Local Kernel Research Articles

Limits of determinantal processes near a tacnode

We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter e > 0. The domain has two cusps, one pointing up and one pointing down. In the limit e ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime e ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process.

Confident Predictability: Identifying reliable gene expression patterns for individualized tumor classification using a local minimax kernel algorithm

BackgroundMolecular classification of tumors can be achieved by global gene expression profiling. Most machine learning classification algorithms furnish global error rates for the entire population. A few algorithms provide an estimate of probability of malignancy for each queried patient but the degree of accuracy of these estimates is unknown. On the other hand local minimax learning provides such probability estimates with best finite sample bounds on expected mean squared error on an individual basis for each queried patient. This allows a significant percentage of the patients to be identified as confidently predictable, a condition that ensures that the machine learning algorithm possesses an error rate below the tolerable level when applied to the confidently predictable patients.ResultsWe devise a new learning method that implements: (i) feature selection using the k-TSP algorithm and (ii) classifier construction by local minimax kernel learning. We test our method on three publicly available gene expression datasets and achieve significantly lower error rate for a substantial identifiable subset of patients. Our final classifiers are simple to interpret and they can make prediction on an individual basis with an individualized confidence level.ConclusionsPatients that were predicted confidently by the classifiers as cancer can receive immediate and appropriate treatment whilst patients that were predicted confidently as healthy will be spared from unnecessary treatment. We believe that our method can be a useful tool to translate the gene expression signatures into clinical practice for personalized medicine.

Can state-of-the-art saliency systems model infant gazing behavior in tutoring situations?

The behavior for a humanoid robot is often modeled in accordance with human behavior. Current research suggests that analyzing infant behavior as a basis for designing the robot behavior can guide us to a natural robot interface. Based on this idea many researchers support saliency systems as a bottom-up inspired way to simulate infant-like gazing behavior. In the field of saliency systems many different approaches have proposed and quantified in terms of speed, quality and other technical issues. But so far, no one compared and quantified them in terms of natural infant tutor interaction. The question we would like to address in this paper is: Can state-of-the-art saliency systems model infant gazing behavior in tutoring situations? By addressing these issues we want to take a step towards an autonomous robot system, which could be used more natural interaction experiments in future.

Local kernel canonical correlation analysis with application to virtual drug screening

Local kernel canonical correlation analysis with application to virtual drug screening

Local Kernel Feature Analysis (LKFA) for object recognition

This paper proposes a new Local Kernel Feature Analysis (LKFA) method for object recognition. LKFA captures the nonlinear local relationship in an image via kernel functions. Different from traditional kernel methods for object recognition, the proposed method does not need to reserve the training samples. LKFA is designed to extract the eigenvalue features from the Hermite matrix of a local feature representation, which we have theoretically proven its robustness to noise and perturbations. Experiment results on palmprint and face recognitions demonstrated the effectiveness of the proposed LKFA that significantly improved the performance of the local feature based object recognition method.

Detailed chemistry flamelet modeling of mixed-mode combustion in spark-assisted HCCI engines

A detailed chemistry mixed-mode flamelet model for the prediction of combustion in spark-assisted homogeneous charge compression ignition (HCCI) engines is presented in this paper. The complex phenomena of spark-channel processes (turbulent corrugation, multiple restrikes) and of early flame kernel propagation (localized flame kernel formation, non-spherical early flame shapes), both induced by spray-guided spark-ignition combustion initiation, are captured by the recently introduced SparkCIMM ignition model. In this paper, laminar burning velocities and flame thicknesses are calculated along the mean turbulent flame front, using tabulated detailed chemistry flamelet calculations to appropriately consider locally rich, highly diluted, and auto-igniting stratified mixtures. Flame extinction criterions are formulated and incorporated into an extended G-equation flame front tracking scheme. Auto-ignition processes in the unburnt mixture, controlled by the flame-induced pressure and temperature increase, are captured by a recently developed multi-zone flamelet model that accounts for detailed chemistry and effects of scalar mixing on turbulent combustion. The laminar burning velocity is shown to increase significantly as the flame propagates into the chemically reacting mixture within the first stage of auto-ignition. After the initiation of the thermal runaway, however, flame extinction occurs rapidly. These interactions of mixed-mode combustion processes are captured by the presented flamelet model. It is developed based on a time and length scale analysis, revealing a scale separation between the ignition delay of diffusion combustion and the flame time of flame propagation. The analysis of the mixture preparation process, along with the simulation of turbulent flame front propagation and its extinction, demonstrates that the prediction of combustion in spark-assisted HCCI engines requires the on hand comprehensive mixed-mode combustion model. A comparison of simulation results from this new model with data from experiments and combustion models of reduced physical complexity proofs its qualification.

