Relevant bibliographies by topics / Hilbert–Schmidt kernels

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Hilbert–Schmidt kernels'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Hilbert–Schmidt kernels"

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ZHANG, HAIZHANG, and LIANG ZHAO. "ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES." Analysis and Applications 11, no. 02 (2013): 1350014. http://dx.doi.org/10.1142/s0219530513500140.

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To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert–Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of reproducing kernels. Finally, we briefly discuss the special inclusion with a norm equivalence.
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Heo, Jaeseong. "Projectively invariant Hilbert–Schmidt kernels and convolution type operators." Studia Mathematica 213, no. 1 (2012): 61–79. http://dx.doi.org/10.4064/sm213-1-5.

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Ferguson, Sarah H., and Richard Rochberg. "Higher order Hilbert-Schmidt Hankel forms and tensors of analytical kernels." MATHEMATICA SCANDINAVICA 96, no. 1 (2005): 117. http://dx.doi.org/10.7146/math.scand.a-14948.

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The symbols of $n^{\hbox{th}}$-order Hankel forms defined on the product of certain reproducing kernel Hilbert spaces $H(k_{i})$, $i=1,2$, in the Hilbert-Schmidt class are shown to coincide with the orthogonal complement in $H(k_{1})\otimes H(k_{2})$ of the ideal of polynomials which vanish up to order $n$ along the diagonal. For tensor products of weighted Bergman and Dirichlet type spaces (including the Hardy space) we introduce a higher order restriction map which allows us to identify the relative quotient of the $n^{\hbox{th}}$-order ideal modulo the $(n+1)^{\hbox{st}}$-order one as a dir
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Kumar, Hemant, and R. C. Singh Chandel. "A THEORY OF MULTIDIMENSIONAL FREDHOLM INTEGRAL EQUATIONS HAVING SEPARABLE KERNELS: SOLVABLE IN A REGION SURROUNDING BY THE HYPERPLANES." jnanabha 54, no. 01 (2024): 169–79. http://dx.doi.org/10.58250/jnanabha.2024.54121.

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In this article, we present a theory of multidimensional Fredholm integral equations, having separable kernels, are solvable in a region surrounded by hyperplanes. In derivation of their solutions, we employ the generalized Hilbert-Schmidt theory involving eigenvalues and corresponding normalized eigen functions obtained by separable kernels in a region surrounded by the hyperplanes. Finally, we apply two variables Gegenbauer polynomials and derive a result on the inequality of the solution for the double symmetric Fredholm integral equation.
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Klimek, Malgorzata. "Spectrum of Fractional and Fractional Prabhakar Sturm–Liouville Problems with Homogeneous Dirichlet Boundary Conditions." Symmetry 13, no. 12 (2021): 2265. http://dx.doi.org/10.3390/sym13122265.

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In this study, we consider regular eigenvalue problems formulated by using the left and right standard fractional derivatives and extend the notion of a fractional Sturm–Liouville problem to the regular Prabhakar eigenvalue problem, which includes the left and right Prabhakar derivatives. In both cases, we study the spectral properties of Sturm–Liouville operators on function space restricted by homogeneous Dirichlet boundary conditions. Fractional and fractional Prabhakar Sturm–Liouville problems are converted into the equivalent integral ones. Afterwards, the integral Sturm–Liouville operato
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Cavoretto, Roberto, Gregory E. Fasshauer, and Michael McCourt. "An introduction to the Hilbert-Schmidt SVD using iterated Brownian bridge kernels." Numerical Algorithms 68, no. 2 (2014): 393–422. http://dx.doi.org/10.1007/s11075-014-9850-z.

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Laumann, Felix, Julius von Kügelgen, Junhyung Park, Bernhard Schölkopf, and Mauricio Barahona. "Kernel-Based Independence Tests for Causal Structure Learning on Functional Data." Entropy 25, no. 12 (2023): 1597. http://dx.doi.org/10.3390/e25121597.

