Search

Lattice-based reformulation techniques have been used successfully both theoretically and computationally. One such reformulation is obtained from the kernel lattice associated with an input matrix. Some of the hard instances [...]

I derive pricing kernels in which the market volatility is endogenously determined. Using the Taylor expansion series of the representative investor's marginal utility, I show that the price of market volatility risk is restricted by the investor's risk aversion and skewness preference. The risk aversion is estimated to be between two and five and is significant. The price of the market volatility is negative. Consistent with economic theory, 1 find that the pricing kernel decreases in the market index return and increases in market volatility. The projection of the estimated pricing kernel onto a polynomial function of the market return produces puzzling behaviors, which can be observed in the pricing kernel and absolute risk aversion functions. The inclusion of additional terms in the Taylor expansion series of the investor's marginal utility produces a pricing kernel function of market stochastic volatility, stochastic skewness, and stochastic kurtosis. The prices of risk of these moments are restricted by the investor's risk aversion, skewness preference, and kurtosis preference. The prices of risk of these moments should not be confused with the price of risk of powers of the market return, such as coskewness and cokurtosis. Key words: pricing kernels; risk aversion; skewness preference; volatility risk History. Received April 1, 2010; accepted July 3, 2011, by Wei Xiong, finance. Published online in Articles in Advance October 7, 2011., 1. Introduction In a setting with standard preferences and static prices of risk, the pricing kernel can be interpreted as a scaled marginal utility. Assuming the scaled marginal utility interpretation, [...]

In recent years, many studies show that kernel methods are computationally efficient, robust, and stable for pattern analysis. Many kernel-based classifiers were designed and applied to classify remote-sensed data, and some results show that kernel-based classifiers have satisfying performances. Many studies about hyperspectral image classification also show that nonparametric weighted feature extraction (NWFE) is a powerful tool for extracting hyperspectral image features. However, NWFE is still based on linear transformation. In this paper, the kernel method is applied to extend NWFE to kernel-based NWFE (KNWFE). The new KNWFE possesses the advantages of both linear and nonlinear transformation, and the experimental results show that KNWFE outperforms NWFE, decision-boundary feature extraction, independent component analysis, kernel-based principal component analysis, and generalized discriminant analysis. Index Terms--Feature extraction, image classification.

The kernel energy method (KEM) is applied to the vesicular stomatitis virus (VSV) nucleoprotein (PDB ID code 2QVJ). The calculations employ atomic coordinates from the crystal structure at 2.8-[Angstrom] resolution, except for the hydrogen atoms, whose positions were modeled by using the computer program HYPERCHEM. The calculated KEM ab initio limited basis Hartree-Fock energy for the full 33,175 atom molecule (including hydrogen atoms) is obtained. In the KEM, a full biological molecule is represented by smaller 'kernels' of atoms, greatly simplifying the calculations. Collections of kernels are well suited for parallel computation. VSV consists of five similar chains, and we obtain the energy of each chain. Interchain hydrogen bonds contribute to the interaction energy between the chains. These hydrogen bond energies are calculated in Hartree-Fock (HF) and Moller-Plesset perturbation theory to second order (MP2) approximations by using 6-31G** basis orbitals. The correlation energy, included in MP2, is a significant factor in the interchain hydrogen bond energies. Hartree-Fock | KEM | Moller-Plesset | quantum mechanics

We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity conditions, we develop a sequence of denoisers that, although independent of the distribution of the underlying "clean" sequence, is universally optimal in the limit of large sequence length. This sequence of denoisers is universal in the sense of performing as well as any sliding-window denoising scheme which may be optimized for the underlying clean signal. Our results are initially developed in a "semi-stochastic" setting, where the noiseless signal is an unknown individual sequence, and the only source of randomness is due to the channel noise. It is subsequently shown that in the fully stochastic setting, where the noiseless sequence is a stationary stochastic process, our schemes universally attain optimum performance. The proposed schemes draw from nonparametric density estimation techniques and are practically implementable. We demonstrate efficacy of the proposed schemes in denoising Gray-scale images in the conventional additive white Gaussian noise (AWGN) setting, with additional promising results for less conventional noise distributions. Index Terms--Denoisability, discrete denoising, kernel density estimation, memoryless channels, quantization, semi-stochastic setting, sliding-window denoiser, universal denoising.

