Sparsity Assumption Research Articles

Inactivation kinetics of waterborne virus by ozone determined by a continuous quench flow system

Ozone has a strong oxidation power that allows effective inactivation of waterborne viruses. Few studies have accurately measured the kinetic relationship between virus inactivation and ozone exposure, because the high reactivity of ozone makes it difficult to measure them simultaneously. A continuous quench flow system (CQFS) is a possible solution for analyzing such a fast reaction; however, previous studies reported that CQFS provided different results of inactivation rate constants from the batch system. The objectives of this study were (1) to develop a CQFS to evaluate the kinetics of microbial inactivation accurately, (2) to evaluate the inactivation rate constants of waterborne virus by ozone, and (3) to compare the results with previous studies. The results indicated that the simple plug flow assumption in the reaction tube of CQFS led to underestimation of the rate constants. The accurate measurement of rate constants was achieved by the pseudo-first-order reaction model that takes the residence time distribution (RTD; i.e., the laminar flow assumption) into account. The results of inactivation experiments suggested that the resistance of viruses were getting higher in the following order: Qβ < MS2, fr, GA < CVB5 Faulkner, φX-174, PV1 Sabin, CVB3 Nancy. The environmental isolates of CVB3 and CVB5 had a 2-fold higher resistance compared with their lab strains. Predicted CT values for 4-log inactivation ranged from 0.018 mg sec L−1 (Qβ) to 0.31 mg sec L−1 (CVB3 Environmental strain). The required CT values for 4-log PV1 inactivation was 0.15 mg sec L−1, which was 166-fold smaller than those reported in the United States Environmental Protection Agency guidance manuals. The overestimation in previous studies was due to the sparse assumption of RTD in the reactor. Consequently, the required ozone CT values for virus inactivation should be reconsidered to minimize the health risks and environmental costs in water treatment.

SAR RFI Suppression for Extended Scene Using Interferometric Data via Joint Low-Rank and Sparse Optimization

Radio frequency interference (RFI) can significantly pollute synthetic aperture radar (SAR) data and images, which is also harmful to SAR interferometry (InSAR) for retrieving elevational information. To address this issue, in recent years, a class of advanced RFI suppression methods has been proposed based on narrowband properties of RFI and sparsity assumptions of radar echoes or target reflectivity. However, for SAR echoes and the associated scene reflectivity, these assumptions are usually not feasible when the imaged scene is spatially extended. In view of these problems, this study proposes an InSAR-based RFI suppression method for the case of extended scenes. For this task, we combine the RFI-polluted SAR data with RFI-free interferometric data to form an interferometric SAR data pair. We show that such an InSAR data pair embeds an interferogram having the image amplitude multiplying by a complex exponential interferometric phase. We treat the interferogram as a kind of natural image and use discrete Fourier cosine transform (DCT) for its sparse representation. Then combining the DCT-domain sparsity with low-rank modeling of RFI, we retrieve the interferogram and reconstruct the SAR image via joint low-rank and sparse optimization. Numerical simulations show that the proposed method can effectively recover SAR images and interferometric phases from RFI-polluted SAR data.

On Nearly Assumption-Free Tests of Nominal Confidence Interval Coverage for Causal Parameters Estimated by Machine Learning

