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Identification of ARX System Based on Shifted Asymmetric Laplace Distribution

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Identification of ARX System Based on Shifted Asymmetric Lap...

第三十八届中国控制会议

作者： Miao Yu Tianyi Zhang Xianqiang Yang Research Institute of Intelligent Control and System Harbin Institute of Technology

The identification of AutoRegressive eXogenous(ARX) model by outliers is addressed in this paper. Shifted(noncentralized) asymmetric Laplace(SAL) distribution and expectation maximization(EM) algorithm are employed to estimate the unknown model parameters. Outliers are common in the signal acquisition process and have a serious impact on data-driven modeling method. In this paper, the probability method is used to solve the problem of outliers. When the noise parameter is regarded as a prior exponential distribution, the model output obeys the SAL distribution which is robust to outliers. The known statistical properties of SAL distribution are applied to calculate the M-step in the EM algorithm and get the iterative parametric formula. The accuracy of the proposed algorithm is verified by a numerical simulation example.

关键词： shifted asymmetric Laplace distribution expectation maximization algorithm autoRegressive eXogenous model

Identification of non-causal systems with arbitrary switching modes

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arXiv 2024年

作者： Zhang, Yanxin Yu, Chengpu Fabiani, Filippo School of Automation Beijing Institute of Technology Beijing100081 China IMT School for Advanced Studies Lucca Piazza San Francesco 19 Lucca55100 Italy

We consider the identification of non-causal systems with arbitrary switching modes (NCS-ASM), a class of models essential for describing typical power load management and department store inventory dynamics. The simultaneous identification of causal-and-anticausal subsystems, along with the presence of possibly random switching sequences, however, make the overall identification problem particularly challenging. To this end, we develop an expectation-maximization (EM) based system identification technique, where the E-step proposes a modified Kalman filter (KF) to estimate the states and switching sequences of causal-and-anticausal subsystems, while the M-step consists in a switching least-squares algorithm to estimate the parameters of individual subsystems. We establish the main convergence features of the proposed identification procedure, also providing bounds on the parameter estimation errors under mild conditions. Finally, the effectiveness of our identification method is validated through two numerical simulations. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Minimization I.I.D. Prophet Inequality via Extreme Value Theory: A Unified Approach

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arXiv 2024年

作者： Livanos, Vasilis Mehta, Ruta EPFL Lausanne Switzerland & Archimedes AI Athens Greece Dept. of Computer Science University of Illinois at Urbana-Champaign IL61801 United States

The I.I.D. Prophet Inequality is a fundamental problem in optimal stopping theory where, given n independent random variables X1, . . ., Xn drawn from a known distribution D, one has to decide at every step i whether to stop and accept Xi or discard it forever and continue. The goal is to maximize (or minimize) the selected value and compete against the all-knowing prophet. For the maximization setting, a tight constant-competitive guarantee of ≈ 0.745 is well-known (Correa, Foncea, Hoeksma, Oosterwijk, Vredeveld, 2019), whereas the minimization setting is qualitatively different: the optimal constant is distribution-dependent and can be arbitrarily large (Livanos and Mehta, 2024). In this paper, we provide a novel framework via the lens of Extreme Value Theory to analyze optimal threshold algorithms. We show that the competitive ratio for the minimization setting has a closed form described by a function Λ, which depends only on the extreme value index γ;in particular, it corresponds to Λ(γ) for γ ≤ 0. Despite the contrast of the optimal guarantees for maximization and minimization, our framework turns out to be universal and is able to recover the results of (Kennedy and Kertz, 1991) for the maximization case as well. Surprisingly, the optimal competitive ratio for the maximization setting is given by the same function Λ(γ), but for γ ≥ 0. Along the way, we obtain several results on the algorithm and the prophet’s objectives from the perspective of extreme value theory, which might be of independent interest. We next study single-threshold algorithms for the minimization setting. Again, using the extreme value theory, we generalize the results of (Livanos and Mehta, 2024) which hold only for special classes of distributions, and obtain poly-logarithmic in n guarantees on the competitive ratio. Finally, we consider the k-multi-unit prophet inequality in the minimization setting and show that there exist constant-competitive single-threshold algorithms when k ≥ log

关键词： expectation maximization algorithm

A Sea Clutter Suppression algorithm by Statistics Estimation and Subspace Analysis

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A Sea Clutter Suppression Algorithm by Statistics Estimation...

