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Journal articles on the topic 'Infinite-Dimensional statistics'

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Author: Grafiati

Published: 1 June 2024

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1

Kleijn, B. J. K., and A. W. van der Vaart. "Misspecification in infinite-dimensional Bayesian statistics." Annals of Statistics 34, no. 2 (April 2006): 837–77. http://dx.doi.org/10.1214/009053606000000029.

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2

Cuchiero, Christa, and Sara Svaluto-Ferro. "Infinite-dimensional polynomial processes." Finance and Stochastics 25, no. 2 (March 4, 2021): 383–426. http://dx.doi.org/10.1007/s00780-021-00450-x.

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3

Song, Yanglei, Xiaohui Chen, and Kengo Kato. "Approximating high-dimensional infinite-order $U$-statistics: Statistical and computational guarantees." Electronic Journal of Statistics 13, no. 2 (2019): 4794–848. http://dx.doi.org/10.1214/19-ejs1643.

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4

Palev, Tchavdar D. "Lie superalgebras, infinite-dimensional algebras and quantum statistics." Reports on Mathematical Physics 31, no. 3 (June 1992): 241–62. http://dx.doi.org/10.1016/0034-4877(92)90017-u.

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5

Bojdecki, Tomasz, and Luis G. Gorostiza. "Inhomogenous infinite dimensional langevin equations." Stochastic Analysis and Applications 6, no. 1 (January 1988): 1–9. http://dx.doi.org/10.1080/07362998808809133.

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6

Dalecky, Yu L., and V. R. Steblovskaya. "On infinite-dimensional variational problems." Stochastic Analysis and Applications 14, no. 1 (January 1996): 47–71. http://dx.doi.org/10.1080/07362999608809425.

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7

Nishikawa, Naoki, Taiji Suzuki, Atsushi Nitanda, and Denny Wu. "Two-layer neural network on infinite-dimensional data: global optimization guarantee in the mean-field regime ^*." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 11 (November 1, 2023): 114007. http://dx.doi.org/10.1088/1742-5468/ad01b2.

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Abstract:

Abstract The analysis of neural network optimization in the mean-field regime is important as the setting allows for feature learning. The existing theory has been developed mainly for neural networks in finite dimensions, i.e. each neuron has a finite-dimensional parameter. However, the setting of infinite-dimensional input naturally arises in machine learning problems such as nonparametric functional data analysis and graph classification. In this paper, we develop a new mean-field analysis of a two-layer neural network in an infinite-dimensional parameter space. We first give a generalization error bound, which shows that the regularized empirical risk minimizer properly generalizes when the data size is sufficiently large, despite the neurons being infinite-dimensional. Next, we present two gradient-based optimization algorithms for infinite-dimensional mean-field networks, by extending the recently developed particle optimization framework to the infinite-dimensional setting. We show that the proposed algorithms converge to the (regularized) global optimal solution, and moreover, their rates of convergence are of polynomial order in the online setting and exponential order in the finite sample setting, respectively. To the best of our knowledge, this is the first quantitative global optimization guarantee of a neural network on infinite-dimensional input and in the presence of feature learning.

8

Schmuland, Byron. "Dirichlet forms: Some infinite-dimensional examples." Canadian Journal of Statistics 27, no. 4 (December 1999): 683–700. http://dx.doi.org/10.2307/3316125.

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9

Vaart, A. W. "Efficiency. of infinite dimensional M- estimators." Statistica Neerlandica 49, no. 1 (March 1995): 9–30. http://dx.doi.org/10.1111/j.1467-9574.1995.tb01452.x.

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10

Heintze, Ernst, and Xiaobo Liu. "Homogeneity of Infinite Dimensional Isoparametric Submanifolds." Annals of Mathematics 149, no. 1 (January 1999): 149. http://dx.doi.org/10.2307/121022.

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11

Aneiros, Germán, and Philippe Vieu. "Variable selection in infinite-dimensional problems." Statistics & Probability Letters 94 (November 2014): 12–20. http://dx.doi.org/10.1016/j.spl.2014.06.025.

