Kernel Fitting Research Articles

Task-Similarity is a Crucial Factor for Few-Shot Meta-Learning of Structure-Activity Relationships.

Machine learning models support computer-aided molecular design and compound optimization. However, the initial phases of drug discovery often face a scarcity of training data for these models. Meta-learning has emerged as a potentially promising strategy, harnessing the wealth of structure-activity data available for known targets to facilitate efficient few-shot model training for the specific target of interest. In this study, we assessed the effectiveness of two different meta-learning methods, namely model-agnostic meta-learning (MAML) and adaptive deep kernel fitting (ADKF), specifically in the regression setting. We investigated how factors such as dataset size and the similarity of training tasks impact predictability. The results indicate that ADKF significantly outperformed both MAML and a single-task baseline model on the inhibition data. However, the performance of ADKF varied across different test tasks. Our findings suggest that considerable enhancements in performance can be anticipated primarily when the task of interest is similar to the tasks incorporated in the meta-learning process.

Rapid calculation of atmospheric molecular absorption characteristics in the terahertz band based on wideband K-distribution method

This paper focuses on rapidly calculating atmospheric molecular absorption properties in the 0.3–30 THz frequency range of terahertz waves. It conducts research related to spectral radiation models and fast computation model databases. Based on the latest version of the High-resolution transmission molecular absorption database-2020, in conjunction with the line-by-line (LBL) spectral radiative calculation method, the spectral absorption characteristics of nine atmospheric molecules (H2O, CO2, O3, NO, N2O, NO2, NH3, SO2, CH4) are analyzed. The relative contributions of the eight other gas molecules absorption abilities in the terahertz range are examined, with H2O molecule serving as the reference. Taking into account the non-gray absorption properties of atmospheric molecules and the need for fast computation, this study divides the frequency range of 0.3–30 THz into 24 calculation bands based on the spectral absorption distribution characteristics of atmospheric molecules. Utilizing LBL calculations with a resolution of 0.01 cm−1, a non-correlated wideband K-distribution model (WBK) is developed, which achieves nearly the same computational accuracy as LBL. Furthermore, the WBK radiation calculation model is validated under both uniform and non-uniform atmospheric conditions based on earth atmospheric environmental parameters. An exponential kernel fitting coefficient table for the rapid calculation of atmospheric molecular absorption coefficients is established based on the WBK radiation calculation model to improve computational efficiency further. This database enables fast calculation of 24 broadband absorption coefficients (corresponding to 7 Gaussian integration points) within 0–100 km altitude in earth atmosphere.

An ex-ante method to verify commercial U.S. nuclear power plant decommissioning cost estimates

There are billions of dollars at stake in the US nuclear power plant decommissioning market. Approximately 92 nuclear power plants are still operating but will come offline and need to be decommissioned over the next few decades. The Nuclear Regulatory Commission (NRC) mandates that the operators of these plants set money aside in segregated funds to finance decommissioning work. However, it is hard for external stakeholders to verify the cost estimations, which ultimately determine how much operators are required to save. In this paper, we develop a method to validate the existing cost models and calculate a contingency empirically for these models. We extend Reference Class Forecasting methods using adaptive kernel fitting and the Wilks’ formula. Based on this method, and assuming a social tolerance for potential cost overruns of 20%, we calculate a new contingency of 48% of the estimated radiological decommissioning cost. After a “stress test” of the current decommissioning trust funds of operating reactor sites, we find that 48% of reactors have sufficient funding—in many cases substantially more than required—and could therefore finance the potential scale of overrun. However, we find that 28 plants would fall short on average $211 million. Still, overruns at every plant are not a foregone conclusion because—while overruns are probable, based on past experience, the actual scale and frequency is not known. Nevertheless, our results add further evidence to the mounting call for the NRC to revise its cost models in light of new information.