For many causal effect parameters of interest, doubly robust machine learning (DRML) estimators $\hat{\psi}_{1}$ are the state-of-the-art, incorporating the good prediction performance of machine learning; the decreased bias of doubly robust estimators; and the analytic tractability and bias reduction of sample splitting with cross-fitting. Nonetheless, even in the absence of confounding by unmeasured factors, the nominal $(1-\alpha)$ Wald confidence interval $\hat{\psi}_{1}\pm z_{\alpha/2}\widehat{\mathsf{s.e.}}[\hat{\psi}_{1}]$ may still undercover even in large samples, because the bias of $\hat{\psi}_{1}$ may be of the same or even larger order than its standard error of order $n^{-1/2}$. In this paper, we introduce essentially assumption-free tests that (i) can falsify the null hypothesis that the bias of $\hat{\psi}_{1}$ is of smaller order than its standard error, (ii) can provide a upper confidence bound on the true coverage of the Wald interval, and (iii) are valid under the null under no smoothness/sparsity assumptions on the nuisance parameters. The tests, which we refer to as Assumption Free Empirical Coverage Tests (AFECTs), are based on a U-statistic that estimates part of the bias of $\hat{\psi}_{1}$. Our claims need to be tempered in several important ways. First no test, including ours, of the null hypothesis that the ratio of the bias to its standard error is smaller than some threshold $\delta$ can be consistent [without additional assumptions (e.g., smoothness or sparsity) that may be incorrect]. Second, the above claims only apply to certain parameters in a particular class. For most of the others, our results are unavoidably less sharp. In particular, for these parameters, we cannot directly test whether the nominal Wald interval $\hat{\psi}_{1}\pm z_{\alpha/2}\widehat{\mathsf{s.e.}}[\hat{\psi}_{1}]$ undercovers. However, we can often test the validity of the smoothness and/or sparsity assumptions used by an analyst to justify a claim that the reported Wald interval’s actual coverage is no less than nominal. Third, in the main text, with the exception of the simulation study in Section 1, we assume we are in the semisupervised data setting (wherein there is a much larger dataset with information only on the covariates), allowing us to regard the covariance matrix of the covariates as known. In the simulation in Section 1, we consider the setting in which estimation of the covariance matrix is required. In the simulation, we used a data adaptive estimator which performs very well in our simulations, but the estimator’s theoretical sampling behavior remains unknown.

Sparse recovery via nonconvex regularized [formula omitted]-estimators over [formula omitted]-balls

The recovery properties of nonconvex regularized M-estimators are analysed, under the general sparsity assumption on the true parameter. In the statistical aspect, the recovery bound for any stationary point of the nonconvex regularized M-estimator is established under some regularity conditions. In the computational aspect, the proximal gradient method is used to solve the nonconvex optimization problem and is proved to achieve a linear convergence rate, by virtue of a slight decomposition of the objective function. In particular, for commonly-used regularizers such as SCAD and MCP, a simpler decomposition is applicable thanks to the assumption on the regularizer, which helps to construct the estimator with better recovery performance. In the aspect of application, theoretical consequences are obtained on the corrupted error-in-variables linear regression model by verifying the required conditions. Finally, statistical and computational results as well as advantages of the assumptions are demonstrated by several numerical experiments. Simulation results show remarkable consistency with the theory under high-dimensional scaling.

A Scalable Estimate of the Out-of-Sample Prediction Error via Approximate Leave-One-Out Cross-Validation

SummaryThe paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as K-fold cross-validation suffer from large biases. Motivated by the low bias of the leave-one-out cross-validation method, we propose a computationally efficient closed form approximate leave-one-out formula ALO for a large class of regularized estimators. Given the regularized estimate, calculating ALO requires a minor computational overhead. With minor assumptions about the data-generating process, we obtain a finite sample upper bound for the difference between leave-one-out cross-validation and approximate leave-one-out cross-validation, |LO−ALO|. Our theoretical analysis illustrates that |LO−ALO|→0 with overwhelming probability, when n, p → ∞, where the dimension p of the feature vectors may be comparable with or even greater than the number of observations, n. Despite the high dimensionality of the problem, our theoretical results do not require any sparsity assumption on the vector of regression coefficients. Our extensive numerical experiments show that |LO−ALO| decreases as n and p increase, revealing the excellent finite sample performance of approximate leave-one-out cross-validation. We further illustrate the usefulness of our proposed out-of-sample risk estimation method by an example of real recordings from spatially sensitive neurons (grid cells) in the medial entorhinal cortex of a rat.