2015 International Industrial Informatics and Computer Engineering Conference(IIICEC 2015)

作者： Wenhu Xue Ling Mao Tao Liu Electronics Engineering College Naval University of Engineering

To solve the problem of target detection in heavy sea clutter,we make simulation study on a subspace-based clutter suppression method to improve signal to clutter ratio in the predicted target location,and thus to improve the detection *** the compound Gaussian model of the sea clutter,we first estimate the statistics of sea clutter by expectation-maximization（EM） algorithm,then exploit a subspace-based approach to further mitigate sea *** the algorithm,the computational complexity is effectively *** the algorithm exhibits good performance of clutter *** results show that the algorithm is effective in sea clutter suppression.

关键词： subspace sea clutter expectation maximization algorithm

Distinctiveness maximization in Datasets Assemblage

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arXiv 2023年

作者： Wang, Tingting Huang, Shixun Bao, Zhifeng Culpepper, J. Shane Dedeoglu, Volkan Arablouei, Reza RMIT University MelbourneVIC Australia The University of Wollongong WollongongNSW Australia The University of Queensland St LuciaQLD Australia CSIRO’s Data61 PullenvaleQLD Australia

In this paper, given a user’s query set and budget, we aim to use the limited budget to help users assemble a set of datasets that can enrich a base dataset by introducing the maximum number of distinct tuples (i.e., maximizing distinctiveness). We prove this problem to be NP-hard. A greedy algorithm using exact distinctiveness computation attains an approximation ratio of (1 − e−1)/2, but it lacks efficiency and scalability due to its frequent computation of the exact distinctiveness marginal gain of any candidate dataset for selection. This requires scanning through every tuple in candidate datasets and thus is unaffordable in practice. To overcome this limitation, we propose an efficient machine learning (ML)-based method for estimating the distinctiveness marginal gain of any candidate dataset. This effectively eliminates the need to test each tuple individually. Estimating the distinctiveness marginal gain of a dataset involves estimating the number of distinct tuples in the tuple sets returned by each query in a query set across multiple datasets. This can be viewed as the cardinality estimation for a query set on a set of datasets, and the proposed method is the first to tackle this cardinality estimation problem. This is a significant advancement over prior methods that were limited to single-query cardinality estimation on a single dataset and struggled with identifying overlaps among tuple sets returned by each query in a query set across multiple datasets. Extensive experiments using five real-world data pools demonstrate that our algorithm, which utilizes ML-based distinctiveness estimation, outperforms all relevant baselines in effectiveness, efficiency, and scalability. A case study on two downstream ML tasks also highlights its potential to find datasets with more useful tuples to enhance the performance of ML tasks. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Bandit Profit-maximization for Targeted Marketing

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arXiv 2024年

作者： Huh, Joon Suk Vitercik, Ellen Kandasamy, Kirthevasan Computer Science Department UW–Madison United States Management Science and Engineering Department Stanford University United States Computer Science Department Stanford University United States

We study a sequential profit-maximization problem, optimizing for both price and ancillary variables like marketing expenditures. Specifically, we aim to maximize profit over an arbitrary sequence of multiple demand curves, each dependent on a distinct ancillary variable, but sharing the same price. A prototypical example is targeted marketing, where a firm (seller) wishes to sell a product over multiple markets. The firm may invest different marketing expenditures for different markets to optimize customer acquisition, but must maintain the same price across all markets. Moreover, markets may have heterogeneous demand curves, each responding to prices and marketing expenditures differently. The firm’s objective is to maximize its gross profit, the total revenue minus marketing costs. Our results are near-optimal algorithms for this class of problems in an adversarial bandit setting, where demand curves are arbitrary non-adaptive sequences, and the firm observes only noisy evaluations of chosen points on the demand curves. For n demand curves (markets), we prove a regret upper bound of Oe(nT3/4) and a lower bound of Ω((nT)3/4) for monotonic demand curves, and a regret bound of Θe (nT2/3) for demands curves that are monotonic in price and concave in the ancillary variables. © 2024, CC BY.