Operators for transforming kernels into quasi-local kernels that improve SVM accuracy

Motivated by the crucial role that locality plays in various learning approaches, we present, in the framework of kernel machines for classification, a novel family of operators on kernels able to integrate local information into any kernel obtaining quasi-local kernels. The quasi-local kernels maintain the possibly global properties of the input kernel and they increase the kernel value as the points get closer in the feature space of the input kernel, mixing the effect of the input kernel with a kernel which is local in the feature space of the input one. If applied on a local kernel the operators introduce an additional level of locality equivalent to use a local kernel with non-stationary kernel width. The operators accept two parameters that regulate the width of the exponential influence of points in the locality-dependent component and the balancing between the feature-space local component and the input kernel. We address the choice of these parameters with a data-dependent strategy. Experiments carried out with SVM applying the operators on traditional kernel functions on a total of 43 datasets with different characteristics and application domains, achieve very good results supported by statistical significance.

Training-Free, Generic Object Detection Using Locally Adaptive Regression Kernels

We present a generic detection/localization algorithm capable of searching for a visual object of interest without training. The proposed method operates using a single example of an object of interest to find similar matches, does not require prior knowledge (learning) about objects being sought, and does not require any preprocessing step or segmentation of a target image. Our method is based on the computation of local regression kernels as descriptors from a query, which measure the likeness of a pixel to its surroundings. Salient features are extracted from said descriptors and compared against analogous features from the target image. This comparison is done using a matrix generalization of the cosine similarity measure. We illustrate optimality properties of the algorithm using a naive-Bayes framework. The algorithm yields a scalar resemblance map, indicating the likelihood of similarity between the query and all patches in the target image. By employing nonparametric significance tests and nonmaxima suppression, we detect the presence and location of objects similar to the given query. The approach is extended to account for large variations in scale and rotation. High performance is demonstrated on several challenging data sets, indicating successful detection of objects in diverse contexts and under different imaging conditions.

Denoising of brain DW-MR data by single and multiple diffusion kernels

Diffusion Weighted Magnetic Resonance Imaging is widely used to study the structure ofthe fiber pathways of white matter in the brain. However, the recovered axon orientationscan be prone to error because of the low signal to noise ratio. Spatial regularization canreduce the error, but it must be done carefully so that real spatial information is not removedand false orientations are not introduced. In this paper we investigate the advantagesof applying an anisotropic filter based on single and multiple axon bundle orientation kernels.To this end, we compute local diffusion kernels based on Diffusion Tensor and multiDiffusion Tensor models. We show the benefits of our approach to three different types ofDW-MRI data: synthetic, in vivo human, and acquired from a diffusion phantom.

Fast and Scalable Local Kernel Machines

A computationally efficient approach to local learning with kernel methods is presented. The Fast Local Kernel Support Vector Machine (FaLK-SVM) trains a set of local SVMs on redundant neighbourhoo...

Nonparametric Profile Monitoring by Mixed Effects Modeling

In some applications, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. Profile monitoring is for checking the stability of this relationship over time. Control charts for monitoring nonparametric profiles are useful when the relationship is too complicated to be described parametrically. Most existing control charts in the literature are for monitoring parametric profiles. They require the assumption that within-profile measurements are independent of each other, which is often invalid in practice. This article focuses on nonparametric profile monitoring when within-profile data are correlated. A novel control chart is suggested, which incorporates local linear kernel smoothing into the exponentially weighted moving average (EWMA) control scheme. In this method, within-profile correlation is described by a nonparametric mixed-effects model. Our proposed control chart is fast to compute and convenient to use. Numerical examples show that it works well in various cases. Some technical details are provided in an Appendix available online as supplemental materials.

