Kernel Smoothing Research Articles

Improved Spike-Based Brain-Machine Interface Using Bayesian Adaptive Kernel Smoother and Deep Learning

Multiunit activity (MUA) has been proposed to mitigate the robustness issue faced by single-unit activity (SUA)-based brain-machine interfaces (BMIs). Most MUA-based BMIs still employ a binning method for estimating firing rates and linear decoder for decoding behavioural parameters. The limitations of binning and linear decoder lead to suboptimal performance of MUA-based BMIs. To address this issue, we propose a method which consists of Bayesian adaptive kernel smoother (BAKS) as the firing rate estimation algorithm and deep learning, particularly quasi-recurrent neural network (QRNN), as the decoding algorithm. We evaluated the proposed method for reconstructing (offline) hand kinematics from intracortical neural data chronically recorded from the primary motor cortex of two non-human primates. Extensive empirical results across recording sessions and subjects showed that the proposed method consistently outperforms other combinations of firing rate estimation algorithm and decoding algorithm. Overall results suggest the effectiveness of the proposed method for improving the decoding performance of MUA-based BMIs.

Minimax optimal conditional density estimation under total variation smoothness

This paper studies the minimax rate of nonparametric conditional density estimation under a weighted absolute value loss function in a multivariate setting. We first demonstrate that conditional density estimation is impossible if one only requires that $p_{X|Z}$ is smooth in $x$ for all values of $z$. This motivates us to consider a sub-class of absolutely continuous distributions, restricting the conditional density $p_{X|Z}(x|z)$ to not only be H\"older smooth in $x$, but also be total variation smooth in $z$. We propose a corresponding kernel-based estimator and prove that it achieves the minimax rate. We give some simple examples of densities satisfying our assumptions which imply that our results are not vacuous. Finally, we propose an estimator which achieves the minimax optimal rate adaptively, i.e., without the need to know the smoothness parameter values in advance. Crucially, both of our estimators (the adaptive and non-adaptive ones) impose no assumptions on the marginal density $p_Z$, and are not obtained as a ratio between two kernel smoothing estimators which may sound like a go to approach in this problem.

Electromagnetic Source Imaging via Bayesian Modeling With Smoothness in Spatial and Temporal Domains.

Accurate reconstruction of cortical activation from electroencephalography and magnetoencephalography (E/MEG) is a long-standing challenge because of the inherently ill-posed inverse problem. In this paper, a novel algorithm under the empirical Bayesian framework, source imaging with smoothness in spatial and temporal domains (SI-SST), is proposed to address this issue. In SI-SST, current sources are decomposed into the product of spatial smoothing kernel, sparseness encoding coefficients, and temporal basis functions (TBFs). Further smoothness is integrated in the temporal domain with the employment of an underlying autoregressive model. Because sparseness encoding coefficients are constructed depending on overlapped clusters over cortex in this model, we derived a novel update rule based on fixed-point criterion instead of the convexity based approach which becomes invalid in this scenario. Entire variables and hyper parameters are updated alternatively in the variational inference procedure. SI-SST was assessed by multiple metrics with both simulated and experimental datasets. In practice, SI-SST had the superior reconstruction performance in both spatial extents and temporal profiles compared to the benchmarks.

DUT: Learning Video Stabilization by Simply Watching Unstable Videos.

Previous deep learning-based video stabilizers require a large scale of paired unstable and stable videos for training, which are difficult to collect. Traditional trajectory-based stabilizers, on the other hand, divide the task into several sub-tasks and tackle them subsequently, which are fragile in textureless and occluded regions regarding the usage of hand-crafted features. In this paper, we attempt to tackle the video stabilization problem in a deep unsupervised learning manner, which borrows the divide-and-conquer idea from traditional stabilizers while leveraging the representation power of DNNs to handle the challenges in real-world scenarios. Technically, DUT is composed of a trajectory estimation stage and a trajectory smoothing stage. In the trajectory estimation stage, we first estimate the motion of keypoints, initialize and refine the motion of grids via a novel multi-homography estimation strategy and a motion refinement network, respectively, and get the grid-based trajectories via temporal association. In the trajectory smoothing stage, we devise a novel network to predict dynamic smoothing kernels for trajectory smoothing, which can well adapt to trajectories with different dynamic patterns. We exploit the spatial and temporal coherence of keypoints and grid vertices to formulate the training objectives, resulting in an unsupervised training scheme. Experiment results on public benchmarks show that DUT outperforms state-of-the-art methods both qualitatively and quantitatively. The source code is available at https://github.com/Annbless/DUTCode.

