检索结果-内蒙古大学图书馆

Multilevel Particle Filters for a Class of Partially Observed Piecewise Deterministic Markov Processes

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Jasra, Ajay Kamatani, Kengo Maama, Mohamed Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Institute of Statistical Mathematics Tokyo190-0014 Japan

In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in [20], a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameter of that algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Ordinary differential equations

Transductive and inductive outlier detection with robust autoencoders 24

学校读者我要写书评

暂无评论

Transductive and inductive outlier detection with robust aut...

Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence

作者： Ofir Lindenbaum Yariv Aizenbud Yuval Kluger Faculty of Engineering Bar-Ilan University Ramat Gan Israel School of Mathematical Sciences Tel Aviv University Tel Aviv Israel Program in Applied Mathematics Yale University New Haven CT and Department of Pathology Yale University School of Medicine New Haven CT and Computational Biology & Bioinformatics Program Yale University New Haven CT

Accurate detection of outliers is crucial for the success of numerous data analysis tasks. In this context, we propose the Probabilistic Robust AutoEncoder (PRAE) that can simultaneously remove outliers during training (transductive) and learn a mapping that can be used to detect outliers in new data (inductive). We first present the Robust AutoEncoder (RAE) objective that excludes outliers while including a subset of samples (inliers) that can be effectively reconstructed using an AutoEncoder (AE). RAE minimizes the autoencoder's reconstruction error while incorporating as many samples as possible. This could be formulated via regularization by subtracting an ℓ0 norm, counting the number of selected samples from the reconstruction term. As this leads to an intractable combinatorial problem, we propose two probabilistic relaxations of RAE, which are differentiable and alleviate the need for a combinatorial search. We prove that the solution to the PRAE problem is equivalent to the solution of RAE. We then use synthetic data to demonstrate that PRAE can accurately remove outliers in various contamination levels. Finally, we show that using PRAE for outlier detection leads to state-of-the-art results for inductive and transductive outlier detection.

关键词：

Unbiased Estimation using Underdamped Langevin Dynamics

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Ruzayqat, Hamza 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 Thuwal23955-6900 Saudi Arabia

In this work we consider the unbiased estimation of expectations w.r.t. probability measures that have non-negative Lebesgue density, and which are known point-wise up-to a normalizing constant. We focus upon developing an unbiased method via the underdamped Langevin dynamics, which has proven to be popular of late due to applications in statistics and machine learning. Specifically in continuous-time, the dynamics can be constructed so that as the time goes to infinity they admit the probability of interest as a stationary measure. In many cases, time-discretized versions of the underdamped Langevin dynamics are used in practice which are run only with a fixed number of iterations. We develop a novel scheme based upon doubly randomized estimation as in [17, 19], which requires access only to time-discretized versions of the dynamics. The proposed scheme aims to remove the dicretization bias and the bias resulting from running the dynamics for a finite number of iterations. We prove, under standard assumptions, that our estimator is of finite variance and either has finite expected cost, or has finite cost with a high probability. To illustrate our theoretical findings we provide numerical experiments which verify our theory, which include challenging examples from Bayesian statistics and statistical *** Codes 60J22, 65C05, 65C40, 82C31, 62G08, 35Q56 © 2022, CC BY.

关键词： Dynamics

To Trust or Not to Trust: Evolutionary Dynamics of an Asymmetric N-player Trust Game

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Soo Lim, Ik. Masuda, Naoki School of Computing and Mathematical Sciences University of Greenwich LondonSE10 9LS United Kingdom Department of Mathematics and Computational and Data-Enabled Science and Engineering Program State University of New York Buffalo United States

Trusting others and reciprocating the received trust with trustworthy actions are fundaments of economic and social interactions. The trust game (TG) is widely used for studying trust and trustworthiness and entails a sequential interaction between two players, an investor and a trustee. It requires at least two strategies or options for an investor (e.g. to trust versus not to trust a trustee). According to the evolutionary game theory, the antisocial strategies (e.g. not to trust) evolve such that the investor and trustee end up with lower payoffs than those that they would get with the prosocial strategies (e.g. to trust). A generalisation of the TG to a multiplayer (i.e. more than two players) TG was recently proposed. However, its outcomes hinge upon two assumptions that various real situations may substantially deviate from: (i) investors are forced to trust trustees and (ii) investors can turn into trustees by imitation and vice versa. We propose an asymmetric multiplayer TG that allows investors not to trust and prohibits the imitation between players of different roles;instead, investors learn from other investors and the same for trustees. We show that the evolutionary game dynamics of the proposed TG qualitatively depends on the nonlinearity of the payoff function and the amount of incentives collected from and distributed to players through an institution. We also show that incentives given to trustees can be useful and sufficient to cost-effectively promote trust and trustworthiness among self-interested players. © 2023, CC BY.