Spline-Based Nonparametric Estimation of the Altimeter Sea-State Bias Correction

This letter presents a new nonparametric approach, based on spline (SP) regression, for estimating the satellite altimeter sea-state bias (SSB) correction. Model evaluation is performed with models derived from a local linear kernel (LK) smoothing, the method which is currently used to build operational altimeter SSB models. The key reasons for introducing this alternative approach for the SSB application are simplicity in accurate model generation, ease in model replication among altimeter research teams, reduced computational requirements, and its suitability for higher dimensional SSB estimation. It is shown that the SP- and LK-based SSB solutions are effectively equivalent within the data-dense portion, with an offset below 0.1 mm and a rms difference of 1.9 mm for the 2-D (wave height and wind speed) model. Small differences at the 1-5-mm level do exist in the case of low data density, particularly at low wind speed and high sea state. Overall, the SP model appears to more closely follow the bin-averaged SSB estimates.

Aid and investment in LDCs: A robust approach

This paper uses panel data and the Local Linear Kernel Estimator (LLKE), to investigate the effects of aid on physical capital investment in developing countries. Specifically, we investigate the robustness of the relationship between aid and physical capital investment in Less Developed countries (LDCs) using two different measures of aid and five measures of the policy environment. We find that external aid has a positive and significant impact on physical capital investment given the support of the sample data we use. This effect is robust to the measurement of aid as well as the policy environment. However, the character of the positive relationship between aid and investment varies with the combination of the aid measure and the policy environment. We find that conditional on inflows, the better the policy environment, the higher the investment rate, all things being equal. The results have implications for aid research and aid policy.

ROC curve and covariates: extending induced methodology to the non-parametric framework

Continuous diagnostic tests are often used to discriminate between diseased and healthy populations. The receiver operating characteristic (ROC) curve is a widely used tool that provides a graphical visualisation of the effectiveness of such tests. The potential performance of the tests in terms of distinguishing diseased from healthy people may be strongly influenced by covariates, and a variety of regression methods for adjusting ROC curves has been developed. Until now, these methodologies have assumed that covariate effects have parametric forms, but in this paper we extend the induced methodology by allowing for arbitrary non-parametric effects of a continuous covariate. To this end, local polynomial kernel smoothers are used in the estimation procedure. Our method allows for covariate effect not only on the mean, but also on the variance of the diagnostic test. We also present a bootstrap-based method for testing for a significant covariate effect on the ROC curve. To illustrate the method, endocrine data were analysed with the aim of assessing the performance of anthropometry for predicting clusters of cardiovascular risk factors in an adult population in Galicia (NW Spain), duly adjusted for age. The proposed methodology has proved useful for providing age-specific thresholds for anthropometric measures in the Galician community.

Using Local Alignments for Relation Recognition

This paper discusses the problem of marrying structural similarity with semantic relatedness for Information Extraction from text. Aiming at accurate recognition of relations, we introduce local alignment kernels and explore various possibilities of using them for this task. We give a definition of a local alignment (LA) kernel based on the Smith-Waterman score as a sequence similarity measure and proceed with a range of possibilities for computing similarity between elements of sequences. We show how distributional similarity measures obtained from unlabeled data can be incorporated into the learning task as semantic knowledge. Our experiments suggest that the LA kernel yields promising results on various biomedical corpora outperforming two baselines by a large margin. Additional series of experiments have been conducted on the data sets of seven general relation types, where the performance of the LA kernel is comparable to the current state-of-the-art results.