The hazard level set

The hazard rate function plays a fundamental role in survival analysis. Its statistical inference methods have been systemically and exclusively studied. When does the hazard rate reach a particular warning level? This is a basic question of interest to the investigator but largely left to be explored in practice. We define a level set of hazard rate to address this issue and propose a kernel smoothing estimator for such a level set. In terms of the Hausdorff distance, we establish the consistency, convergence rate and asymptotic distribution of the level set estimator. The validity of the proposed confidence set, based on the bootstrap method, for the level set of hazard rate function is theoretically justified. We conduct comprehensive simulation studies to assess the finite-sample performance of the proposed method, which is further illustrated with a breast cancer study.

Multi-resolution super learner for voxel-wise classification of prostate cancer using multi-parametric MRI

Multi-parametric MRI (mpMRI) is a critical tool in prostate cancer (PCa) diagnosis and management. To further advance the use of mpMRI in patient care, computer aided diagnostic methods are under continuous development for supporting/supplanting standard radiological interpretation. While voxel-wise PCa classification models are the gold standard, few if any approaches have incorporated the inherent structure of the mpMRI data, such as spatial heterogeneity and between-voxel correlation, into PCa classification. We propose a machine learning-based method to fill in this gap. Our method uses an ensemble learning approach to capture regional heterogeneity in the data, where classifiers are developed at multiple resolutions and combined using the super learner algorithm, and further account for between-voxel correlation through a Gaussian kernel smoother. It allows any type of classifier to be the base learner and can be extended to further classify PCa sub-categories. We introduce the algorithms for binary PCa classification, as well as for classifying the ordinal clinical significance of PCa for which a weighted likelihood approach is implemented to improve the detection of less prevalent cancer categories. The proposed method has shown important advantages over conventional modeling and machine learning approaches in simulations and application to our motivating patient data.

Comparison of parametric and semi-parametric models with randomly right-censored data by weighted estimators: Two applications in colon cancer and hepatocellular carcinoma datasets.

In this study, parametric and semi-parametric regression models are examined for random right censorship. The components of the aforementioned regression models are estimated with weights based on Cox and Kaplan-Meier estimates, which are semi-parametric and nonparametric methods used in survival analysis, respectively. The Tobit based on weights obtained from a Cox regression is handled as a parametric model instead of other parametric models requiring distribution assumptions such as exponential, Weibull, and gamma distributions. Also, the semi-parametric smoothing spline and the semi-parametric smoothing kernel estimators based on Kaplan-Meier weights are used. Therefore, estimates are obtained from two models with flexible approaches. To show the flexible shape of the models depending on the weights, Monte Carlo simulations are conducted, and all results are presented and discussed. Two empirical datasets are used to show the performance of the aforementioned estimators. Although three approaches gave similar results to each other, the semi-parametric approach was slightly superior to the parametric approach. The parametric approach method, on the other hand, yields good results in medium and large sample sizes and at a high censorship level. All other findings have been shared and interpreted.

Topography of hippocampal connectivity with sensorimotor cortex revealed by optimizing smoothing kernel and voxel size.

Studies of the hippocampus use smaller voxel sizes and smoothing kernels than cortical activation studies, typically using a multivoxel seed with specified radius for connectivity analysis. This study identified optimal processing parameters for evaluating hippocampal connectivity with sensorimotor cortex (SMC), comparing effectiveness by varying parameters during both activation and connectivity analysis. Using both 3mm and 4mm isovoxels, smoothing kernels of 0-10mm were evaluated on the amplitude and extent of motor activation and hippocampal connectivity with SMC. Psychophysiological interactions (PPI) identified hippocampal connectivity with SMC during volitional movements, and connectivity effects from multivoxel seeds were compared with alternate methods; a structural seed represented the mean connectivity map from all voxels within a region, whereas a functional seed represented the regional voxel with maximal SMC connectivity. With few exceptions, the same parameters were optimal for activation and connectivity. Larger isovoxels showed larger activation volumes in both SMC and the hippocampus; connectivity volumes from structural seeds were also larger, except from the posterior hippocampus. Regardless of voxel size, the 10mm smoothing kernel generated larger activation and connectivity volumes from structural seeds, as well as larger beta estimates at connectivity maxima; structural seeds also produced larger connectivity volumes than multivoxel seeds. Functional seeds showed lesser effects from voxel size and smoothing kernels. Optimal parameters revealed topography in structural seed connectivity along both the longitudinal axis and mediolateral axis of the hippocampus. These results indicate larger voxels and smoothing kernels can improve sensitivity for detecting both cortical activation and hippocampal connectivity.

Semiparametric additive time-varying coefficients model for longitudinal data with censored time origin.

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time-varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan-Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two-stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two-stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccinestudy.