The recognition of program constructs that are frequently used by software developers is a powerful mechanism for optimizing and parallelizing compilers to improve the performance of the object code. The development of techniques for automatic recognition of computational kernels such as inductions, reductions and array recurrences has been an intensive research area in the scope of compiler technology during the 90's. This article presents a new compiler framework that, unlike previous techniques that focus on specific and isolated kernels, recognizes a comprehensive collection of computational kernels that appear frequently in full-scale real applications. The XARK compiler operates on top of the Gated Single Assignment (GSA) form of a high-level intermediate representation (IR) of the source code. Recognition is carried out through a demand-driven analysis of this high-level IR at two different levels. First, the dependences between the statements that compose the strongly connected components (SCCs) of the data-dependence graph of the GSA form are analyzed. As a result of this intra-SCC analysis, the computational kernels corresponding to the execution of the statements of the SCCs are recognized. Second, the dependences between statements of different SCCs are examined in order to recognize more complex kernels that result from combining simpler kernels in the same code. Overall, the XARK compiler builds a hierarchical representation of the source code as kernels and dependence relationships between those kernels. This article describes in detail the collection of computational kernels recognized by the XARK compiler. Besides, the internals of the recognition algorithms are presented. The design of the algorithms enables to extend the recognition capabilities of XARK to cope with new kernels, and provides an advanced symbolic analysis framework to run other compiler techniques on demand. Finally, extensive experiments showing the effectiveness of XARK for a collection of benchmarks from different application domains are presented. In particular, the SparsKit-II library for the manipulation of sparse matrices, the Perfect benchmarks, the SPEC CPU2000 collection and the PLTMG package for solving elliptic partial differential equations are analyzed in detail. Categories and Subject Descriptors: D.3.4 [Programming Languages]: Processor--Compilers, optimization General Terms: Algorithms, Languages, Experimentation Additional Key Words and Phrases: Automatic kernel recognition, demand-driven algorithms, use-def chains, symbolic analysis, gated single assignment, strongly connected component DOI = 10.1145/1391956.1391959 http://doi.acm.org/10.1145/1391956.1391959

Linear and kernel discriminant analyses are popular approaches for supervised dimensionality reduction. Uncorrelated and regularized discriminant analyses have been proposed to overcome the singularity problem encountered by classical discriminant analysis. In this paper, we study the properties of kernel uncorrelated and regularized discriminant analyses, called KUDA and KRDA, respectively. In particular, we show that under a mild condition, both linear and kernel uncorrelated discriminant analysis project samples in the same class to a common vector in the dimensionality-reduced space. This implies that uncorrelated discriminant analysis may suffer from the overfitting problem if there are a large number of samples in each class. We show that as the regularization parameter in KRDA tends to zero, KRDA approaches KUDA. This shows that KUDA is a special case of KRDA and that regularization can be applied to overcome the overfitting problem in uncorrelated discriminant analysis. As the performance of KRDA depends on the value of the regularization parameter, we show that the matrix computations involved in KRDA can be simplified, so that a large number of candidate values can be cross-validated efficiently. Finally, we conduct experiments to evaluate the proposed theories and algorithms. Index Terms--Discriminant analysis, kernel methods, regularization, model selection, singular value decomposition.

In kernel discriminant analysis, one common practice is to use a fixed level of smoothing (estimated from training data) for classifying all unlabeled observations. But, in classification, a good choice of smoothing parameters also depends on the observation to be classified. Therefore, instead of using a fixed level of smoothing over the entire measurement space, it may be more useful to estimate the smoothing parameters depending on that specific observation. Here, we propose a simple method for this case-specific smoothing. Some benchmark data sets are analyzed to illustrate the performance of the proposed method. Index Terms--Bandwidth, Bayes risk, bootstrap, cross validation, kernel smoothing, misclassification rate, nearest neighbor, p-value.

