Adaptive Kernel Method Research Articles

A scalable adaptive quadratic kernel method for interpretable epistasis analysis in complex traits.

Our knowledge of the contribution of genetic interactions (epistasis) to variation in human complex traits remains limited, partly due to the lack of efficient, powerful, and interpretable algorithms to detect interactions. Recently proposed approaches for set-based association tests show promise in improving the power to detect epistasis by examining the aggregated effects of multiple variants. Nevertheless, these methods either do not scale to large Biobank data sets or lack interpretability. We propose QuadKAST, a scalable algorithm focused on testing pairwise interaction effects (quadratic effects) within small to medium-sized sets of genetic variants (window size ≤100) on a trait and provide quantified interpretation of these effects. Comprehensive simulations show that QuadKAST is well-calibrated. Additionally, QuadKAST is highly sensitive in detecting loci with epistatic signals and accurate in its estimation of quadratic effects. We applied QuadKAST to 52 quantitative phenotypes measured in ≈300,000 unrelated white British individuals in the UK Biobank to test for quadratic effects within each of 9515 protein-coding genes. We detect 32 trait-gene pairs across 17 traits and 29 genes that demonstrate statistically significant signals of quadratic effects (accounting for the number of genes and traits tested). Across these trait-gene pairs, the proportion of trait variance explained by quadratic effects is comparable to additive effects, with five pairs having a ratio >1. Our method enables the detailed investigation of epistasis on a large scale, offering new insights into its role and importance.

Adaptive Kernel by Layer-wise Convolution

Convolutional Neural Networks (CNN) have demonstrated outstanding performance in computer vision tasks such as image classification, detection, segmentation, and medical image analysis. Adaptive kernels have been successfully used to gain better performance in CNN-based variants. In general, the optimizer updates the weights of the kernel. Recent research suggests that applying a deterministic adaptive kernel after a convolution operation can help a CNN to gain better generalization. However, how to generate the weights of the deterministic adaptive kernel is still a field of active research. To answer this question, we propose an adaptive kernel method that utilizes convoluted data of a layer to construct a set of dynamic Gaussian kernels. Then we perform the convolution operation on the convoluted data and a randomly chosen Gaussian kernel from the set. To validate the proposed adaptive kernel method, we use eighteen different CNN variants and three different datasets (CIFAR10, CIFAR100, and SVHN) on the image classification task. Our method can be applied to any CNN variant as a plug-and-play, and it does not introduce any trainable parameter to the network. We also provide a detailed analysis of the impact of our proposed adaptive kernel method.

Home Range of the Caspian Whipsnake Dolichophis caspius (Gmelin, 1789) in a Threatened Peri-Urban Population.

Semi-natural environments within cities can provide habitats for vulnerable reptile species. Better understanding of their habitat use and home range sizes is important for their conservation. We investigated the spatial ecology of Caspian whipsnakes (Dolicophis caspius) in a peri-urban habitat in Budapest, Hungary. We used radiotelemetry to track five adult snakes and analyzed their microhabitat preferences, home range sizes and daily movements. The Caspian whipsnakes intensively utilized areas covered with woody vegetation, with a high density of hibernacula. The tracked snakes used an area of 40.15 ha during the activity period from spring to autumn, but for the winter, they withdrew to a central area of 1.75 ha, abundant in hibernacula. During the activity period the individual home range sizes varied between 6.1 and 15.5 ha, estimated using the minimum convex polygon (MCP); however, for the entire datasets of the individuals, the adaptive kernel method gave the highest mean (13.8 ha), while the LoCoH-R yielded the smallest home ranges (5.19 ha). We found that the average daily displacement for the different individuals ranged between 12.6 and 36.6 m during their main activity season. In the study area, the whipsnakes currently have enough space for foraging, but the restricted spatial distribution of hibernacula, which is mainly available in the central dry rocky forest and partly in the shrubby areas, can limit the extent of the suitable habitat. Human activities and anthropogenic disturbances, especially around hibernacula, may exert pressure on this peri-urban snake population.