Optimization of hyperparameters for SMS reconstruction

PurposeSimultaneous multi-slice (SMS) imaging accelerates MRI data acquisition by exciting multiple image slices with a single radiofrequency pulse. Overlapping slices encoded in acquired signal are separated using a mathematical model, which requires estimation of image reconstruction kernels using calibration data. Several parameters used in SMS reconstruction impact the quality and fidelity of final images. Therefore, finding an optimal set of reconstruction parameters is critical to ensure that accelerated acquisition does not significantly degrade resulting image quality. MethodsGradient-echo echo planar imaging data were acquired with a range of SMS acceleration factors from a cohort of five volunteers with no known neurological pathology. Images were collected using two available phased-array head coils (a 48-channel array and a reduced diameter 32-channel array) that support SMS. Data from these coils were identically reconstructed offline using a range of coil compression factors and reconstruction kernel parameters. A hybrid space (k-x), externally-calibrated coil-by-coil slice unaliasing approach was used for image reconstruction. The image quality of the resulting reconstructed SMS images was assessed by evaluating correlations with identical echo-planar reference data acquired without SMS. A finger tapping functional MRI (fMRI) experiment was also performed and group analysis results were compared between data sets reconstructed with different coil compression levels. ResultsBetween the two RF coils tested in this study, the 32-channel coil with smaller dimensions clearly outperformed the larger 48-channel coil in our experiments. Generally, a large calibration region (144–192 samples) and small kernel sizes (2–4 samples) in ky direction improved image quality. Use of regularization in the kernel fitting procedure had a notable impact on the fidelity of reconstructed images and a regularization value 0.0001 provided good image quality. With optimal selection of other hyperparameters in the hybrid space SMS unaliasing algorithm, coil compression caused small reduction in correlation between single-band and SMS unaliased images. Similarly, group analysis of fMRI results did not show a significant influence of coil compression on resulting image quality. ConclusionsThis study demonstrated that the hyperparameters used in SMS reconstruction need to be fine-tuned once the experimental factors such as the RF receive coil and SMS factor have been determined. A cursory evaluation of SMS reconstruction hyperparameter values is therefore recommended before conducting a full-scale quantitative study using SMS technologies.

PyGAPS: a Python-based framework for adsorption isotherm processing and material characterisation

Material characterisation through adsorption is a widely-used laboratory technique. The isotherms obtained through volumetric or gravimetric experiments impart insight through their features but can also be analysed to determine material characteristics such as specific surface area, pore size distribution, surface energetics, or used for predicting mixture adsorption. The pyGAPS (Python General Adsorption Processing Suite) framework was developed to address the need for high-throughput processing of such adsorption data, independent of the data origin, while also being capable of presenting individual results in a user-friendly manner. It contains many common characterisation methods such as: Brunauer–Emmett–Teller and Langmuir surface area, t and αs plots, pore size distribution calculations (Barrett–Joyner–Halenda, Dollimore–Heal, Horvath–Kawazoe, DFT/NLDFT kernel fitting), isosteric enthalpy calculations, ideal adsorbed solution theory calculations, isotherm modelling and more, as well as the ability to import and store data from Excel, CSV, JSON and SQLite databases. In this work, a description of the capabilities of pyGAPS is presented. The code is then be used in two case studies: a routine characterisation of a UiO-66(Zr) sample and in the processing of an adsorption dataset of a commercial carbon (Takeda 5A) for applications in gas separation.

Illumination-Robust Subpixel Fourier-Based Image Correlation Methods Based on Phase Congruency

The Fourier-based image correlation technique has been widely concerned due to its accuracy, efficiency, and robustness to image contrast and brightness. Accordingly, a variety of subpixel methods have been proposed. However, the detailed subpixel-level influence of the complicated radiometric variations has yet to be investigated, and few corresponding improvements have been made. This paper presents a novel illumination-robust subpixel Fourier-based image correlation method based on phase congruency. Both the magnitude and orientation information of the phase congruency features are adopted to construct a structural image representation. The image representation is then embedded into the correlation scheme of the subpixel methods, either by linear phase estimation in the frequency domain or by kernel fitting in the spatial domain, achieving two improved subpixel methods. The proposed methods integrate the advantages of the structural image representation and the original correlation scheme, and make full use of both global and local phase information to achieve illumination-robust correlation. Experiments undertaken with both simulated and real radiometric differences were carried out with ground-truth subpixel shifts. The performances of the proposed methods and the other state-of-the-art subpixel Fourier-based correlation methods were evaluated and compared. The experimental results indicate that the proposed methods outperform the other methods in the presence of diverse radiometric variations, in both accuracy and robustness.