The article talks about the development and the applications of a new transformation kernel density estimator, which is based on the semiparametric transformation function that transforms data to normality. The discussed estimator is shown to be extremely suitable for the unimodal, low and high kurtosis densities.

The article explains the working and features of the Potts model clustering, which is shown to share the same Hamiltonian with the kernel K-means and MNCut criteria. A new method and a simple rule for the selection of appropriate temperature for the procedure are also presented.

A control-based object tracking approach is presented. Findings reveal the superior performance of the proposed approach.

In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We introduce an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model. Simulations are used to examine the finite sample performance of the proposed estimators and the test statistics. Keywords: Fixed effects models; Model specification tests; Nonparametric kernel method; Panel data; Partially linear model; Profile method; Random effects models; Semiparametric efficiency bound

The problem of specification tests for conditional models is studied when the data are subject to left truncation and right censoring. A general method is applied to derive tests for the polynomial regression, the proportional hazards, the additive risks and the proportional odds models. Bootstrap versions to approximate the critical values of the test are introduced and proved to work both from a theoretical viewpoint as well as in a small simulation study. JEL classifications: C12; C15; C24 Keywords. Additive risks model; Duration data; Kernel method; Polynomial regression; Proportional hazards model; Proportional odds; Survival analysis

In this paper, we develop a new effective multiple kernel learning algorithm. First, we map the input data into m different feature spaces by m empirical kernels, where each generated feature space is taken as one view of the input space. Then, through borrowing the motivating argument from Canonical Correlation Analysis (CCA) that can maximally correlate the m views in the transformed coordinates, we introduce a special term called Inter-Function Similarity Loss [R.sub.IFSL] into the existing regularization framework so as to guarantee the agreement of multiview outputs. In implementation, we select the Modification of Ho-Kashyap algorithm with Squared approximation of the misclassification errors (MHKS) as the incorporated paradigm and the experimental results on benchmark data sets demonstrate the feasibility and effectiveness of the proposed algorithm named MultiK-MHKS. Index Terms--Multiple kernel learning, canonical correlation analysis, regularization learning, modified Ho-Kashyap algorithm, single learning process, pattern recognition.

Linear dynamics of Euler-Bernoulli beams with nonviscous non-local damping is considered. It is assumed that the damping force at a given point in the beam depends on the past history of velocities at different points via convolution integrals over exponentially decaying kernel functions. Conventional viscous and viscoelastic damping models can be obtained as special cases of this general damping model. The equation of motion of the beam with such a general damping model results in a linear partial integro-differential equation. Exact closed-form equations of the natural frequencies and mode shapes of the beam are derived. Numerical examples are provided to illustrate the new results. [DOI: 10.1115/1.2712315]

Some specific reproducing kernels have allowed any kernel learning machine to operate in the time-frequency domain. New perspectives are provided in the field of non-stationary signal and analysis, which can benefit from the developments of pattern recognition and Statistical Learning Theory.

The proposed global kernel local density mode significantly decreases the number of iterations required to achieve convergence and is hence found to be extremely reliable and rapid for the localization and tracking of the various video images, in addition to several other real-time applications.

The mean-shift algorithm, based on ideas proposed by Fukunaga and Hostetler [16], is a hill-climbing algorithm on the density defined by a finite mixture or a kernel density estimate. Mean-shift can be used as a nonparametric clustering method and has attracted recent attention in computer vision applications such as image segmentation or tracking. We show that, when the kernel is Gaussian, mean-shift is an expectation-maximization (EM) algorithm and, when the kernel is non-Gaussian, mean-shift is a generalized EM algorithm. This implies that mean-shift converges from almost any starting point and that, in general, its convergence is of linear order. For Gaussian mean-shift, we show: 1) the rate of linear convergence approaches 0 (superlinear convergence) for very narrow or very wide kernels, but is often close to 1 (thus, extremely slow) for intermediate widths and exactly 1 (sublinear convergence) for widths at which modes merge, 2) the iterates approach the mode along the local principal component of the data points from the inside of the convex hull of the data points, and 3) the convergence domains are nonconvex and can be disconnected and show fractal behavior. We suggest ways of accelerating mean-shift based on the EM interpretation. Index Terms--Mean-shift algorithm, Gaussian mixtures, kernel density estimators, EM algorithm, clustering.