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Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering. Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and co
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Friesen, Martin, and Sven Karbach. "Stationary covariance regime for affine stochastic covariance models in Hilbert spaces." Finance and Stochastics 28, no. 4 (2024): 1077–116. http://dx.doi.org/10.1007/s00780-024-00543-3.

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AbstractThis paper introduces stochastic covariance models in Hilbert spaces with stationary affine instantaneous covariance processes. We explore the applications of these models in the context of forward curve dynamics within fixed-income and commodity markets. The affine instantaneous covariance process is defined on positive self-adjoint Hilbert–Schmidt operators, and we prove the existence of a unique limit distribution for subcritical affine processes, provide convergence rates of the transition kernels in the Wasserstein distance of order $p \in [1,2]$ p ∈ [ 1 , 2 ] , and give explicit
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Oehring, Charles. "Singular numbers of smooth kernels." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 3 (1988): 511–14. http://dx.doi.org/10.1017/s0305004100065129.

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In [12] we elaborate the vague principle that the behaviour at infinity of the decreasing sequence of singular numbers sn(K) of a Hilbert–Schmidt kernel K is at least as good as that of the sequence {n−1/qω(n−1;K)}, where ωp is an Lp-modulus of continuity of K and q = p/(p − 1), where 1 ≤ p ≤ 2. Despite the author's effort to justify his study of refinements of the half-century old theorem of Smithies [13], that theorem remains the central result of the subject (viz. that for 0 < a ≤ 1, K∈Lip(a, p) implies that sn(K) = O(n−α−1/q)). For example, Cochran's omnibus theorems [5, 6] that delimit
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Raman, S. Ganapathi, and R. Vittal Rao. "Extended Kac-Akhiezer formulae and the Fredholm determinant of finite section Hilbert-Schmidt kernels." Proceedings Mathematical Sciences 104, no. 3 (1994): 581–91. http://dx.doi.org/10.1007/bf02867122.

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Dissertations / Theses on the topic "Hilbert–Schmidt kernels"

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Dorri, Fatemeh. "Adapting Component Analysis." Thesis, 2012. http://hdl.handle.net/10012/6738.

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A main problem in machine learning is to predict the response variables of a test set given the training data and its corresponding response variables. A predictive model can perform satisfactorily only if the training data is an appropriate representative of the test data. This intuition is re???ected in the assumption that the training data and the test data are drawn from the same underlying distribution. However, the assumption may not be correct in many applications for various reasons. For example, gathering training data from the test population might not be easily possible, due to i
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Book chapters on the topic "Hilbert–Schmidt kernels"

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Georgiev, Svetlin G. "Hilbert-Schmidt Theory of Generalized Integral Equations with Symmetric Kernels." In Integral Equations on Time Scales. Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-228-1_6.

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Wang, Tinghua, Wei Li, and Xianwen He. "Kernel Learning with Hilbert-Schmidt Independence Criterion." In Communications in Computer and Information Science. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-3002-4_58.

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Collins, Peter J. "Hilbert–Schmidt Theory." In Differential and Integral Equations. Oxford University PressOxford, 2006. http://dx.doi.org/10.1093/oso/9780198533825.003.0010.

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Abstract In this chapter, we shall recount some elements of the Hilbert–Schmidt theory of the homogeneous Fredholm equation where λ is a constant and the kernel K = K(x, t) is real-valued, continuous, and symmetric: We recall that an eigenvalue of (H) is a value of λ for which there is a continuous solution y(x) of (H), which is not identically zero on [a, b]. Such a y(x) is an eigenfunction corresponding to the eigenvalue λ. Notice that all eigenvalues must necessarily be non-zero. Although the material in this chapter fits nicely into our discussion of integral equations in Chapters 8–10, th
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"Hilbert-Schmidt Theory of Symmetric Kernel." In Applied Mathematical Methods in Theoretical Physics. Wiley-VCH Verlag GmbH & Co. KGaA, 2005. http://dx.doi.org/10.1002/3527605843.ch5.

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"Stable Computation via the Hilbert–Schmidt SVD." In Kernel-based Approximation Methods using MATLAB. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814630146_0013.