A PDE-BASED ADAPTIVE KERNEL METHOD FOR SOLVING OPTIMAL FILTERING PROBLEMS

In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a target stochastic dynamical system based on partial noisy observational data. The mathematical model that we use to formulate the propagation of the state dynamics is the Fokker-Planck equation, and we introduce an operator decomposition method to efficiently solve the Fokker-Planck equation. An adaptive kernel method is introduced to adaptively construct Gaussian kernels to approximate the probability distribution of the target state. Bayesian inference is applied to incorporate the observational data into the state model simulation. Numerical experiments have been carried out to validate the performance of our kernel method.

Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model

Estimation of probability density functions (pdf) is considered an essential part of statistical modelling. Heteroskedasticity and outliers are the problems that make data analysis harder. The Cauchy mixture model helps us to cover both of them. This paper studies five different significant types of non-parametric multivariate density estimation techniques algorithmically and empirically. At the same time, we do not make assumptions about the origin of data from any known parametric families of distribution. The method of the inversion formula is made when the cluster of noise is involved in the general mixture model. The effectiveness of the method is demonstrated through a simulation study. The relationship between the accuracy of evaluation and complicated multidimensional Cauchy mixture models (CMM) is analyzed using the Monte Carlo method. For larger dimensions (d ~ 5) and small samples (n ~ 50), the adaptive kernel method is recommended. If the sample is n ~ 100, it is recommended to use a modified inversion formula (MIDE). It is better for larger samples with overlapping distributions to use a semi-parametric kernel estimation and more isolated distribution-modified inversion methods. For the mean absolute percentage error, it is recommended to use a semi-parametric kernel estimation when the sample has overlapping distributions. In the smaller dimensions (d = 2) and a sample is with overlapping distributions, it is recommended to use the semi-parametric kernel method (SKDE) and for isolated distributions, it is recommended to use modified inversion formula (MIDE). The inversion formula algorithm shows that with noise cluster, the results of the inversion formula improved significantly.

Local Linear Forests

Random forests are a powerful method for nonparametric regression, but are limited in their ability to fit smooth signals. Taking the perspective of random forests as an adaptive kernel method, we pair the forest kernel with a local linear regression adjustment to better capture smoothness. The resulting procedure, local linear forests, enables us to improve on asymptotic rates of convergence for random forests with smooth signals, and provides substantial gains in accuracy on both real and simulated data. We prove a central limit theorem valid under regularity conditions on the forest and smoothness constraints, and propose a computationally efficient construction for confidence intervals. Moving to a causal inference application, we discuss the merits of local regression adjustments for heterogeneous treatment effect estimation, and give an example on a dataset exploring the effect word choice has on attitudes to the social safety net. Last, we include simulation results on real and generated data. A software implementation is available in the R package grf. Supplementary materials for this article are available online.

Home range and foraging habitat preference of Scopoli's shearwater Calonectris diomedea during the early chick‐rearing phase in the eastern Mediterranean

Pelagic seabirds that breed colonially are central‐place foragers; their spatial distribution is restricted to marine areas around their colonies during the chick‐rearing period, when attendance and food provision to their chicks has to be intense. In this study we analyzed the foraging trips of 11 Scopoli's shearwater Calonectris diomedea breeders that were tagged with GPS data loggers during 2014 in oligotrophic waters (Ionian Sea, western Greece), and assessed the range and oceanographic parameters of their foraging habitat. Contrary to previous findings suggesting a varying foraging strategy depending on the breeding stage, the tracked shearwaters made short trips, less than 4 days long, in the vicinity of the colony. By applying the Adaptive Kernel method, their 50% and 95% foraging range was estimated at 6871 km2 and 23 014 km2 respectively. In addition, generalized additive models showed that sea surface temperature (<25.5°C), minimum distance from the colony (<100 km), fishing pressure index from small scale fisheries (medium values) along with a two‐dimensional soap film smoother for space (easting, northing) were the most significant factors affecting at‐sea distribution of this marine top predator during the early chick‐rearing period (i.e. 99.9% of the final model deviance). Our study will contribute to the revision of the boundaries of the local Special Protection Area (SPA) of Strofades. It will also address the implementation of specific conservation measures for the species at regional and national scale, and the development of a management plan for the protection of the study area.