In this article we consider quantile regression in reproducing kernel Hilbert spaces, which we call kernel quantile regression (KQR). We make three contributions: (1) we propose an efficient algorithm that computes the entire solution path of the KQR, with essentially the same computational cost as fitting one KQR model; (2) we derive a simple formula for the effective dimension of the KQR model, which allows convenient selection of the regularization parameter; and (3) we develop an asymptotic theory for the KQR model. KEY WORDS: Degrees of freedom; Metric entropy; Model selection; Quadratic programming; Quantile regression; Reproducing kernel Hilbert space.

A new estimation procedure for true unknown parameter vector [theta.sub.0] is proposed which extends the classical least squares procedure for nonlinear regression to the case where the response is subject to censoring. This new method outperforms an earlier developed method in most cases, thus this method can be recommended to practice.

Kernel regression is proposed as an effective tool for both denoising and interpolation in image processing and its relation is established with some popular existing techniques. A novel adaptive generalization of kernel regression is described with excellent results in both denoising and interpolation applications.

While distance function learning for supervised learning tasks has a long history, extending it to learning tasks with weaker supervisory information has only been studied recently. In particular, some methods have been proposed for semisupervised metric learning based on pairwise similarity or dissimilarity information. In this paper, we propose a kernel approach for semisupervised metric learning and present in detail two special cases of this kernel approach. The metric learning problem is thus formulated as an optimization problem for kernel learning. An attractive property of the optimization problem is that it is convex and, hence, has no local optima. While a closed-form solution exists for the first special case, the second case is solved using an iterative majorization procedure to estimate the optimal solution asymptotically. Experimental results based on both synthetic and real-world data show that this new kernel approach is promising for nonlinear metric learning. Index Terms--Clustering, kernel learning, metric learning, semisupervised learning.

A topological and dynamical characterization of the cluster structures described by the support vector clustering is developed. It is shown that each cluster can be decomposed into its constituent basin level cells and can be naturally extended to an enlarged clustered domain, which serves as a basis for inductive clustering. A simplified weighted graph preserving the topological structure of the clusters is also constructed and is employed to develop a robust and inductive clustering algorithm. Simulation results are given to illustrate the robustness and effectiveness of the proposed method. Index Terms--Clustering, kernel methods, support vector machines, inductive learning, dynamical systems.

A kernel-based deformable model is proposed for detecting deformable shapes, and an efficient algorithm without initial solutions is developed. The proposed approach is tested against real images, where results show the effectiveness of the deformable model and prove the feasibility of the proposed approach.

A novel Gabor-based kernel principal component analysis (PCA) with doubly nonlinear mapping is proposed for human face recognition. The proposed algorithm is evaluated based on various databases by using different face recognition methods such as PCA, Gabor wavelets plus PCA, and Gabor wavelets plus kernel PCA with fractional power polynomial methods, where experiments show that consistent and promising results are obtained.

Two data analytic research areas--penalized splines and reproducing kernel methods--have become very vibrant since the mid-1990s. This article shows how the former can be embedded in the latter via theory for reproducing kernel Hilbert spaces. This connection facilitates cross-fertilization between the two bodies of research. In particular, connections between support vector machines and penalized splines are established. These allow for significant reductions in computational complexity, and easier incorporation of special structure such as additivity. KEY WORDS: Bioinformatics; Classification; Data mining; Generalized additive models; Kernel machines; Machine learning; Mixed models; Reproducing kernel Hilbert spaces; Semiparametric regression; Statistical learning: Supervised learning; Support vector machines.