Variance estimation based on blocked 3×2 cross-validation in high-dimensional linear regression

In high-dimensional linear regression, the dimension of variables is always greater than the sample size. In this situation, the traditional variance estimation technique based on ordinary least squares constantly exhibits a high bias even under sparsity assumption. One of the major reasons is the high spurious correlation between unobserved realized noise and several predictors. To alleviate this problem, a refitted cross-validation (RCV) method has been proposed in the literature. However, for a complicated model, the RCV exhibits a lower probability that the selected model includes the true model in case of finite samples. This phenomenon may easily result in a large bias of variance estimation. Thus, a model selection method based on the ranks of the frequency of occurrences in six votes from a blocked 3×2 cross-validation is proposed in this study. The proposed method has a considerably larger probability of including the true model in practice than the RCV method. The variance estimation obtained using the model selected by the proposed method also shows a lower bias and a smaller variance. Furthermore, theoretical analysis proves the asymptotic normality property of the proposed variance estimation.

Reflection-Based Source Inversion for Sparse Imaging of Low-Loss Composite Panels

This article presents a bistatic reflection-based imaging technique for electromagnetic testing of conductor-backed composite panels, which is based on an inverse formulation of the numerical problem at hand, and technically extends a previously demonstrated transmission-based system. The technique exploits the a priori assumption of pixel-based sparsity and retrieves the final image using data from only a single measurement, thereby removing the necessity of a reference measurement to be conducted. To demonstrate the capability of the technique, retrieved images are presented for a synthetic proof-of-concept device under test and an industrially manufactured composite panel. The presented technique can be considered as the initial model in the development of more complex bistatic imaging systems and has been developed for the purpose of extending the opportunities to conduct reflection-based electromagnetic nondestructive testing on aircraft structural components.

Model averaging assisted sufficient dimension reduction

Sufficient dimension reduction that replaces original predictors with their low- dimensional linear combinations without loss of information is a critical tool in modern statistics and has gained considerable research momentum in the past decades since the two pioneers sliced inverse regression and principal Hessian directions. The classical sufficient dimension reduction methods do not handle sparse case well since the estimated linear reductions involve all of the original predictors. Sparse sufficient dimension reduction methods rely on sparsity assumption which may not be true in practice. Motivated by the least squares formulation of the classical sliced inverse regression and principal Hessian directions, several model averaging assisted sufficient dimension reduction methods are proposed. They are applicable to both dense and sparse cases even with weak signals since model averaging adaptively assigns weights to different candidate models. Based on the model averaging assisted sufficient dimension reduction methods, how to estimate the structural dimension is further studied. Theoretical justifications are given and empirical results show that the proposed methods compare favorably with the classical sufficient dimension reduction methods and popular sparse sufficient dimension reduction methods.

Information-Theoretic Lower Bounds for Compressive Sensing With Generative Models

It has recently been shown that for compressive sensing, significantly fewer measurements may be required if the sparsity assumption is replaced by the assumption the unknown vector lies near the range of a suitably-chosen generative model. In particular, in (Bora et al., 2017) it was shown roughly O(k log L) random Gaussian measurements suffice for accurate recovery when the generative model is an L-Lipschitz function with bounded k-dimensional inputs, and O(kdlogw) measurements suffice when the generative model is a k-input ReLU network with depth d and width w. In this paper, we establish corresponding algorithm-independent lower bounds on the sample complexity using tools from minimax statistical analysis. In accordance with the above upper bounds, our results are summarized as follows: (i) We construct an L-Lipschitz generative model capable of generating group-sparse signals, and show that the resulting necessary number of measurements is Ω(k logL); (ii) Using similar ideas, we construct ReLU networks with high depth and/or high depth for which the necessary number of measurements scales as Ω(kd logw/logn) (with output dimension n), and in some cases Ω(kd logw). As a result, we establish that the scaling laws derived in (Bora et al., 2017) are optimal or near-optimal in the absence of further assumptions.