Maximum Correntropy Criterion Kalman Filter for α-Jerk Tracking Model with Non-Gaussian Noise

As one of the most critical issues for target track, α -jerk model is an effective maneuver target track model. Non-Gaussian noises always exist in the track process, which usually lead to inconsistency and divergence of the track filter. A novel Kalman filter is derived and applied on α -jerk tracking model to handle non-Gaussian noise. The weighted least square solution is presented and the standard Kalman filter is deduced firstly. A novel Kalman filter with the weighted least square based on the maximum correntropy criterion is deduced. The robustness of the maximum correntropy criterion is also analyzed with the influence function and compared with the Huber-based filter, and, moreover, the kernel size of Gaussian kernel plays an important role in the filter algorithm. A new adaptive kernel method is proposed in this paper to adjust the parameter in real time. Finally, simulation results indicate the validity and the efficiency of the proposed filter. The comparison study shows that the proposed filter can significantly reduce the noise influence for α -jerk model.

Wolf (<i>Canis lupus</i>) Winter Density and Territory Size in a Low Biomass Moose (<i>Alces alces</i>) System

We investigated the winter density and territory size of wolves ( Canis lupus ) on the Yukon Flats, Alaska, where moose ( Alces alces ) was the sole ungulate prey, occurring at a low density and representing a biomass of ungulate food lower than previously studied in North America. Using locations (GPS coordinates) from collars deployed on seven wolves, we estimated territory sizes with adaptive kernel and minimum convex polygon methods. We then estimated wolf density from a population area defined by these territory sizes and counts of wolves in five marked packs. From November 2009 to April 2010, we obtained 6263 GPS locations. Pack size ranged from two to 10 wolves, with average size of 5.0 in November 2009 and 4.8 in March 2010. Average winter territory size for five packs was 1433 km2 with the 95% adaptive kernel method and 1608 km2 with the minimum convex polygon method. Density (wolves/1000 km2) was 3.6 in November and 3.4 in March with the 95% adaptive kernel method and 3.4 in both November and March with the minimum convex polygon method. Territories were large and estimates produced by the two methods differed by 11%. Densities were low, and the two analysis methods yielded densities that differed from each other by 3% to 6%. Low wolf density corresponded with low biomass of ungulate food, suggesting that moose availability on the Yukon Flats likely limited wolf density.

Fault diagnosis of wind turbine planetary gearbox under nonstationary conditions via adaptive optimal kernel time–frequency analysis

Planetary gearboxes play an important role in wind turbine (WT) drivetrains. WTs usually work under time-varying running conditions due to the volatile wind conditions. The planetary gearbox vibration signals in such an environment are hence highly nonstationary. Conventional spectral analysis and demodulation analysis methods are unable to identify the characteristic frequency of gear fault from such nonstationary signals. As such, this paper presents a time–frequency analysis methods to reveal the constituent frequency components of nonstationary signals and their time-varying features for WT planetary gearbox monitoring. More specifically, we exploit the adaptive optimal kernel (AOK) method for this challenging application because of its fine time–frequency resolution and cross-term free nature, as demonstrated by our simulation analysis. In this study, the AOK method has been applied to identify the time-varying characteristic frequencies of gear fault or to extract different levels of impulses induced by gear faults from lab WT experimental signals and in-situ WT signals under time-varying running conditions. We have demonstrated that the AOK is effective diagnosis of: (a) both the local damage (a single chipped tooth) and distributed faults (wear of all teeth), (b) both sun gear and planet gear faults, and (c) faults with very weak signature (e.g., the sun gear fault at the low speed stage of a WT planetary gearbox).