A study proposes the multiclass proximal support vector machine (MPSVM) classifier, which extends the binary PSVM to the multiclass case. The effectiveness of MPSVM is demonstrated by both simulation studies and applications to cancer classifications using microarray data.

A new generalized correlation function is developed that includes the information of both the distribution and that of the time structure of a stochastic process. An attempt is made to find out how this measure is interpreted from a kernel method as well as from information theoretic learning points of view, demonstrating some relevant properties.

This paper addresses the problem of characterizing ensemble similarity from sample similarity in a principled manner. Using reproducing kernel as a characterization of sample similarity, we suggest a probabilistic distance measure in the reproducing kernel Hilbert space (RKHS) as the ensemble similarity. Assuming normality in the RKHS, we derive analytic expressions for probabilistic distance measures that are commonly used in many applications, such as Chernoff distance (or the Bhattacharyya distance as its special case), Kullback-Leibler divergence, etc. Since the reproducing kernel implicitly embeds a nonlinear mapping, our approach presents a new way to study these distances whose feasibility and efficiency is demonstrated using experiments with synthetic and real examples. Further, we extend the ensemble similarity to the reproducing kernel for ensemble and study the ensemble similarity for more general data representations. Index Terms--Ensemble similarity, kernel methods, Chernoff distance, Bhattacharyya distance, Kullback-Leibler (KL) divergence/relative entropy, Patrick-Fisher distance, Mahalonobis distance, reproducing kernel Hilbert space.

The geometric framework for the support vector machine (SVM) classification problem provides an intuitive ground for the understanding and the application of geometric optimization algorithms, leading to practical solutions of real world classification problems. In this work, the notion of 'reduced convex hull' is employed and supported by a set of new theoretical results. These results allow existing geometric algorithms to be directly and practically applied to solve not only separable, but also nonseparable classification problems both accurately and efficiently. As a practical application of the new theoretical results, a known geometric algorithm has been employed and transformed accordingly to solve nonseparable problems successfully. Index Terms--Classification, kernel methods, pattern recognition, reduced convex hulls, support vector machines (SVMs).

This paper presents kernel regularization information criterion (KRIC), which is a new criterion for tuning regularization parameters in kernel logistic regression (KLR) and support vector machines (SVMs). The main idea of the KRIC is based on the regularization information criterion (RIC). We derive an eigenvalue equation to calculate the KRIC and solve the problem. The computational cost for parameter tuning by the KRIC is reduced drastically by using the Nystrom approximation. The test error rate of SVMs or KLR with the regularization parameter tuned by the KRIC is comparable with the one by the cross validation or evaluation of the evidence. The computational cost of the KRIC is significantly lower than the one of the other criteria. Index Terms--Kernel logistic regression (KLR), kernel machine, parameter tuning, regularization information criterion, support vector machine (SVM).

This paper presents a novel pattern recognition framework by capitalizing on dimensionality increasing techniques. In particular, the framework integrates Gabor image representation, a novel multiclass Kernel Fisher Analysis (KFA) method, and fractional power polynomial models for improving pattern recognition performance. Gabor image representation, which increases dimensionality by incorporating Gabor filters with different scales and orientations, is characterized by spatial frequency, spatial locality, and orientational selectivity for coping with image variabilities such as illumination variations. The KFA method first performs nonlinear mapping from the input space to a high-dimensional feature space, and then implements the multiclass Fisher discriminant analysis in the feature space. The significance of the nonlinear mapping is that it increases the discriminating power of the KFA method, which is linear in the feature space but nonlinear in the input space. The novelty of the KFA method comes from the fact that 1) it extends the two-class kernel Fisher methods by addressing multiclass pattern classification problems and 2) it improves upon the traditional Generalized Discriminant Analysis (GDA) method by deriving a unique solution (compared to the GDA solution, which is not unique). The fractional power polynomial models further improve performance of the proposed pattern recognition framework. Experiments on face recognition using both the FERET database and the FRGC (Face Recognition Grand Challenge) databases show the feasibility of the proposed framework. In particular, experimental results using the FERET database show that the KFA method performs better than the GDA method and the fractional power polynomial models help both the KFA method and the GDA method improve their face recognition performance. Experimental results using the FRGC databases show that the proposed pattern recognition framework improves face recognition performance upon the BEE baseline algorithm and the LDA-based baseline algorithm by large margins. Index Terms--Dimensionality increasing techniques, face recognition, Face Recognition Grand Challenge (FRGC), fractional power polynomial models, Gabor image representation, Kernel Fisher Analysis (KFA) method.