Performance Comparison of Various Smoothing Methods For Detection of Device-Free Target

In the device-free localization systems, it is major issue how to detect a device-free target, which does not carry any assistant electronical devices. When a target crosses the communication links, the target causes the fluctuation of received signal strength (RSS) values at the receiver side. However, the performance of the detection scheme based on RSS tends to be degraded because of noises in indoor environments. In this paper, we present various smoothing methods to mitigate the effect of noises for enhanced performance of target detection. To compare the performance of various smoothing methods, we performed experiments with IEEE 802.15.4 ZigBee devices. According to the experimental results, it is shown that the Gaussian kernel smoothing, the weighted moving average smoothing, and the exponential moving average smoothing methods can provide more suitable performance than other methods in terms of mean square error, while the exponential moving average smoothing provides more suitable performance in terms of detection accuracy and detection temporal accuracy.

A cost-effective algorithm for calibrating multiscale geographically weighted regression models

ABSTRACT The multiscale geographically weighted regression (MGWR) model is a useful extension of the geographically weighted regression (GWR) model. MGWR, however, is a kind of Nadaraya–Watson kernel smoother, which usually leads to inaccurate estimates for the regression function and suffers from the boundary effect. Moreover, the widely used calibration technique for the MGWR with a back-fitting estimator (MGWR-BF) is computationally demanding, preventing it from being applied to large-scale data. To overcome these problems, we proposed a local linear-fitting-based MGWR (MGWR-LL) by introducing a local spatially varying coefficient model in which coefficients of different variables could be characterised as linear functions of spatial coordinates with different degrees of smoothness. Then the model was calibrated with a two-step least-squared estimated algorithm. Both simulated and actual data were implemented to validate the performance of the proposed method. The results consistently showed that the MGWR-LL automatically corrected for the boundary effect and improved the accuracy in most cases, not only in the goodness-of-fit measure but also in reducing the bias of the coefficient estimates. Moreover, the MGWR-LL significantly outperformed the MGWR-BF in computational cost, especially for larger-scale data. These results demonstrated that the proposed method can be a useful tool for the MGWR calibration.

Numerical approximation of modified Kawahara equation using Kernel smoothing method

In this article, a numerical approximation of modified Kawahara equation is investigated by Kernel smoothing method. The spatial derivatives involved in the modified Kawahara equation are approximated by smoothing Kernel method. Whereas, for the time integration, we employ Crank–Nicolson method. The conservative nature of the proposed scheme is demonstrated by the mass conservation constant (I1) and energy conservation constant (I2). To quantify the quality of the proposed scheme, we also have performed numerical testing on a collection of test problems.

Determinants and Dynamic Changes of Generic Quality of Life in Human Bladder Cancer Patients.

We measured and determined the factors associated with long-term generic quality-of-life (QOL) changes in human bladder cancer patients. We utilized the World Health Organization QOL-Brief questionnaire to assess consecutive patients’ QOL at outpatient clinics of our hospital. A mixed-effects model was constructed to investigate the determinants of QOL changes according to each domain and individual item after controlling for demographic and clinical factors, as well as the effect of radical cystectomy. We also applied a kernel smoothing method to describe the long-term dynamic changes after the first definite treatment. In total, 1185 repeated measurements were collected from 343 bladder cancer patients. The mixed-effects models demonstrated that marital status, monthly income, and comorbidity with heart disease and diabetes were significant determinants among all the study participants. Regardless of the urinary diversion type, radical cystectomy contributed to lower scores for all four domains, mainly from 4–5 years after cystectomy, which declined significantly in patients who were older than 60 years. As for non-muscle-invasive bladder cancer (NMIBC) patients with preserved bladders, tumor recurrence was a major predictor for lower scores for sexual activity in the social domain. In summary, generic QOL can be independently influenced by many factors, not only cystectomy and tumor recurrence, which should be discussed with patients before treatment.

Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake

We present a numerical scheme for the solution of nonlinear mixed-dimensional PDEs describing coupled processes in embedded tubular network system in exchange with a bulk domain. Such problems arise in various biological and technical applications such as in the modeling of root-water uptake, heat exchangers, or geothermal wells. The nonlinearity appears in form of solution-dependent parameters such as pressure-dependent permeability or temperature-dependent thermal conductivity. We derive and analyze a numerical scheme based on distributing the bulk-network coupling source term by a smoothing kernel with local support. By the use of local analytical solutions, interface unknowns and fluxes at the bulk-network interface can be accurately reconstructed from coarsely resolved numerical solutions in the bulk domain. Numerical examples give confidence in the robustness of the method and show the results in comparison to previously published methods. The new method outperforms these existing methods in accuracy and efficiency. In a root water uptake scenario, we accurately estimate the transpiration rate using only a few thousand 3D mesh cells and a structured cube grid whereas other state-of-the-art numerical schemes require millions of cells and local grid refinement to reach comparable accuracy.