Graph kernels for chemical compounds using topological and three-dimensional local atom pair environments

Approaches that can predict the biological activity or properties of a chemical compound are an important application of machine learning. In this paper, we introduce a new kernel function for measuring the similarity between chemical compounds and for learning their related properties and activities. The method is based on local atom pair environments which can be rapidly computed by using the topological all-shortest paths matrix and the geometrical distance matrix of a molecular graph as lookup tables. The local atom pair environments are stored in prefix search trees, so called tries, for an efficient comparison. The kernel can be either computed as an optimal assignment kernel or as a corresponding convolution kernel over all local atom similarities. We implemented the Tanimoto kernel, min kernel, minmax kernel and the dot product kernel as local kernels, which are computed recursively by traversing the tries. We tested the approach on eight structure-activity and structure-property molecule benchmark data sets from the literature. The models were trained with ε - support vector regression and support vector classification. The local atom pair kernels showed to be at least competitive to state-of-the-art kernels in seven out of eight cases in a direct comparison. A comparison against literature results using similar experimental setups as in the original works confirmed these findings. The method is easy to implement and has robust default parameters.

FRATS: Functional Regression Analysis of DTI Tract Statistics

Diffusion tensor imaging (DTI) provides important information on the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo. This paper presents a functional regression framework, called FRATS, for the analysis of multiple diffusion properties along fiber bundle as functions in an infinite dimensional space and their association with a set of covariates of interest, such as age, diagnostic status and gender, in real applications. The functional regression framework consists of four integrated components: the local polynomial kernel method for smoothing multiple diffusion properties along individual fiber bundles, a functional linear model for characterizing the association between fiber bundle diffusion properties and a set of covariates, a global test statistic for testing hypotheses of interest, and a resampling method for approximating the p-value of the global test statistic. The proposed methodology is applied to characterizing the development of five diffusion properties including fractional anisotropy, mean diffusivity, and the three eigenvalues of diffusion tensor along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment. Significant age and gestational age effects on the five diffusion properties were found in both tracts. The resulting analysis pipeline can be used for understanding normal brain development, the neural bases of neuropsychiatric disorders, and the joint effects of environmental and genetic factors on white matter fiber bundles.

On Semiparametric Mode Regression Estimation

It has been found that, for a variety of probability distributions, there is a surprising linear relation between mode, mean, and median. In this article, the relation between mode, mean, and median regression functions is assumed to follow a simple parametric model. We propose a semiparametric conditional mode (mode regression) estimation for an unknown (unimodal) conditional distribution function in the context of regression model, so that any m-step-ahead mean and median forecasts can then be substituted into the resultant model to deliver m-step-ahead mode prediction. In the semiparametric model, Least Squared Estimator (LSEs) for the model parameters and the simultaneous estimation of the unknown mean and median regression functions by the local linear kernel method are combined to infer about the parametric and nonparametric components of the proposed model. The asymptotic normality of these estimators is derived, and the asymptotic distribution of the parameter estimates is also given and is shown to follow usual parametric rates in spite of the presence of the nonparametric component in the model. These results are applied to obtain a data-based test for the dependence of mode regression over mean and median regression under a regression model.

Supervised learning of local projection kernels

We formulate a supervised, localized dimensionality reduction method using a gating model that divides up the input space into regions and selects the dimensionality reduction projection separately in each region. The gating model, the locally linear projections, and the kernel-based supervised learning algorithm which uses them in its kernels are coupled and their training is performed with an alternating optimization procedure. Our proposed local projection kernel projects a data instance into different feature spaces by using the local projection matrices, combines them with the gating model, and performs the dot product in the combined feature space. Empirical results on benchmark data sets for visualization and classification tasks validate the idea. The method is generalizable to regression estimation and novelty detection.

A Day by Day Measure of Legislator Ideology: Non-Parametric Smoothing of Legislator Ideal Points with Optimal Classification

This paper presents a method of adapting Poole’s Optimal Classification to smooth ideal points by recovering legislator estimates from localized subsets of the data. Each legislator trend consists of a series of localized kernel estimates, one for each roll call on which the legislator casts a vote. In contrast to the only widely used estimation technique that allows for inter-temporal movement of ideal points, McCarty, Poole, and Rosenthal's DW-NOMINATE, the method presented measures time by the exact date of the roll call rather than by a single integer value for each two-year Congress. The method also does not constrain inter-temporal movement to polynomial functions of time. The result is a set of LOESS-like trends that describe legislator movement through time, thus marking the first roll-call scaling method capable of summarizing legislator movement within and across legislative periods. I illustrate with scalings of the US Senate and the French Fourth Republic.