Kernel Density Estimators for Gaussian Mixture Models

The problem of nonparametric estimation of probability density function is considered. The performance of kernel estimators based on various common kernels and a new kernel K (see (14)) with both fixed and adaptive smoothing bandwidth is compared in terms of the symmetric mean absolute percentage error using the Monte Carlo method. The kernel K is everywhere positive but has lighter tails than the Gaussian density. Gaussian mixture models from a collection introduced by Marron and Wand (1992) are taken for Monte Carlo simulations. The adaptive kernel method outperforms the smoothing with a fixed bandwidth in the majority of models. The kernel K shows better performance for Gaussian mixtures with considerably overlapping components and multiple peaks (double claw distribution).

A novel online adaptive kernel method with kernel centers determined by a support vector regression approach

The optimality of the kernel number and kernel centers plays a significant role in determining the approximation power of nearly all kernel methods. However, the process of choosing optimal kernels is always formulated as a global optimization task, which is hard to accomplish. Recently, an improved algorithm called recursive reduced least squares support vector regression (IRR-LSSVR) was proposed for establishing a global nonparametric offline model. IRR-LSSVR demonstrates a significant advantage in choosing representing support vectors compared with others. Inspired by the IRR-LSSVR, a new online adaptive parametric kernel method called Weights Varying Least Squares Support Vector Regression (WV-LSSVR) is proposed in this paper using the same type of kernels and the same centers as those used in the IRR-LSSVR. Furthermore, inspired by the multikernel semiparametric support vector regression, the effect of the kernel extension is investigated in a recursive regression framework, and a recursive kernel method called Gaussian Process Kernel Least Squares Support Vector Regression (GPK-LSSVR) is proposed using a compound kernel type which is recommended for Gaussian process regression. Numerical experiments on benchmark data sets confirm the validity and effectiveness of the presented algorithms. The WV-LSSVR algorithm shows higher approximation accuracy than the recursive parametric kernel method using the centers calculated by the k-means clustering approach. The extended recursive kernel method (i.e. GPK-LSSVR) has not shown any advantage in terms of global approximation accuracy when validating the test data set without real-time updates, but it can increase modeling accuracy if real-time identification is involved.

Defining a novel k-nearest neighbours approach to assess the applicability domain of a QSAR model for reliable predictions

BackgroundWith the growing popularity of using QSAR predictions towards regulatory purposes, such predictive models are now required to be strictly validated, an essential feature of which is to have the model’s Applicability Domain (AD) defined clearly. Although in recent years several different approaches have been proposed to address this goal, no optimal approach to define the model’s AD has yet been recognized.ResultsThis study proposes a novel descriptor-based AD method which accounts for the data distribution and exploits k-Nearest Neighbours (kNN) principle to derive a heuristic decision rule. The proposed method is a three-stage procedure to address several key aspects relevant in judging the reliability of QSAR predictions. Inspired from the adaptive kernel method for probability density function estimation, the first stage of the approach defines a pattern of thresholds corresponding to the various training samples and these thresholds are later used to derive the decision rule. Criterion deciding if a given test sample will be retained within the AD is defined in the second stage of the approach. Finally, the last stage tries reflecting upon the reliability in derived results taking model statistics and prediction error into account.ConclusionsThe proposed approach addressed a novel strategy that integrated the kNN principle to define the AD of QSAR models. Relevant features that characterize the proposed AD approach include: a) adaptability to local density of samples, useful when the underlying multivariate distribution is asymmetric, with wide regions of low data density; b) unlike several kernel density estimators (KDE), effectiveness also in high-dimensional spaces; c) low sensitivity to the smoothing parameter k; and d) versatility to implement various distances measures. The results derived on a case study provided a clear understanding of how the approach works and defines the model’s AD for reliable predictions.