Nested anisotropic geostatistical gridding of airborne geophysical data

Airborne geophysical surveys routinely collect data along traverse lines at sample spacing distances that are two or more orders of magnitude less than between-line separations. Grids and maps interpolated from such surveys can produce aliasing; features that cross flight lines can exhibit boudinage or string-of-beads artifacts. Boudinage effects can be addressed by novel gridding methods. Following developments in geostatistics, a nonstationary nested anisotropic gridding scheme is proposed that accommodates sampling and data anisotropy in geophysical surveys. Computation is reduced by including anchor points throughout the interpolation region that contain localized anisotropy information that is propagated throughout the survey area with a smoothing kernel. Additional anisotropy can be required at certain locations in the region to be gridded. A model selection scheme is proposed that uses Laplace approximations for determining whether increased model complexity is supported by the surrounding data. The efficacy of the method is shown using a synthetic data set obtained from satellite imagery. A pseudogeophysical survey is created from the image and reconstructed with this method. Two case histories are selected for further elucidation from airborne geophysical surveys conducted in Western Australia (WA). The first example illustrates improvement in gridding the depth of paleochannels interpreted from along-line conductivity-depth models of a regional airborne electromagnetic (AEM) survey in the Mid West WA region. The second example indicates how improvements can be made in producing grids of aeromagnetic data and inverted electrical conductivity from an AEM survey conducted in the Pilbara region. In both case histories, nested anisotropic kriging reduces the expression of boudinage patterns and sharpens crossline features in the final gridded products permitting increased confidence in interpretations based on such products.

The Influence of Spatial Smoothing Kernel Size on the Whole-brain Dynamic Functional Network Connectivity and Meta-state Parameters.

In functional magnetic resonance imaging (fMRI), spatial smoothing procedure is generally a stable step in the preprocessing stream. Previous research (including ours) suggested dependency of the static functional connectivity on the size of the spatial smoothing kernel size. But its impact on the time-varying patterns of functional connectivity has not been investigated. Here, we sought to identify the effects of spatial smoothing on brain dynamics by performing dynamic functional network connectivity (dFNC) and meta-state analysis, a unique approach capable of examining a higher-dimensional temporal dynamism of whole-brain functional connectivity. Gaussian smoothing kernel with different widths at half of the maximum of the height of the Gaussian (4, 8, and 12 mm FWHM) were used during preprocessing prior to the group independent component analysis (ICA) with a relatively high model order of 75. dFNC was conducted using the sliding-time window approach and k-means clustering algorithm. Meta-state dynamics method was performed by reducing the number of windowed FNC correlations using principal components analysis (PCA), temporal and spatial ICA and k-means. Results revealed robust effects of spatial smoothing on the connectivity dynamics of several network pairs including a variety of cognitive/attention networks in a connectivity state with the highest occurrence (FDR corrected-p < 0.01). Meta-state analyses indicated significant changes in meta-state metrics including the number of meta-states, meta-state changes, meta-state span, and the total distance. These changes were particularly pronounced when we compared resting state data smoothed with 8 vs. 12 mm FWHM. Our preliminary findings give insights into the effects of spatial smoothing kernel size on the dynamics of functional connectivity and its consequences on meta-state parameters. It also provides further indication of the importance of evaluating variance associated with preprocessing steps on analysis outcomes.

Examining the Influence of Spatial Smoothing on Spatiotemporal Features of Intrinsic Connectivity Networks at Low ICA Model Order.

Using a relatively high model order of independent component analysis (ICA with 75 ICs) of functional magnetic resonance imaging (fMRI) data, we have reported a clear effect of spatial smoothing Gaussian kernel size on spatiotemporal properties of intrinsic connectivity networks (ICNs). However, many if not the majority of ICA fMRI studies are usually performed at low model order, e.g., 20-IC decomposition, as such low order is generally enough to extract the few networks of interest such as the default-mode network (DMN). The aim of this study is to investigate if we can replicate the spatial smoothing effects on spatiotemporal features of ICNs at low ICA model order. Same resting state fMRI data that we used with 75-IC analysis were used here. Spatial smoothing using an isotropic Gaussian filter kernel with full width at half maximum (FWHM) of 4, 8, and 12 mm was applied during preprocessing. ICNs were identified from 20-IC decomposition and evaluated in terms of three primary features: spatial map intensity, functional network connectivity (FNC), and power spectra. The results identified similar effects of spatial smoothing on spatial map intensities and power spectra at p < 0.01, false discovery rate (FDR) corrected for multiple comparisons. Reduced spatial smoothing kernel size resulted in decreased spatial map intensities as well as a generally decreased low-frequency power (0.01 - 0.10 Hz) but increased high-frequency power (0.15 - 0.25 Hz). FNC, however, did not show a uniform change in correlation values with the size of smoothing kernel. Notably, FNC between DMNs decreased but FNC between central executive and visual networks increased with an increase in smoothing kernel size. These preliminary findings confirm spatial smoothing influences ICN features regardless of model order. The discussion focuses on differences between observed changes at low and high ICA model orders.