关键词： Dynamics

Modeling of Measurement Error in Financial Returns Data

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Jasra, Ajay Maama, Mohamed Mijatović, Aleksandar School of Data Science The Chinese University of Hong Kong Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics University of Warwick United Kingdom

In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a Lévy process and the data as a measurement error there-of. The main technical difficulty of trying to infer this model, for instance Bayesian parameter estimation, is that the joint transition density of the return and maximum is seldom known, nor can it be simulated exactly. Based upon the novel stick breaking representation of [12] we provide an approximation of the model. We develop a Markov chain Monte Carlo (MCMC) algorithm to sample from the Bayesian posterior of the approximated posterior and then extend this to a multilevel MCMC method which can reduce the computational cost to approximate posterior expectations, relative to ordinary MCMC. We implement our methodology on several applications including for real data. Copyright © 2024, The Authors. All rights reserved.

关键词： Markov chains

Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

学校读者我要写书评

暂无评论

arXiv 2022年

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

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling;the approximation reduces the time (in terms of total observation time T) by O(T). This method is extended by using a multilevel MCMC method which can reduce the computational cost to achieve a given mean square error (MSE) versus using a single time discretization. Our methods are illustrated on simulated and real data. Copyright © 2022, The Authors. All rights reserved.

关键词： Mean square error

Alternative Role of Motif B in Template Dependent Polymerase Inhibition

学校读者我要写书评

暂无评论

Chinese Journal of Chemical Physics 2022年第3期35卷 407-412,I0001页

作者： Xueying Luo Tiantian Xu Xin Gao Lu Zhang State Key Laboratory of Structural Chemistry Fujian Institute of Research on the Structure of MatterChinese Academy of SciencesFuzhou 350002China University of Chinese Academy of Sciences Beijing 100049China Computer Science Program ComputerElectrical and Mathematical Sciences and Engineering(CEMSE)DivisionKing Abdullah University of Science and TechnologyThuwal 23955-6900King-dom of Saudi Arabia KAUST Computational Bioscience Research Center(CBRC) King Abdullah University of Science and TechnologyThuwal 23955-6900Kingdom of Saudi Arabia Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry Xiamen 361005China

Severe acute respiratory syndrome coronavirus 2(SARS-Co V-2) relies on the central molecular machine RNA-dependent RNA polymerase(Rd Rp) for the viral replication and transcription. Remdesivir at the template strand has been shown to effectively inhibit the RNA synthesis in SARS-Co V-2 Rd Rp by deactivating not only the complementary UTP incorporation but also the next nucleotide addition. However, the underlying molecular mechanism of the second inhibitory point remains unclear. In this work, we have performed molecular dynamics simulations and demonstrated that such inhibition has not directly acted on the nucleotide addition at the active site. Instead, the translocation of Remdesivir from +1 to-1 site is hindered thermodynamically as the posttranslocation state is less stable than the pre-translocation state due to the motif B residue G683. Moreover, another conserved residue S682 on motif B further hinders the dynamic translocation of Remdesivir due to the steric clash with the 1′-cyano substitution. Overall,our study has unveiled an alternative role of motif B in mediating the translocation when Remdesivir is present in the template strand and complemented our understanding about the inhibitory mechanisms exerted by Remdesivir on the RNA synthesis in SARS-Co V-2 Rd Rp.

关键词： SARS-CoV-2 RNA-dependent RNA polymerase Inhibitory mechanism Nu-cleotide analog Molecular dynamics simulation

Unbiased Parameter Estimation for Bayesian Inverse Problems

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China Applied Mathematics and Computational Science 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 estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

Representing and extending ensembles of parsimonious evolutionary histories with a directed acyclic graph

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Dumm, Will Barker, Mary Howard-Snyder, William DeWitt, William S. Matsen, Frederick A. Computational Biology Program Fred Hutchinson Cancer Research Center SeattleWA United States Howard Hughes Medical Institute Computational Biology Program Fred Hutchinson Cancer Research Center SeattleWA United States Paul G. Allen School of Computer Science and Engineering University of Washington SeattleWA United States Department of Electrical Engineering and Computer Sciences University of California BerkeleyCA United States Department of Genome Sciences University of Washington SeattleWA United States Department of Statistics University of Washington SeattleWA United States

In many situations, it would be useful to know not just the best phylogenetic tree for a given data set, but the collection of high-quality trees. This goal is typically addressed using Bayesian techniques, however, current Bayesian methods do not scale to large data sets. Furthermore, for large data sets with relatively low signal one cannot even store every good tree individually, especially when the trees are required to be bifurcating. In this paper, we develop a novel object called the "history subpartition directed acyclic graph" (or "history sDAG" for short) that compactly represents an ensemble of trees with labels (e.g. ancestral sequences) mapped onto the internal nodes. The history sDAG can be built efficiently and can also be efficiently trimmed to only represent maximally parsimonious trees. We show that the history sDAG allows us to find many additional equally parsimonious trees, extending combinatorially beyond the ensemble used to construct it. We argue that this object could be useful as the "skeleton" of a more complete uncertainty *** Codes 92-08 (Primary) 92B10, 92-04 (Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Phylogenetic