Byline: A. B. Aleksandrov (1) Abstract: Let [alpha] &gt 0. We consider the linear span .sub.[alpha] ( R.sup.n ) of scalar Riesz's kernels \ \tfrac1| x - a |.sup.[alpha] \.sub.a [member of] R.sup.n and the linear span .sub.[alpha] ( R.sup.n ) of vector Riesz's kernels \ \tfrac1| x - a |.sup.[alpha] + 1 ( x - a ) \.sub.a [member of] R.sup.n . We study the following problems. (1) When is the intersection .sub.[alpha] ( R.sup.n ) [intersection] L.sup.p ( R.sup.n ) dense in L.sup.p([].sup.n)? (2) When is the intersection .sub.[alpha] ( R.sup.n ) [intersection] L.sup.p ( R.sup.n ,R.sup.n ) dense in L.sup.p([].sup.n, [].sup.n)? Bibliography: 15 titles. Author Affiliation: (1) St.Petersburg Department, Steklov Mathematical Institute, St.Petersburg, Russia Article History: Registration Date: 01/03/2006 Received Date: 20/06/2004 Article note: Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 315, 2004, pp. 5--38.

Survival analysis is a branch of statistics concerned with the time elapsing before 'failure,' with diverse applications in medical statistics and the analysis of the reliability of electrical or mechanical components. We introduce a parametric accelerated life survival analysis model based on kernel learning methods that, at least in principal, is able to learn arbitrary dependencies between a vector of explanatory variables and the scale of the distribution of survival times. The proposed kernel survival analysis method is then used to model the growth domain of Clostridium botulinum, the food processing and storage conditions permitting the growth of this foodborne microbial pathogen, leading to the production of the neurotoxin responsible for botulism. A Bayesian training procedure, based on the evidence framework, is used for model selection and to provide a credible interval on model predictions. The kernel survival analysis models are found to be more accurate than models based on more traditional survival analysis techniques but also suggest a risk assessment of the foodborne botulism hazard would benefit from the collection of additional data. Index Terms--Bayesian learning, kernel methods, survival analysis.

This paper deals with identification of Wiener systems with nonlinearity being a discontinuous piece-wise linear function. Recursive estimation algorithms are proposed to estimate six unknown parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem by using the iid Gaussian inputs. The estimates are proved to converge to the corresponding true values with probability one. A numerical example is given to justify the obtained theoretical results. Index Terms--Identification, kernel function, strong consistency, Wiener system.

In this paper, we investigate the problem of estimating high-density regions from univariate or multivariate data samples. We estimate minimum volume sets, whose probability is specified in advance, known in the literature as density contour clusters. This problem is strongly related to One-Class Support Vector Machines (OCSVM). We propose a new method to solve this problem, the One-Class Neighbor Machine (OCNM) and we show its properties. In particular, the OCNM solution asymptotically converges to the exact minimum volume set prespecified. Finally, numerical results illustrating the advantage of the new method are shown. Index Terms--Density estimation, kernel methods, One-Class Support Vector Machines.

A multiscale approach along with a graphical device leading to a more informative discriminant analysis than the usual approach based on a single optimum scale of smoothing for each class density estimate was presented. When there are more than two competing classes, this method splits the problem into number of two-class problems, allowing the flexibility of using different bandwidths for different pairs of competing classes.