A partial-robust-ridge-based regression model with fuzzy predictors-responses

This paper extends the conventional semi-parametric partial linear regression model with fuzzy predictors and fuzzy response in cases where 1—outliers occur in data set, 2—multicollinearity exists in predictors. For this purpose, the classical kernel fitting method is first extended for estimating unknown fuzzy smooth function. Then, inspired by the conventional local linear smoothing method, a kernel-based weighted criterion is suggested for determining the exact coefficients on the basis of ridge methodology. Some common goodness-of-fit criteria are also used to examine the performance of the proposed method. The effectiveness of the proposed method is then illustrated through two numerical examples including a simulation study. The proposed method is also compared with some common fuzzy multiple regression models with fuzzy predictors and fuzzy responses. The numerical results clearly indicate that 1—the proposed method is not sensitive to the outliers, 2—the proposed method provides sufficiently accurate results in cases where multicollinearity happens among predictors and 3—comparing to existing fuzzy multiple regressions, the proposed model provides more efficient predictions. • A fuzzy semi-parametric regression model is proposed when multicollinearity and/or outliers occur. • The fuzzy model contains the fuzzy predictors-responses. • The ridge methodology and a novel robust method are applied to evaluate crisp coefficients. • The method is compared with several methods using various goodness-of-fit-measures.

Encoded Semantic Tree for Automatic User Profiling Applied to Personalized Video Summarization

We propose an innovative method of automatic video summary generation with personal adaptations. User interests are mined from their personal image collections. To reduce the semantic gap, we propose to extract visual representations based on a novel semantic tree (SeTree). A SeTree is a hierarchy that captures the conceptual relationships between the visual scenes in a codebook. This idea builds upon the observation that such semantic connections among the elements have been overlooked in the previous work. To construct the SeTree , we adopt a normalized graph cut clustering algorithm by conjunctively exploiting visual features, textual information, and social user-image connections. Using this technique, we obtain an 8.1% improvement of normalized discounted cumulative gain in personalized video segments ranking compared with existing methods. Furthermore, to promote the interesting parts of a video, we extract a space–time saliency map and estimate the attractiveness of segments by kernel fitting and matching. A linear function is utilized to combine the two factors, based on which the playback rate of a video is adapted to generate the summary. We play the less important segments in a fast-forward mode to keep users updated with the context. Subjective experiments were conducted which showed that our proposed video summarization approach outperformed the state-of-the-art techniques by 6.2%.

A Segmentation Kernel Fitting Technique to Circumvent Extreme Deviation from Exponentially Descent Tail Distribution

A Segmentation Kernel Fitting Technique to Circumvent Extreme Deviation from Exponentially Descent Tail Distribution

Simultaneous multislice magnetic resonance fingerprinting (SMS-MRF) with direct-spiral slice-GRAPPA (ds-SG) reconstruction.

To develop a reconstruction method to improve SMS-MRF, in which slice acceleration is used in conjunction with highly undersampled in-plane acceleration to speed up MRF acquisition. In this work two methods are employed to efficiently perform the simultaneous multislice magnetic resonance fingerprinting (SMS-MRF) data acquisition and the direct-spiral slice-GRAPPA (ds-SG) reconstruction. First, the lengthy training data acquisition is shortened by employing the through-time/through-k-space approach, in which similar k-space locations within and across spiral interleaves are grouped and are associated with a single set of kernel. Second, inversion recovery preparation (IR prepped), variable flip angle (FA), and repetition time (TR) are used for the acquisition of the training data, to increase signal variation and to improve the conditioning of the kernel fitting. The grouping of k-space locations enables a large reduction in the number of kernels required, and the IR-prepped training data with variable FA and TR provide improved ds-SG kernels and reconstruction performance. With direct-spiral slice-GRAPPA, tissue parameter maps comparable to that of conventional MRF were obtained at multiband (MB) = 3 acceleration using t-blipped SMS-MRF acquisition with 32-channel head coil at 3 Tesla (T). The proposed reconstruction scheme allows MB = 3 accelerated SMS-MRF imaging with high-quality T1 , T2 , and off-resonance maps, and can be used to significantly shorten MRF acquisition and aid in its adoption in neuro-scientific and clinical settings. Magn Reson Med 77:1966-1974, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Model averaging for genome-enabled prediction with reproducing kernel Hilbert spaces: a case study with pig litter size and wheat yield

