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Antithetic Multilevel Particle Filters

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arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando Applied Mathematics and Computational Science Program United States Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate dimensional problems is the multilevel particle filter of [12]. This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of [10]. We show that for a class of diffusion problems, for ϵ > 0 given, that the cost to produce a mean square error (MSE) in estimation of the filter, of O(ϵ2) is O(ϵ−2 log(ϵ)2). In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of [12] has a cost of O(ϵ−2.5) to achieve the same MSE. We support our theory with numerical results in several examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman–Bucy Filters

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arXiv 2022年

作者： Álvarez Ballesteros, Miguel Ángel Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the development of an unbiased estimator for the ensemble Kalman–Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work [Rhee & Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization, and through the number of samples at each level. Our estimator will be specific to linear and Gaussian settings, where we know that the EnKBF is consistent, in the particle limit N → ∞, with the KBF. We highlight this for two particular variants of the EnKBF, i.e. the deterministic and vanilla variants, and demonstrate this on a linear Ornstein–Uhlenbeck process. We compare this with the EnKBF and the multilevel (MLEnKBF), for experiments with varying dimension size. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods. © 2022, CC BY-NC-SA.

关键词： Continuous time systems

Bayesian Parameter Inference for Partially Observed Stochastic Volterra Equations

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arXiv 2023年

作者： Jasra, Ajay Ruzayqat, Hamza Wu, Amin Applied Mathematics & Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider Bayesian parameter inference for a type of partially observed stochastic Volterra equation (SVE). SVEs are found in many areas such as physics and mathematical finance. In the latter field they can be used to represent long memory in unobserved volatility processes. In many cases of practical interest, SVEs must be time-discretized and then parameter inference is based upon the posterior associated to this time-discretized process. Based upon recent studies on time-discretization of SVEs (e.g. [24]) we use Euler-Maruyama methods for the afore-mentioned discretization. We then show how multilevel Markov chain Monte Carlo (MCMC) methods [19] can be applied in this context. In the examples we study, we give a proof that shows that the cost to achieve a 4 mean square error (MSE) of O(ϵ2), ϵ > 0, is O(ϵ− 4/2H+1 ), where H is the Hurst parameter. If one uses a single level MCMC method then the cost is O(ϵ−2(2H+3)/ 2H+1 ) to achieve the same MSE. We illustrate these results in the context of state-space and stochastic volatility models, with the latter applied to real *** Codes 62F15, 62M20, 60J10, 60J22, 65C40 © 2023, CC BY.

关键词： Mean square error

Unbiased and Multilevel Methods for a Class of Diffusions Partially Observed via Marked Point Processes

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arXiv 2023年

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity driven by a diffusion, with the associated marks also depending upon the diffusion process. We assume that one must resort to time-discretizing the diffusion process and develop particle and multilevel particle filters to recursively approximate the filter. In particular, we prove that our multilevel particle filter can achieve a mean square error (MSE) of O(∈2) (∈ > 0 and arbitrary) with a cost of O(∈-2.5) versus using a particle filter which has a cost of O(∈-3) to achieve the same MSE. We then show how this methodology can be extended to give unbiased (that is with no time-discretization error) estimators of the filter, which are proved to have finite variance and with high-probability have finite cost. Finally, we extend our methodology to the problem of online static-parameter estimation. Key words: Unbiased Methods, Multilevel Monte Carlo, Non-Linear Filtering, Point Processes, Parameter *** Codes 60G55, 60G35, 62M20, 62F30 © 2023, CC BY.

关键词： Diffusion

Hamiltonicity, vertex symmetry, and broadcasting of uni-directional hypercubes

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Hamiltonicity, vertex symmetry, and broadcasting of uni-dire...

Aizu International Symposium on Parallel Algorithms/Architecture Synthesis

作者： Shyh-Chain Chern Tai-Ching Tuan Jung-Sing Jwo Applied Mathematics Department Computer Science Program National Sun Yat-Sen University Kaohsiung Taiwan Department of Computer and Information Sciences Tunghai University Taichung Taiwan

ISBN: (纸本)081867038X

We show that the two uni-directional n-cubes, namely UHC1/sub n/ and UHC2/sub n/ proposed by Chou and Du (1990) as interconnection schemes are Hamiltonian. In addition, we show that (1) if n is even, both architectures are vertex symmetric; and (2) if n is odd, both architectures have exactly two vertex-symmetric components. By studying symmetry, we further prove that the maximum delay of one-port one-to-all broadcasting for either architecture is at most 1.5n.< >

关键词： Broadcasting Hypercubes Delay Network topology computer architecture computer networks Concurrent computing Distributed computing Contracts Bidirectional control

Value function approximation with diffusion wavelets and Laplacian eigenfunctions 05

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Value function approximation with diffusion wavelets and Lap...

