables model with many regressors and many instruments. We conclude with a review of other developments in post-selection inference and note that many can be viewed as special cases of the general encompassing framework of orthogonal estimating equations provided in this article.

Data-driven combined state and parameter reduction for inverse problems

In this contribution we present an accelerated optimization-based approach for combined state and parameter reduction of a parametrized linear control system which is then used as a surrogate model in a Bayesian inverse setting. Following the basic ideas presented in [Lieberman, Willcox, Ghattas. Parameter and state model reduction for large-scale statistical inverse settings, SIAM J. Sci. Comput., 32(5):2523-2542, 2010], our approach is based on a generalized data-driven optimization functional in the construction process of the surrogate model and the usage of a trust-region-type solution strategy that results in an additional speed-up of the overall method. In principal, the model reduction procedure is based on the offline construction of appropriate low-dimensional state and parameter spaces and an online inversion step based on the resulting surrogate model that is obtained through projection of the underlying control system onto the reduced spaces. The generalization and enhancements presented in this work are shown to decrease overall computational time and increase accuracy of the reduced order model and thus allow an application to extreme-scale problems. Numerical experiments for a generic model and a fMRI connectivity model are presented in order to compare the computational efficiency of our improved method with the original approach.

Asymptotic normality and optimalities in estimation of large Gaussian graphical models

The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gaussian graphical model? A novel regression approach is proposed to obtain asymptotically efficient estimation of each entry of a precision matrix under a sparseness condition relative to the sample size. When the precision matrix is not sufficiently sparse, or equivalently the sample size is not sufficiently large, a lower bound is established to show that it is no longer possible to achieve the parametric rate in the estimation of each entry. This lower bound result, which provides an answer to the delicate sample size question, is established with a novel construction of a subset of sparse precision matrices in an application of Le Cam's lemma. Moreover, the proposed estimator is proven to have optimal convergence rate when the parametric rate cannot be achieved, under a minimal sample requirement. The proposed estimator is applied to test the presence of an edge in the Gaussian graphical model or to recover the support of the entire model, to obtain adaptive rate-optimal estimation of the entire precision matrix as measured by the matrix $\ell_q$ operator norm and to make inference in latent variables in the graphical model. All of this is achieved under a sparsity condition on the precision matrix and a side condition on the range of its spectrum. This significantly relaxes the commonly imposed uniform signal strength condition on the precision matrix, irrepresentability condition on the Hessian tensor operator of the covariance matrix or the $\ell_1$ constraint on the precision matrix. Numerical results confirm our theoretical findings. The ROC curve of the proposed algorithm, Asymptotic Normal Thresholding (ANT), for support recovery significantly outperforms that of the popular GLasso algorithm.

Active Manifold Learning via Gershgorin Circle Guided Sample Selection

In this paper, we propose an interpretation of active learning from a pure algebraic view and combine it with semi-supervised manifold learning. The proposed active manifold learning algorithm aims to learn the low-dimensional parameter space of the manifold with high accuracy from smartly labeled samples. We demonstrate that this problem is equivalent to a condition number minimization problem of the alignment matrix. Focusing on this problem, we first give a theoretical upper bound for the solution. Then we develop a heuristic but effective sample selection algorithm with the help of the Gershgorin circle theorem. We investigate the rationality, the feasibility, the universality and the complexity of the proposed method and demonstrate that our method yields encouraging active learning results.

Improving low bitrate video coding via computation incorporating a priori information

The growing number of mobile users, as well as the diversification in types of services have resulted in increasing demands for wireless network bandwidth in recent years. Although evolving transmission techniques are able to enlarge the network capacity to some degree, they still cannot satisfy the requirements of mobile users. Meanwhile, following Moore's Law, the data processing capabilities of mobile user terminals are continuously improving. In this paper, we explore possible methods of trading strong computational power at wireless terminals for transmission efficiency of communications. Taking the specific scenario of wireless video conversation, we propose a model-based video coding scheme by learning the structures in multimedia contents. Benefiting from both strong computing capability and pre-learned model priors, only low-dimensional parameters need to be transmitted; and the intact multimedia contents can also be reconstructed at the receivers in real-time. Experiment results indicate that, compared to conventional video codecs, the proposed scheme significantly reduces the data rate with the aid of computational capability at wireless terminals.