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12

Schmidt, Thorsten, Stefan Tappe, and Weijun Yu. "Infinite dimensional affine processes." Stochastic Processes and their Applications 130, no. 12 (December 2020): 7131–69. http://dx.doi.org/10.1016/j.spa.2020.07.009.

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13

Bobkov, Sergey G., and James Melbourne. "Hyperbolic measures on infinite dimensional spaces." Probability Surveys 13 (2016): 57–88. http://dx.doi.org/10.1214/14-ps238.

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14

Millet, Annie, David Nualart, and Marta Sanz. "Time reversal for infinite-dimensional diffusions." Probability Theory and Related Fields 82, no. 3 (August 1989): 315–47. http://dx.doi.org/10.1007/bf00339991.

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15

Seidler, Jan. "Weak convergence of infinite-dimensional diffusions1." Stochastic Analysis and Applications 15, no. 3 (January 1997): 399–417. http://dx.doi.org/10.1080/07362999708809484.

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16

AB, Gopinath Kallianpur, and Jie Xiong. "Stochastic Differential Equations in Infinite Dimensional Spaces." Journal of the American Statistical Association 92, no. 438 (June 1997): 799. http://dx.doi.org/10.2307/2965750.

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17

Osipov, L. V., and V. I. Rotar’. "On an Infinite-Dimensional Central Limit Theorem." Theory of Probability & Its Applications 29, no. 2 (January 1985): 375–83. http://dx.doi.org/10.1137/1129048.

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18

Chakraborty, Anirvan, and Probal Chaudhuri. "On data depth in infinite dimensional spaces." Annals of the Institute of Statistical Mathematics 66, no. 2 (July 3, 2013): 303–24. http://dx.doi.org/10.1007/s10463-013-0416-y.

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19

Račkauskas, Alfredas, and Charles Suquet. "Testing Epidemic Changes of Infinite Dimensional Parameters." Statistical Inference for Stochastic Processes 9, no. 2 (July 2006): 111–34. http://dx.doi.org/10.1007/s11203-005-0728-5.

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20

Tappe, Stefan, and Stefan Weber. "Stochastic mortality models: an infinite-dimensional approach." Finance and Stochastics 18, no. 1 (December 10, 2013): 209–48. http://dx.doi.org/10.1007/s00780-013-0219-2.

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21

Hasegawa, Yoshihei. "Brownian motions on infinite dimensional quadric hypersurfaces." Probability Theory and Related Fields 80, no. 3 (September 1989): 347–64. http://dx.doi.org/10.1007/bf01794428.

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22

Léandre, R. "Lebesgue measure in infinite dimension as an infinite-dimensional distribution." Journal of Mathematical Sciences 159, no. 6 (June 2009): 833–36. http://dx.doi.org/10.1007/s10958-009-9475-2.

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23

Simão, Isabel. "Regular transition densities for infinite dimensional diffusions." Stochastic Analysis and Applications 11, no. 3 (January 1993): 309–36. http://dx.doi.org/10.1080/07362999308809319.

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24

Tsoi, Allanus H. "Time reversal of infinite-dimensional point processes." Journal of Theoretical Probability 6, no. 3 (July 1993): 451–61. http://dx.doi.org/10.1007/bf01066711.

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25

Goia, Aldo, and Philippe Vieu. "An introduction to recent advances in high/infinite dimensional statistics." Journal of Multivariate Analysis 146 (April 2016): 1–6. http://dx.doi.org/10.1016/j.jmva.2015.12.001.

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26

Ouknine, Youssef, and Mohamed Erraoui. "Noncanonical representation with an infinite-dimensional orthogonal complement." Statistics & Probability Letters 78, no. 10 (August 2008): 1200–1205. http://dx.doi.org/10.1016/j.spl.2007.11.015.

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27

Hall, W. J., and Wei-Min Huang. "Large deviations and estimation in infinite-dimensional models." Statistics & Probability Letters 6, no. 6 (May 1988): 433–39. http://dx.doi.org/10.1016/0167-7152(88)90104-6.

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28

Aihara, ShinIchi, and Arunabha Bagchi. "Infinite dimensional parameter identification for stochastic parabolic systems." Statistics & Probability Letters 8, no. 3 (August 1989): 279–87. http://dx.doi.org/10.1016/0167-7152(89)90134-x.