Proceedings of the 19th International Conference on Neural Information Processing Systems

作者： Sridhar Mahadevan Mauro Maggioni Department of Computer Science University of Massachusetts Amherst MA Program in Applied Mathematics Department of Mathematics Yale University New Haven CT

We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one approach uses the eigenfunctions of the Laplacian, in effect performing a global Fourier analysis on the graph; the second approach is based on diffusion wavelets, which generalize classical wavelets to graphs using multiscale dilations induced by powers of a diffusion operator or random walk on the graph. Together, these approaches form the foundation of a new generation of methods for solving large Markov decision processes, in which the underlying representation and policies are simultaneously learned.

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Beyond trees: classification with sparse pairwise dependencies

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2020年第1期21卷 7728-7760页

作者： Yaniv Tenzer Amit Moscovich Mary Frances Dorn Boaz Nadler Clifford Spiegelman Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ Los Alamos National Laboratory Los Alamos NM Department of Statistics Texas A&M University College Station TX

Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attaining low classification errors. In this setting, the optimal classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges. In practice, observed data may not be well approximated by trees. Yet, motivated by the importance of pairwise dependencies for accurate classification, here we propose to approximate the optimal decision boundary by a sparse linear combination of the univariate and bivariate log-transformed densities. Our proposed approach is semi-parametric in nature: we non-parametrically estimate the univariate and bivariate densities, remove pairs of variables that are nearly independent using the Hilbert-Schmidt independence criterion, and finally construct a linear SVM using the retained log-transformed densities. We demonstrate on synthetic and real data sets, that our classifier, named SLB (sparse log-bivariate density), is competitive with other popular classification methods.

关键词： binary classification graphical model Bayesian network sparsity semi-parametric

Detection and Recognition of Vehicle Components Using Image Processing and Deep Learning Techniques 4

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Detection and Recognition of Vehicle Components Using Image ...

4th Research, Invention, and Innovation Congress: Innovative Electricals and Electronics, RI2C 2023

作者： Ketcham, Mahasak Ganokratanaa, Thittaporn Pramkeaw, Patiyuth Boonthai, Phumraphi Chumuang, Narumol Department of Information Technology Management King Mongkut's University of Technology North Bangkok Bangkok Thailand Applied Computer Science Program King Mongkut’s University of Technology Thonburi Bangkok Thailand Media Technology Program King Mongkut’s University of Technology Thonburi Bangkok Thailand Department Media Technology Muban Chombueng Rajabhat University Ratchaburi Thailand

ISBN: (纸本)9798350330618

This research study presents an algorithmic approach for the detection and identification of key components on license plates, including numerical digits, province codes, vehicle colors, and vehicle makes and types. The methodology integrates image processing techniques and deep learning methodologies to achieve comprehensive image analysis. The algorithm incorporates image preprocessing techniques to optimize the input images, followed by a deep neural network trained on a large annotated dataset. The algorithm utilizes image segmentation and character recognition techniques to detect and classify numerical digits on license plates. Similarly, it employs segmentation and classification processes for identifying province codes, vehicle colors, makes, and types. Extensive training ensures the algorithm's accuracy and robustness under varying conditions. The proposed algorithm demonstrates the potential for accurate license plate component detection and identification, with applications in law enforcement and traffic monitoring systems. . ©2023 IEEE.

关键词： License plates (automobile)

Non-Hermitian selective thermal emitter for thermophotovoltaics

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Non-Hermitian selective thermal emitter for thermophotovolta...

2023 Conference on Lasers and Electro-Optics, CLEO 2023

作者： Prasad, Ciril S. Raphaelson, Samuel C. Naik, Gururaj V. Department of Electrical and Computer Engineering Rice University HoustonTX77005 United States Applied Physics Graduate Program Smalley-Curl Institute Rice University HoustonTX77005 United States Department of Material Science and NanoEngineering Rice University HoustonTX United States

ISBN: (纸本)9781957171258

Selective thermal emitters can boost the efficiency of heat-to-electricity conversion in thermophotovoltaic systems only if their spectral selectivity is high. We demonstrate a non-Hermitian metasurface-based selective emitter operating at 1200 K in a GaSb-thermophotovoltaic cell. © Optica Publishing Group 2023 © 2023 The Author(s)

关键词： III-V semiconductors