Sparse magnetic vector inversion in spherical coordinates

Magnetic vector inversion (MVI) has received considerable attention over recent years for processing magnetic field data that are affected by remanent magnetization. However, the magnetization models obtained with current inversion algorithms are generally too smooth to be easily interpreted geologically. To address this, we have reviewed the MVI formulated in a spherical coordinate system. We tackle convergence issues posed by the nonlinear transformation from Cartesian to spherical coordinates by using an iterative sensitivity weighting approach and a scaling of the spherical parameters. The spherical formulation allows us to impose sparsity assumptions on the magnitude and direction of magnetization independently and, as a result, the inversion recovers simpler and more coherent magnetization orientations. The numerical implementation of our algorithm on large-scale problems is facilitated by discretizing the forward problem using tiled octree meshes. All of our results are generated using the open-source SimPEG software. We determine the enhanced capabilities of our algorithm on a large airborne magnetic survey collected over the Kevitsa Ni-Cu-platinum group elements (PGE) deposit. The recovered magnetization direction inside the ultramafic intrusion and in the host stratigraphy is consistent with laboratory measurements and provides evidence for tectonic deformation.

A comparison of compressive equivalent source methods for distributed sources.

Sparse sound-field reconstruction methods based on compressive sensing and the equivalent source method have gained a lot of interest in recent years, offering a wide frequency range. An irregular array must be employed, and the sound field must be representable by a sparse vector of source-model amplitudes. With few and concentrated physical sources, the sparsity assumption can be fulfilled, but distributed sources cause problems. Several methods have therefore been introduced to support sparse representation of distributed sources. One set of such methods represents the amplitude vector as a linear combination of modal amplitude distributions. In that case, the coefficient vector just has to be sparse. The present paper gives an overview of such methods, and the performance of the methods is compared based on a set of simulated measurements. Overall the modal representations work well if the true source distribution can be represented by relatively few modes. The results show that even for a vibrating plate this may not be the case if the source model size does not match the plate size and/or if a non-central plate excitation is applied. If, in addition, there are also compact sources, then the basic method without modes may be the best choice.

A global approach for learning sparse Ising models

We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. Under sparsity assumption, we propose a method based on l1-regularized logistic regression, which estimate globally the whole set of edges and link parameters. Unlike the more recent methods discussed in literature that learn the edges and the corresponding link parameters one node at a time, in this work we propose a method that learns all the edges and corresponding link parameters simultaneously for all nodes. The idea behind this proposal is to exploit the reciprocal information of the nodes between each other during the estimation process. Numerical experiments highlight the advantage of this technique and confirm the intuition behind it.

Variable selection via penalized generalized estimating equations for a marginal survival model.

Clustered and multivariate survival times, such as times to recurrent events, commonly arise in biomedical and health research, and marginal survival models are often used to model such data. When a large number of predictors are available, variable selection is always an important issue when modeling such data with a survival model. We consider a Cox's proportional hazards model for a marginal survival model. Under the sparsity assumption, we propose a penalized generalized estimating equation approach to select important variables and to estimate regression coefficients simultaneously in the marginal model. The proposed method explicitly models the correlation structure within clusters or correlated variables by using a prespecified working correlation matrix. The asymptotic properties of the estimators from the penalized generalized estimating equations are established and the number of candidate covariates is allowed to increase in the same order as the number of clusters does. We evaluate the performance of the proposed method through a simulation study and analyze two real datasets for the application.