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29

Budhiraja, Amarjit, Paul Dupuis, and Vasileios Maroulas. "Large deviations for infinite dimensional stochastic dynamical systems." Annals of Probability 36, no. 4 (July 2008): 1390–420. http://dx.doi.org/10.1214/07-aop362.

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30

Torres, A., M. P. Frías, and M. D. Ruiz-Medina. "Log-Gaussian Cox processes in infinite-dimensional spaces." Theory of Probability and Mathematical Statistics 95 (February 28, 2018): 173–93. http://dx.doi.org/10.1090/tpms/1028.

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31

Carone, Marco, Alexander R. Luedtke, and Mark J. van der Laan. "Toward Computerized Efficient Estimation in Infinite-Dimensional Models." Journal of the American Statistical Association 114, no. 527 (September 13, 2018): 1174–90. http://dx.doi.org/10.1080/01621459.2018.1482752.

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32

Zagorodnyuk, A. V. "TheNulstellensatz on infinite-dimensional complex spaces." Journal of Mathematical Sciences 96, no. 2 (August 1999): 2951–56. http://dx.doi.org/10.1007/bf02169686.

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33

Horbacz, Katarzyna. "Random dynamical systems with jumps." Journal of Applied Probability 41, no. 3 (September 2004): 890–910. http://dx.doi.org/10.1239/jap/1091543432.

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Abstract:

We consider random dynamical systems with randomly chosen jumps on infinite-dimensional spaces. The choice of deterministic dynamical systems and jumps depends on a position. The system generalizes dynamical systems corresponding to learning systems, Poisson driven stochastic differential equations, iterated function system with infinite family of transformations and random evolutions. We will show that distributions which describe the dynamics of this system converge to an invariant distribution. We use recent results concerning asymptotic stability of Markov operators on infinite-dimensional spaces obtained by T. Szarek.

34

Horbacz, Katarzyna. "Random dynamical systems with jumps." Journal of Applied Probability 41, no. 03 (September 2004): 890–910. http://dx.doi.org/10.1017/s0021900200020611.

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Abstract:

We consider random dynamical systems with randomly chosen jumps on infinite-dimensional spaces. The choice of deterministic dynamical systems and jumps depends on a position. The system generalizes dynamical systems corresponding to learning systems, Poisson driven stochastic differential equations, iterated function system with infinite family of transformations and random evolutions. We will show that distributions which describe the dynamics of this system converge to an invariant distribution. We use recent results concerning asymptotic stability of Markov operators on infinite-dimensional spaces obtained by T. Szarek.

35

Antoniadis, Anestis, and Rene Carmona. "Eigenfunction expansions for infinite dimensional Ornstein-Uhlenbeck processes." Probability Theory and Related Fields 74, no. 1 (March 1987): 31–54. http://dx.doi.org/10.1007/bf01845638.

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36

Kesten, Harry. "The incipient infinite cluster in two-dimensional percolation." Probability Theory and Related Fields 73, no. 3 (1986): 369–94. http://dx.doi.org/10.1007/bf00776239.

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37

Wenner, B. R. "Invariance of infinite-dimensional classes of spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 1 (February 1985): 76–83. http://dx.doi.org/10.1017/s1446788700022618.

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Abstract:

AbstractThe central area of investigation is in the isolation of conditions on mappings which leave invariant the classes of locally finite-dimensional metric spaces and strongly countable-dimensional metric spaces. Examples of such properties are open and closed with discrete point-inverses, open and finite-to-one, or open, closed, and countable-to-one.

38

Dobson, Paul, and Joris Bierkens. "Infinite dimensional Piecewise Deterministic Markov Processes." Stochastic Processes and their Applications 165 (November 2023): 337–96. http://dx.doi.org/10.1016/j.spa.2023.08.010.

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39

Chow, Pao-Liu. "Infinite-dimensional Kolmogorov equations in gauss-sobolev spaces." Stochastic Analysis and Applications 14, no. 3 (January 1996): 257–82. http://dx.doi.org/10.1080/07362999608809439.