Multidimensional smoothing by adaptive local kernel-weighted log-likelihood: Application to long-term care insurance

We are interested in modeling the mortality of long-term care (LTC) claimants having the same level of severeness (heavy claimant). Practitioners often use empirical methods that rely heavily on expert opinions. We propose approaches not depending on an expert’s advice. We analyze the mortality as a function of both the age of occurrence of the claim and the duration of the care. LTC claimants are marked by a relatively complex mortality pattern. Hence, rather than using parametric approaches or models with expert opinions, adaptive local likelihood methods allow us to extract the information from the data more pertinently. We characterize a locally adaptive smoothing pointwise method using the intersection of confidence intervals rule, as well as a global method using local bandwidth correction factors. The latter is an extension of the adaptive kernel method proposed by Gavin et al. (1995) to likelihood techniques. We vary the amount of smoothing in a location-dependent manner and allow adjustments based on the reliability of the data. Tests, and single indices summarizing the lifetime probability distribution are used to compare the graduated series obtained by adaptive local kernel-weighted log-likelihoods to p-spline and local likelihood models.

Information‐theoretic model selection affects home‐range estimation and habitat preference inference: a case study of male Reeves’s Pheasants Syrmaticus reevesii

Reeves’s Pheasant Syrmaticus reevesii is a vulnerable forest bird inhabiting broadleaved habitats dominated by oaks Quercus spp. in central China. Identifying home‐ranges and habitat associations is important for understanding the biology of this species and developing effective management and conservation plans. We used information‐theoretic criteria to evaluate the relative performance of four parametric (exponential power, one‐mode bivariate normal, two‐mode bivariate normal and two‐mode bivariate circle) and two non‐parametric models (adaptive and fixed kernel) for estimating home‐ranges and habitat associations of Reeves’s Pheasants. For parametric models, Akaike’s information criterion (AICc) and the likelihood cross‐validation criterion (CVC) were relatively consistent in ranking the bivariate exponential power model the least acceptable, whereas the two‐mode bivariate models performed better. The CVC suggested that kernel models, particularly the adaptive kernel, performed best among all six models evaluated. The average core area and 95% contour area based on the model with greatest support were 6.1 and 54.9 ha, respectively, and were larger than those estimated from other models. The discrepancy in estimates between models with highest and the lowest support decreased as the contour size increased; however, home‐range shapes differed between models. Minimum convex polygons that removed 5% of extreme data points (MCP95) were roughly half the size of home‐ranges based on kernel models. Estimates of home‐range and model evaluation were not affected by sample size (> 50 observations for each bird). Inference about habitat preference based on composition analysis and home‐range overlap varied between models. That with strongest support suggested that Reeves’s Pheasants selected mature fir and mixed forest, avoided farmland, and had mean among‐individual home‐range overlaps of 20%. We recommend non‐parametric methods, particularly the adaptive kernel method, for estimating home‐ranges and core areas for species with complex multi‐polar habitat preferences in heterogeneous environments with large habitat patches. However, we caution against the traditional convenience of using a single model to estimate home‐ranges and recommend exploration of multiple models for describing and understanding the ecological processes underlying space use and habitat associations.

Studying the dynamical properties of 20 nearby galaxy clusters

Using SDSS-DR7, we construct a sample of 42382 galaxies with redshifts in the region of 20 galaxy clusters. Using two successive iterative methods, the adaptive kernel method and the spherical infall model, we obtained 3396 galaxies as members belonging to the studied sample. The 2D projected map for the distribution of the clusters members is introduced using the 2D adaptive kernel method to get the clusters centers. The cumulative surface number density profile for each cluster is fitted well with the generalized King model. The core radii of the clusters' sample are found to vary from 0.18 Mpc $\mbox{h}^{-1}$ (A1459) to 0.47 Mpc $\mbox{h}^{-1}$ (A2670) with mean value of 0.295 Mpc $\mbox{h}^{-1}$. The infall velocity profile is determined using two different models, Yahil approximation and Praton model. Yahil approximation is matched with the distribution of galaxies only in the outskirts (infall regions) of many clusters of the sample, while it is not matched with the distribution within the inner core of the clusters. Both Yahil approximation and Praton model are matched together in the infall region for about 9 clusters in the sample but they are completely unmatched for the clusters characterized by high central density. For these cluster, Yahil approximation is not matched with the distribution of galaxies, while Praton model can describe well the infall pattern of such clusters.