Random Noise Attenuation of Common Offset Gathers Using Iteratively Reweighted $\ell_{2,1}$ Norm Minimization

Sparse representation (SR)-based denoising method attenuates random seismic noise trace-by-trace, which may not be able to employ the coherency between neighboring traces. To address this, we propose a multiple measurement vector (MMV)-based algorithm for robust denoising of multichannel seismic gathers. Seismic reflectors in common offset gather (COG) is characterized by horizontal events, which satisfy the common sparsity assumption, making it ideal for the MMV approach. $\ell _{2,1}$ -norm regularization, which enforces two constraints on source matrix, i.e., temporal sparsity and the horizontal continuity, is then adopted in the MMV model to stabilize the lateral variation between channels. Besides, $\ell _{2,1}$ -norm regularization provides a reasonable intrinsic structure to reduce the multisolution of the algorithm. Celebrating the strengths of iteratively reweighted (IR), we present a novel MMV algorithm, IR $\ell _{2,1}$ norm minimization (IR- $\ell _{2,1}$ ), that further improves the performance. The formulated IR- $\ell _{2,1}$ can be minimized by the alternating direction method of multipliers. Both synthetic and field data applications confirm the effectiveness of the proposed denoising method.

Testing Stochastic Dominance with Many Conditioning Variables

We propose a test of the hypothesis of conditional stochastic dominance in the presence of many conditioning variables (whose dimension may grow to infinity as the sample size diverges). Our approach builds on a semiparametric location scale model in the sense that the conditional distribution of the outcome given the covariates is characterized by a nonparametric mean function and a nonparametric skedastic function with an independent innovation whose distribution is unknown. We propose to estimate the nonparametric mean and skedastic regression functions by the l₁-penalized nonparametric series estimation with thresholding. Under the sparsity assumption, where the number of truly relevant series terms are relatively small (but their identities are unknown), we develop the estimation error bounds for the regression functions and series coefficients estimates allowing for the time series dependence. We derive the asymptotic distribution of the test statistic, which is not pivotal asymptotically, and introduce the smooth stationary bootstrap to approximate its sample distribution. We investigate the finite sample performance of the bootstrap critical values by a set of Monte Carlo simulations. Finally, our method is illustrated by an application to stochastic dominance among portfolio returns given all the past information.

Improved estimation of elastic attributes from prestack seismic data for reservoir characterization

Seismic derivable elastic attributes, e.g., elastic impedance, lambda-rho, mu-rho, and Poisson impedance (PI), are routinely being used for reservoir characterization practice. These attributes could be derived from inverted [Formula: see text], [Formula: see text], and density, and usually indicate high sensitivity to reservoir lithology and fluid. Due to the high sensitivity of such elastic attributes, errors or measurement noise associated with the acquisition, processing, and inversion of prestack seismic data will propagate through the inversion products, and will lead to even larger errors in the computed attributes. To solve this problem, we have developed a two-step cascade workflow that combines linear inversion and nonlinear optimization techniques for the improved estimation of elastic attributes and better prediction and delineation of reservoir lithology and fluids. The linear inversion in the first step is an inversion scheme with a sparseness assumption, based on L1-norm regularization. This step is used to select the major reflective layer locations, followed in the second step by a nonlinear optimization process with the predefined layer structure. The combination of these two procedures produces a reasonable blocky earth model with consistent elastic properties, including the ones that are sensitive to reservoir lithology and fluid change, and thus provides an accurate approach for seismic reservoir characterization. Using PI, as one of the target elastic attributes, as an example, this workflow has been successfully applied to synthetic and field data examples. The results indicate that our workflow improves the estimation of elastic attributes from the noisy prestack seismic data and may be used for the identification of the reservoir lithology and fluid.

A Graphical Lasso Approach to Estimating Network Connections: The Case of U.S. Lawmakers

In this paper, we propose a new approach to the estimation of social networks and we apply it to the estimation of productivity spillovers in the U.S. Congress. Social networks such as the social connections among lawmakers are not generally directly observed, they can be recovered only using the observable outcomes that they contribute to determine (such as, for example, the legislators' effectiveness). Moreover, they are typically stable for relatively short periods of time, thus generating only short panels of observations. Our estimator has three appealing properties that allows it to work in these environments. First, it is constructed for small asymptotic, thus requiring only short panels of observations. Second, it requires relatively nonrestrictive sparsity assumptions for identification, thus being applicable to dense networks with (potentially) star shaped connections. Third, it allows for heterogeneous common shocks across subnetworks. The application to the U.S. Congress gives us new insights about the nature of social interactions among lawmakers. We estimate a significant decrease over time in the importance of productivity spillovers among individual lawmakers, compensated by an increase in the party level common shock over time. This suggests that the rise of partisanship is not affecting only the ideological position of legislators when they vote, but more generally how lawmakers collaborate in the U.S. Congress.