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40

Benth, Fred Espen, Giulia Di Nunno, and Iben Cathrine Simonsen. "Sensitivity analysis in the infinite dimensional Heston model." Infinite Dimensional Analysis, Quantum Probability and Related Topics 24, no. 02 (June 2021): 2150014. http://dx.doi.org/10.1142/s0219025721500144.

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Abstract:

We consider the infinite dimensional Heston stochastic volatility model proposed in Ref. 7. The price of a forward contract on a non-storable commodity is modeled by a generalized Ornstein–Uhlenbeck process in the Filipović space with this volatility. We prove a representation formula for the forward price. Then we consider prices of options written on these forward contracts and we study sensitivity analysis with computation of the Greeks with respect to different parameters in the model. Since these parameters are infinite dimensional, we need to reinterpret the meaning of the Greeks. For this we use infinite dimensional Malliavin calculus and a randomization technique.

41

Grigorescu, I. "An infinite dimensional central limit theorem for correlated martingales." Annales de l'Institut Henri Poincare (B) Probability and Statistics 40, no. 2 (April 2004): 167–96. http://dx.doi.org/10.1016/s0246-0203(03)00045-1.

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42

Wong, Wing Hung, and Thomas A. Severini. "On Maximum Likelihood Estimation in Infinite Dimensional Parameter Spaces." Annals of Statistics 19, no. 2 (June 1991): 603–32. http://dx.doi.org/10.1214/aos/1176348113.

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43

GRIGORESCU, I. "An infinite dimensional central limit theorem for correlated martingales." Annales de l?Institut Henri Poincare (B) Probability and Statistics 40, no. 2 (April 2004): 167–96. http://dx.doi.org/10.1016/j.anihpb.2003.03.001.

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44

BENDIKOV, A., and L. SALOFF-COSTE. "CENTRAL GAUSSIAN CONVOLUTION SEMIGROUPS ON COMPACT GROUPS: A SURVEY." Infinite Dimensional Analysis, Quantum Probability and Related Topics 06, no. 04 (December 2003): 629–59. http://dx.doi.org/10.1142/s0219025703001456.

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Abstract:

This is a survey article on Brownian motions on compact connected groups and the associated Gaussian convolution semigroups. The emphasize is on infinite dimensional groups such as the infinite dimensional torus and infinite products of special orthogonal groups. We discuss the existence of Brownian motions having nice properties such as marginales having a continuous density with respect to Haar measure. We relate the existence of these Brownian motions to the algebraic structure of the group. The results we describe reflect the conflicting effects of, on the one hand, the infinite dimensionality and, on the other hand, the compact nature of the underlying group.

45

Assing, Sigurd. "Infinite-dimensional Langevin equations: uniqueness and rate of convergence for finite-dimensional approximations." Probability Theory and Related Fields 120, no. 2 (June 2001): 143–67. http://dx.doi.org/10.1007/pl00008778.

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46

Feng, Shui, Laurent Miclo, and Feng-Yu Wang. "Poincaré Inequality for Dirichlet Distributions and Infinite-Dimensional Generalizations." Latin American Journal of Probability and Mathematical Statistics 14, no. 1 (2017): 361. http://dx.doi.org/10.30757/alea.v14-20.

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47

Benth, Fred Espen, and André Süss. "Integration theory for infinite dimensional volatility modulated Volterra processes." Bernoulli 22, no. 3 (August 2016): 1383–430. http://dx.doi.org/10.3150/15-bej696.

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48

Chakraborty, Anirvan, and Probal Chaudhuri. "The deepest point for distributions in infinite dimensional spaces." Statistical Methodology 20 (September 2014): 27–39. http://dx.doi.org/10.1016/j.stamet.2013.04.004.

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49

Chowdhury, Joydeep, and Probal Chaudhuri. "Convergence rates for kernel regression in infinite-dimensional spaces." Annals of the Institute of Statistical Mathematics 72, no. 2 (November 17, 2018): 471–509. http://dx.doi.org/10.1007/s10463-018-0697-2.

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50

Osada, Hirofumi. "Infinite-dimensional stochastic differential equations related to random matrices." Probability Theory and Related Fields 153, no. 3-4 (March 15, 2011): 471–509. http://dx.doi.org/10.1007/s00440-011-0352-9.

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