The Influence of Spatial Smoothing Kernel Size on the Temporal Features of Intrinsic Connectivity Networks.

Spatial smoothing is a common preprocessing step in the analysis of functional magnetic resonance imaging (fMRI) data. However, little is known about the effect of spatial smoothing kernel size on the temporal properties of functional brain networks. This study presents a pilot investigation on the influence of spatial smoothing using independent component analysis (ICA) as a data-driven technique to extract functional networks of brain in the form of intrinsic connectivity networks (ICNs). BOLD resting state fMRI data were collected from 22 healthy subjects on a 3.0 T MRI scanner. 3D spatial smoothing was applied using a Gaussian filter with full width at half maximum (FWHM) kernel sizes of 4 mm, 8 mm, and 12 mm in the preprocessing step. Group ICA with the Infomax algorithm was performed at 75-IC decomposition. Network temporal features including functional network connectivity (FNC) and BOLD power spectra were calculated and compared pairwise using a paired t-test with a false discovery rate (FDR) correction for multiple comparisons. Results revealed robust effects of smoothing kernel size on FNC measures of most ICNs, largely indicating a decrease in inter-network connectivity as the smoothing kernel size decreased. Power spectra analysis showed increased high-frequency power (0.15 - 0.25 Hz) but decreased low-frequency power (0.01 - 0.10 Hz) with a decrease in the smoothing kernel size (corrected p< 0.01). These findings provide a preliminary observation on the effect of spatial smoothing kernel size on the FNC and power spectra.

Longitudinal Predictive Curves of Health Risk Factors for American Adolescent Girls

PurposeThe aim of this study is to compare age-variant 18 health risk factors by constructing longitudinal predictive curves between African-American (AA) and Caucasian American (CA) adolescent girls. MethodsA total of 2,379 girls (51% AA) from ages 9 to 10 were recruited in the National Heart, Lung, and Blood Institute Growth and Health Study. The various health indicators and dietary habits of these girls were assessed annually for 10 years. We model 2nd, 5th, 95th, and 98th percentile values of the health risk factors to compare trajectories between AA and CA adolescents by employing novel kernel smoothing regression and global tests of equality for regression curves. Health risk factors such as dietary fiber, intake of sodium, sugar, and total calories, systolic blood pressure, weight, body fat percentage, and high-density lipoprotein levels were compared. ResultsTrajectories of sugar, sodium, and total calories intake and systolic blood pressure, weight, body fat percentage, and high-density lipoprotein among AA girls were significantly higher than those of CA girls throughout their adolescence. ConclusionsAA girls exhibit several health risk factors that are significantly higher than those of CA adolescent girls at the 95th and 98th percentile. Interventions may be warranted for the purposes of ensuring access to health risk information as well as a greater ease of access to healthier food choices within the educational food system.

A Fast-Converging Kernel Density Estimator for Dispersion in Horizontally Homogeneous Meteorological Conditions

Kernel smoothers are often used in Lagrangian particle dispersion simulations to estimate the concentration distribution of tracer gasses, pollutants etc. Their main disadvantage is that they suffer from the curse of dimensionality, i.e., they converge at a rate of 4/(d+4) with d the number of dimensions. Under the assumption of horizontally homogeneous meteorological conditions, we present a kernel density estimator that estimates a 3D concentration field with the faster convergence rate of a 1D kernel smoother, i.e., 4/5. This density estimator has been derived from the Langevin equation using path integral theory and simply consists of the product between a Gaussian kernel and a 1D kernel smoother. Its numerical convergence rate and efficiency are compared with that of a 3D kernel smoother. The convergence study shows that the path integral-based estimator has a superior convergence rate with efficiency, in mean integrated squared error sense, comparable with the one of the optimal 3D Epanechnikov kernel. Horizontally homogeneous meteorological conditions are often assumed in near-field range dispersion studies. Therefore, we illustrate the performance of our method by simulating experiments from the Project Prairie Grass data set.