Predictive ability of yet-to-be observed litter size (pig) grain yield (wheat) records of several reproducing kernel Hilbert spaces (RKHS) regression models combining different number of Gaussian or t kernels was evaluated. Predictive performance was assessed as the average (over 50 replicates) predictive correlation in the testing set. Predictions from these models were combined using three different types of model averaging: (i) mean of predicted phenotypes obtained in each model, (ii) weighted average using mean squared error as weight or (iii) using the marginal likelihood as weight. (ii) and (iii) were obtained in a validation set with 5% of the data. Phenotypes consisted of 2598, 1604 and 1879 average litter size records from three commercial pig lines and wheat grain yield of 599 lines evaluated in four macro-environments. SNPs from the PorcineSNP60 BeadChip and 1447 DArT markers were used as predictors for the pig and wheat data analyses, respectively. Gaussian and univariate t kernels led to same predictive performance. Multikernel RKHS regression models overcame shortcomings of single kernel models (increasing the predictive correlation of RKHS models by 0.05 where 3 Gaussian or t kernels were fitted in the RKHS models simultaneously). None of the proposed averaging strategies improved the predictive correlations attained with single models using multiple kernel fitting.

Southeastern United States summer rainfall framework and its implication for seasonal prediction

A new rainfall framework is constructed to describe the complex probability distribution of southeastern United States (SE US) summer (June–July–August) rainfall, which cannot be well represented by traditional kernel fitting methods. The new framework is based on the configuration of a three-cluster finite normal mixture model and is realized by Bayesian inference and a Markov Chain Monte Carlo (MCMC) algorithm. The three rainfall clusters reflect the probability distribution of light, moderate, and heavy rainfall in summer, and are linked to different climate factors. The variation of light rainfall intensity is likely associated with the combined effects of La Niña and the tri-pole sea surface temperature anomaly (SSTA) over the North Atlantic. Heavy rainfall concurs with a ‘horseshoe-like’ SSTA over the North Atlantic. In contrast, moderate rainfall is less correlated with the SSTA and likely caused by atmospheric internal dynamics. Rainfall characteristics and their linkages with SSTAs help improve seasonal predictions of regional climate. Such a new framework has an important implication in understanding the response of regional hydrology to climate variability and climate change; and our study suggest that it can be extended to other regions and seasons with similar climate.

Assessment of spatial discordance of primary and effective seed dispersal of European beech (Fagus sylvatica L.) by ecological and genetic methods

Spatial discordance between primary and effective dispersal in plant populations indicates that postdispersal processes erase the seed rain signal in recruitment patterns. Five different models were used to test the spatial concordance of the primary and effective dispersal patterns in a European beech (Fagus sylvatica) population from central Spain. An ecological method was based on classical inverse modelling (SSS), using the number of seed/seedlings as input data. Genetic models were based on direct kernel fitting of mother-to-offspring distances estimated by a parentage analysis or were spatially explicit models based on the genotype frequencies of offspring (competing sources model and Moran-Clark's Model). A fully integrated mixed model was based on inverse modelling, but used the number of genotypes as input data (gene shadow model). The potential sources of error and limitations of each seed dispersal estimation method are discussed. The mean dispersal distances for seeds and saplings estimated with these five methods were higher than those obtained by previous estimations for European beech forests. All the methods show strong discordance between primary and effective dispersal kernel parameters, and for dispersal directionality. While seed rain was released mostly under the canopy, saplings were established far from mother trees. This discordant pattern may be the result of the action of secondary dispersal by animals or density-dependent effects; that is, the Janzen-Connell effect.

Particle Based Smoothed Marginal MAP Estimation for General State Space Models

We consider the smoothing problem for a general state space system using sequential Monte Carlo (SMC) methods. The marginal smoother is assumed to be available in the form of weighted random particles from the SMC output. New algorithms are developed to extract the smoothed marginal maximum a posteriori (MAP) estimate of the state from the existing marginal particle smoother. Our method does not need any kernel fitting to obtain the posterior density from the particle smoother. The proposed estimator is then successfully applied to find the unknown initial state of a dynamical system and to address the issue of parameter estimation problem in state space models.