Reliability Method for Strain-Based Fatigue Life Design under Random Loading

A fatigue reliability method has been developed for strain-based fatigue under random loading. The adaptive kernel method is employed to establish the probabilistic random stress model. The probability-based cyclic stress-strain curve considering entire material constants as random variable is proposed. The probabilistic model of cyclic strain life relations is established by introducing a standard normal distribution. Based on these probabilistic models, the random characteristic value of fatigue life is obtained by Monte Carlo method. According to the mean value first order second moment reliability method, the probability of failure can be given out. The example of application is demonstrated.

Distribution and home range of bottlenose dolphins (Tursiops truncatus) off Veracruz, Mexico

With the goal of gathering ecological data to develop future cetacean management and conservation plans, the distribution, home range, and residency of bottlenose dolphins (Tursiops truncatus) were studied in the central-north Mexican Gulf of Mexico. Between July 2005 and June 2008, 59 boat surveys were carried out for a total of 313 h of effort at sea. During these surveys, 471 individuals were observed in 88 different groups. Photographs of naturally marked animals resulted in 275 different individuals photo-identified. Their distribution was homogeneous throughout the study area at a mean distance from the coast of 2.5 km (SD = 2.9, n = 471) and depths less than 20 m. Of the total of dolphins identified, 202 (73%) had a low sighting rate and were considered transients, whereas 34 individuals (12%) had medium and high sighting rates and were considered resident animals. At the population level, home range estimates calculated using the minimum convex polygon method showed a mean of 2771 ± 1116 km2. Using the adaptive kernel method, the mean size of home range was 1199 ± 143 km2, with five core areas identified. These areas decreased in size during the rainy season because dolphins remained close to the river plumes. At individual level, the mean home range was 129.2 km2 (n = 66), concurring with other reports from the Gulf of Mexico (Texas and Florida) in spite of habitat differences. The main component determining the size of the home range was the presence of rivers, rather than the geomorphology of the coast.

Home range and habitat use by the roadside hawk, Rupornis magnirostris (Gmelin, 1788) (Aves: Falcaniformes) in southeastern Brazil

Although most raptor species are found mainly in the tropics, information on their home range and spatial requirements in the Neotropics is still scarce. In this study, we used radio telemetry to evaluate the home range and the habitat use and selection of five Roadside hawks, Rupornis magnirostris (Gmelin, 1788) in a heterogeneous landscape in southeastern Brazil. The average home range size calculated using the adaptive kernel method (95% isopleth) was 126.1 ha (47.4–266.7 ha), but using the minimum convex polygon method (95% isopleth) it was 143.54 ha (32.6–382.3 ha). The roadside hawk explored a wide variety of habitats, most of them opportunistically, as suggested in the literature. Despite this, habitat quality could influence home range size and promote habitat selection. The observation of habitat use as expected, as well as the relatively small home range size, could be related to the generalist/opportunistic behaviour of the roadside hawk.

Ecological Relationships of Bobcats (Lynx rufus) in the Chihuahuan Desert of New Mexico

Abstract I studied ecological relationships of 10 bobcats (Lynx rufus; 4 males, 6 females) from an unexploited population in the Chihuahuan Desert of southern New Mexico during 2004–2008. Using the 95% adaptive-kernel method, I estimated annual size of home ranges to be 12,887 ha for males and 2,847 ha for females. Average activity during nighttime and daytime was 80.6 and 18.8%, respectively. Desert cottontails (Sylvilagus audubonii) were the most common prey in scats. Annual rate of survival was 0.875 for males and 0.917 for females. Average weight of males and females was 12.6 and 9.0 kg, respectively. Two bobcats tested positive for toxoplasmosis. Compared to other areas, bobcats in my study area were heavier, there was more contrast between daytime and nighttime levels of activity, and males had larger home ranges. Rate of survival was similar to other unexploited populations.