Intelligent Missing Shots’ Reconstruction Using the Spatial Reciprocity of Green’s Function Based on Deep Learning

The trace interval in the common shot and receiver gathers is always inconsistent. The inconsistency affects the final performance of seismic data processing, and the reconstruction methods can enhance the consistency. Unfortunately, most interpolation algorithms are suitable in randomly missing cases, and the difficulty increases sharply in regularly missing cases, especially with big gaps. As deep learning (DL) has a strong self-learning ability in nonlinear characterizations to avoid linear events, sparsity, and low rank assumptions, we introduce DL into missing shots’ reconstruction. The spatial reciprocity of Green’s function is used to provide reasonable training data sets. First, the residual learning networks (ResNets) and the interpolation issue are briefly illustrated. Then, the spatial reciprocity is reviewed and illustrated qualitatively using the common shot and receiver gathers. The similar features in the common shot and receiver gathers guarantee the reasonability to regard the common shot gathers as the training sets and to regard the common receiver gathers as the test sets. The common shot gathers are divided into the training sets to train ResNets and the validation sets to verify the performance of the trained ResNets. Finally, the trained ResNets are used to reconstruct missing shots intelligently in the common receiver gather. Three different data sets are used to prove the validity of the proposed strategy. After reconstruction, the events are more continuous with less serrations and serious frequency wavenumber (FK) aliasing is attenuated effectively. The reconstructed data with a better consistency can improve the accuracy of migration and the final reservoir characterization.

Regularized Partially Functional Autoregressive Model

Functional time series and high-dimensional scalar predictors frequently arise in a wide range of modern economic and business applications, which require statistical models that can simultaneously handle the temporal and causal dependence that are prevalent in large sets of mixed-type data. We propose a partially functional autoregressive model (pFAR) to describe the dynamic evolution of the serially correlated functional response on its own lagged values and the causal relation with a large amount of exogenous scalar predictors. Our estimation is conducted by facilitating the sieve method and a two-layer sparsity assumption that is imposed on groups and elements. In the high-dimensional setting, the sparse structure is completely unknown and it is identified entirely data-driven with a forward-looking criterion. In addition, asymptotic properties of the estimators are established. Extensive simulation studies show that the pFAR model accurately identifies the sparse structure with a convincing and stable predictive performance. The power of the pFAR model is further confirmed by real data analysis of day-ahead gas demand and supply curve predictions of multiple nodes in the German natural gas transmission network with different functions. Given the historical values of the daily curves and 85 scalar predictors, the model detects several essential categories of mixed-type predictors with insightful economic interpretation. It also provides appealing out-of-sample forecast accuracy when compared to a number of popular alternative models.

Sign consistency for the linear programming discriminant rule

Linear discriminant analysis (LDA) is an important conventional model for data classification. Classical theory shows that LDA is Bayes consistent for a fixed data dimensionality p and a large training sample size n. However, in high-dimensional settings when p ≫ n, LDA is difficult due to the inconsistent estimation of the covariance matrix and the mean vectors of populations. Recently, a linear programming discriminant (LPD) rule was proposed for high-dimensional linear discriminant analysis, based on the sparsity assumption over the discriminant function. It is shown that the LPD rule is Bayes consistent in high-dimensional settings. In this paper, we further show that the LPD rule is sign consistent under the sparsity assumption. Such sign consistency ensures the LPD rule to select the optimal discriminative features for high-dimensional data classification problems. Evaluations on both synthetic and real data validate our result on the sign consistency of the LPD rule.