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"Kernel-Based Feature Selection with the Hilbert-Schmidt Independence Criterion." In Feature Selection and Ensemble Methods for Bioinformatics. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-60960-557-5.ch010.

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Lou Qiang and Obradovic Zoran. "Feature Selection by Approximating the Markov Blanket in a Kernel-Induced Space." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2010. https://doi.org/10.3233/978-1-60750-606-5-797.

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The proposed feature selection method aims to find a minimum subset of the most informative variables for classification/regression by efficiently approximating the Markov Blanket which is a set of variables that can shield a certain variable from the target. Instead of relying on the conditional independence test or network structure learning, the new method uses Hilbert-Schmidt Independence criterion as a measure of dependence among variables in a kernel-induced space. This allows effective approximation of the Markov Blanket that consists of multiple dependent features rather than being lim
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Conference papers on the topic "Hilbert–Schmidt kernels"

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Hu, Chenge, Huaqing Zhang, Yuyu Zhou, and Ruixin Guan. "Measuring Hilbert-Schmidt Independence Criterion with Different Kernels." In 2021 IEEE International Conference on Computer Science, Artificial Intelligence and Electronic Engineering (CSAIEE). IEEE, 2021. http://dx.doi.org/10.1109/csaiee54046.2021.9543403.

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Hu, Chenge, Huaqing Zhang, Yuyu Zhou, and Ruixin Guan. "Measuring Hilbert-Schmidt Independence Criterion with Different Kernels." In 2021 IEEE International Conference on Computer Science, Artificial Intelligence and Electronic Engineering (CSAIEE). IEEE, 2021. http://dx.doi.org/10.1109/csaiee54046.2021.9543403.

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Li, Jue, Yuhua Qian, Jieting Wang, and Saixiong Liu. "PHSIC against Random Consistency and Its Application in Causal Inference." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/233.

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The Hilbert-Schmidt Independence Criterion (HSIC) based on kernel functions is capable of detecting nonlinear dependencies between variables, making it a common method for association relationship mining. However, in situations with small samples, high dimensions, or noisy data, it may generate spurious associations, causing two unrelated variables to have certain scores. To address this issue, we propose a novel criterion, named as Pure Hilbert-Schmidt Independence Criterion (PHSIC). PHSIC is achieved by subtracting the mean HSIC obtained under random conditions from the original HSIC value.
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Shan, Zijuan, Zhenyu Ni, and Zhengzhi Li. "Improvement of the properties of SISAM using the theory of Hilbert and Schmidt." In OSA Annual Meeting. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.thaa1.

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The original spectrum measured in the interferometric spectrometer with selection by amplitude modulation (SISAM) has been reconstructed, we believe for the first time, by solving the integral equation associated with the irradiance distribution in the receiving plane, using the theory of Hilbert and Schmidt. The number of sampling points is reduced greatly by dividing the larger range of wavenumber into several smaller ones and choosing the appropriate parameter. The instrumental function we obtain has a very small width and does not show noticeable sidelobes. A pure rotational spectrum of 14
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Brivadis, Lucas, Antoine Chaillet, and Jean Auriol. "Online estimation of Hilbert-Schmidt operators and application to kernel reconstruction of neural fields." In 2022 IEEE 61st Conference on Decision and Control (CDC). IEEE, 2022. http://dx.doi.org/10.1109/cdc51059.2022.9992414.

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Yokoi, Sho, Daichi Mochihashi, Ryo Takahashi, Naoaki Okazaki, and Kentaro Inui. "Learning Co-Substructures by Kernel Dependence Maximization." In Twenty-Sixth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/465.

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Modeling associations between items in a dataset is a problem that is frequently encountered in data and knowledge mining research. Most previous studies have simply applied a predefined fixed pattern for extracting the substructure of each item pair and then analyzed the associations between these substructures. Using such fixed patterns may not, however, capture the significant association. We, therefore, propose the novel machine learning task of extracting a strongly associated substructure pair (co-substructure) from each input item pair. We call this task dependent co-substructure extrac
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