Marked point pattern analysis on genetic paternity data for uncertainty assessment of pollen dispersal kernels

Summary 1. Obtaining accurate estimates of the pollen dispersal kernel is central to a wide range of ecological studies. Assessing their statistical uncertainty is as important, but rarely considered. 2. We developed a new method of marked point processes for nonparametric estimation of dispersal kernels based on data of genetic paternity analysis that does not require assumptions about the shape of the dispersal distribution. This allows for construction of Monte Carlo simulation envelopes of a given null model, such as random mating, and for uncertainty assessment of the observed dispersal kernel. 3. We applied our method to characterize spatial patterns of pollen flow in an isolated population of Populus nigra in Central Germany and to assess the associated statistical uncertainty in estimates of within-population dispersal kernels. We compared our nonparametric within-population kernel estimate with that of established methods of parametric kernel fitting including: (i) a general mating model, (ii) a simplified mating model using categorical paternity data and (iii) least-squares regression of the nonparametric kernel estimate. 4. Our analysis showed a significant departure from the random mating null model. We found a highly significant excess of mating events at short distances ( 2000 m), indicating large uncertainty on the detailed shape of the kernel’s tail. 5. Results of the point pattern analysis were consistent with kernel fits using published maximum-likelihood mating models. Model selection revealed that two-component pollen dispersal kernels were the most parsimonious functions. 6. Synthesis. Our approach of nonparametric kernel estimation could be widely applied for dispersal data from genetic paternity analysis and complements traditional kernel estimation by providing a nonparametric kernel estimate and effective methods for an uncertainty assessment in kernel estimation. Our results indicate that statistical model fitting may substantially underestimate the uncertainty in kernel estimation, especially at larger distances.

Niche overlap estimates based on quantitative functional traits: a new family of non-parametric indices

The concept of niche overlap appears in studies of the mechanisms of the maintenance of species diversity, in searches for assembly rules, and in estimation of within-community species redundancy. For plant traits measured on a continuous scale, existing indices are inadequate because they split the scale into a number of categories thus losing information. An index is easy to construct if we assume a normal distribution for each trait within a species, but this assumption is rarely true. We extend and apply an index, NO(K), which is based on kernel density functions, and can therefore work with distributions of any shape without prior assumptions. For cases where the ecologist wishes to downweight traits that are inter-correlated, we offer a variant that does this: NO(Kw). From either of these indices, an index of the mean niche overlap in a community can be calculated: NO(K,community) and NO(Kw,community). For all these indices, the variance can be calculated and formulae for this are given. To give examples of the new indices in use, we apply them to a coastal fish dataset and a sand-dune plant dataset. The former exhibits considerable non-normality, emphasising the need for kernel-based indices. Accordingly, there was a considerable difference in index values, with those for an index based on a normal distribution being significantly higher than those from an index which, being based on kernel fitting, is not biased by an assumption for the distribution. The NO(K) values were ecologically consistent for the fish species concerned, varying from 0.02 to 0.53. The sand-dune plant data also showed a wide range of overlap values. Interestingly, the least overlap was between two graminoids, which would have been placed in the same functional group in the coarse classification often used in functional-type/ecosystem-function work.

Robust normalization of DNA chromatograms by regression for improved base-calling

The accuracy of base-calling software depends critically on the data normalization method it is using. A new regression-based method for normalizing electrophoretic DNA traces is presented. It is based on a channel-coupled exponential decay model that can track accurately the trend of dropping peak heights (the so-called signal “skyline”) even in the low SNR region of the trace. We provide the justification and formulation of the regression model as well as the analytical estimation of its parameters. The proposed skyline-based normalization scheme is not affected by the presence of artifacts, compressions, false peaks, etc. and does not depend on the dye chemistry used. We demonstrate that it can improve the interpretation of chromatograms and therefore increase base-calling accuracy when employed in the pre-processing stage of either a pattern classification type base-caller (such as the BEM presented in Pereira et al. (Discrete Appl. Math. 104(1–3) (2000) 229)) or a kernel fitting base-calling method.