关键词： expectation maximization algorithm

LOGISTIC MULTIDIMENSIONAL DATA ANALYSIS FOR ORDINAL RESPONSE VARIABLES USING A CUMULATIVE LINK FUNCTION

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arXiv 2024年

作者： de Rooij, Mark Breemer, Ligaya Woestenburg, Dion Busing, Frank Methodology and Statistics Department Leiden University Netherlands

We present a multidimensional data analysis framework for the analysis of ordinal response variables. Underlying the ordinal variables, we assume a continuous latent variable, leading to cumulative logit models. The framework includes unsupervised methods, when no predictor variables are available, and supervised methods, when predictor variables are available. We distinguish between dominance variables and proximity variables, where dominance variables are analyzed using inner product models, whereas the proximity variables are analyzed using distance models. An expectation-majorization-minimization algorithm is derived for estimation of the parameters of the models. We illustrate our methodology with three empirical data sets highlighting the advantages of the proposed framework. A simulation study is conducted to evaluate the performance of the algorithm. © 2024, CC BY.

关键词： expectation maximization algorithm

A Novel Ecg Qrs Complex Detection algorithm Based on Dynamic Bayesian Network

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SSRN

SSRN 2024年

作者： Li, Qince Liu, Yang Na, Zhao Yuan, Yongfeng He, Runnan Heilongjiang Harbin150001 China School of Instrument Science and Engineering Southeast University Jiangsu Nanjing210000 China Medical School Tianjin University Tianjin300072 China

Accurate detection of the QRS complex, a crucial reference for heartbeat localization in electrocardiogram (ECG) signals, remains inadequate in wearable ECG devices due to complex noise interference. In this study, we propose a novel QRS complex detection method based on dynamic Bayesian network (DBN), integrating the probability distribution of RR intervals. Unlike methods focusing solely on ECG waveforms, our approach explicitly integrates ECG waveform and heart rhythm information into a unified probability model, enhancing noise robustness. Additionally, an unsupervised parameter optimization using expectation maximization (EM) adapts to individual differences of patients. Furthermore, several simplification strategies improve reasoning efficiency, and an online detection mode enables real-time applications. Our method outperforms other state-of-the-art QRS detection methods, including deep learning (DL) methods, on noisy datasets. In conclusion, the proposed DBN-based QRS detection algorithm demonstrates outstanding accuracy, noise robustness, generalization ability, real-time capability, and strong scalability, indicating its potential application in wearable ECG devices. © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

DEEP LEARNING METHODS FOR S SHAPED UTILITY MAXIMISATION WITH A RANDOM REFERENCE POINT

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arXiv 2024年

作者： Davey, Ashley Zheng, Harry Department of Mathematics Imperial College LondonSW7 2BZ United Kingdom

We consider the portfolio optimisation problem where the terminal function is an S-shaped utility applied at the difference between the wealth and a random benchmark process. We develop several numerical methods for solving the problem using deep learning and duality methods. We use deep learning methods to solve the associated Hamilton-Jacobi-Bellman equation for both the primal and dual problems, and the adjoint equation arising from the stochastic maximum principle. We compare the solution of this non-concave problem to that of concavified utility, a random function depending on the benchmark, in both complete and incomplete markets. We give some numerical results for power and log utilities to show the accuracy of the suggested algorithms. © 2024, CC BY.

关键词： expectation maximization algorithm