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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

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

Recursive estimation and identification of wireless ad hoc channels from measurements 07

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Recursive estimation and identification of wireless ad hoc c...

Proceedings of the 3rd international conference on Wireless internet

作者： M. Olama Y. Li S. Djouadi T. Goodspeed T. Kuruganti University of Tennessee Knoxville TN Oak Ridge National Laboratory Oak Ridge TN

ISBN: (纸本)9789639799127

This paper is concerned with a time varying wireless ad hoc channel modeling, its parameter estimation and system identification from received signal measurement data. The channel model is represented in state space form, while the expectation maximization algorithm and Kalman filtering are used in the channel parameter and state estimation, respectively. The proposed algorithm is recursive, and therefore the inphase and quadrature components of the ad hoc channel and its parameters are estimated online from received signal measurements. The proposed algorithm is tested using measurement data collected from moving wireless sensor nodes, and the results are presented.

关键词： Kalman filter stochastic state space representation expectation maximization algorithm ad hoc channel

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

Addressing maximization Bias in Reinforcement Learning with Two-Sample Testing

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arXiv 2022年

作者： Waltz, Martin Okhrin, Ostap Technische Universität Dresden Dresden01062 Germany Leipzig Dresden Germany

Value-based reinforcement-learning algorithms have shown strong results in games, robotics, and other real-world applications. Overestimation bias is a known threat to those algorithms and can sometimes lead to dramatic performance decreases or even complete algorithmic failure. We frame the bias problem statistically and consider it an instance of estimating the maximum expected value (MEV) of a set of random variables. We propose the T-Estimator (TE) based on two-sample testing for the mean, that flexibly interpolates between over- and underestimation by adjusting the significance level of the underlying hypothesis tests. We also introduce a generalization, termed K-Estimator (KE), that obeys the same bias and variance bounds as the TE and relies on a nearly arbitrary kernel function. We introduce modifications of Q-Learning and the Bootstrapped Deep Q-Network (BDQN) using the TE and the KE, and prove convergence in the tabular setting. Furthermore, we propose an adaptive variant of the TE-based BDQN that dynamically adjusts the significance level to minimize the absolute estimation bias. All proposed estimators and algorithms are thoroughly tested and validated on diverse tasks and environments, illustrating the bias control and performance potential of the TE and KE. © 2022, CC BY.

关键词： expectation maximization algorithm

Sound Statistical Model Checking for Probabilities and Expected Rewards

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arXiv 2024年

作者： Budde, Carlos E. Hartmanns, Arnd Meggendorfer, Tobias Weininger, Maximilian Wienhöft, Patrick University of Trento Trento Italy University of Twente Enschede Netherlands Lancaster University Leipzig Leipzig Germany Institute of Science and Technology Austria Klosterneuburg Austria Dresden Germany Technische Universität Dresden Dresden Germany

Statistical model checking estimates probabilities and expectations of interest in probabilistic system models by using random simulations. Its results come with statistical guarantees. However, many tools use unsound statistical methods that produce incorrect results more often than they claim. In this paper, we provide a comprehensive overview of tools and their correctness, as well as of sound methods available for estimating probabilities from the literature. For expected rewards, we investigate how to bound the path reward distribution to apply sound statistical methods for bounded distributions, of which we recommend the Dvoretzky-Kiefer-Wolfowitz inequality that has not been used in SMC so far. We prove that even reachability rewards can be bounded in theory, and formalise the concept of limit-PAC procedures for a practical solution. The modes SMC tool implements our methods and recommendations, which we use to experimentally confirm our results. © 2024, CC BY.

关键词： expectation maximization algorithm

Cost-Effective Community-Hierarchy-Based Mutual Voting Approach for Influence maximization in Complex Networks

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arXiv 2024年

作者： Liu, Yi Tang, Xiaoan Pedrycz, Witold Zhang, Qiang The Key Laboratory of Process Optimization and Intelligent Decision-making Ministry of Education The School of Management Hefei University of Technology Hefei Box 270 Anhui Hefei230009 China The Department of Electrical and Computer Engineering University of Alberta EdmontonABT6G 2R3 Canada The Systems Research Institute Polish Academy of Sciences Warsaw00-901 Poland Istinye University Faculty of Engineering and Natural Sciences Department of Computer Engineering Sariyer Istanbul Turkey

Various types of promising techniques have come into being for influence maximization whose aim is to identify influential nodes in complex networks. In essence, real-world applications usually have high requirements on the balance between time complexity and accuracy of influential nodes identification. To address the challenges of imperfect node influence measurement and inefficient seed nodes selection mechanism in such class of foregoing techniques, this article proposes a novel approach called Cost-Effective Community-Hierarchy-Based Mutual Voting for influence maximization in complex networks. First, we develop a method for measuring the importance of different nodes in networks based on an original concept of Dual-Scale Community-Hierarchy Information that synthesizes both hierarchy structural information and community structural information of nodes. The community structural information contained in the nodes is measured by a new notion of Hierarchical-Community Entropy. Second, we develop a method named Cost-Effective Mutual-Influence-based Voting for seed nodes selection. Hereinto, a low-computational-cost mutual voting mechanism and an updating strategy called Lazy Score Updating Strategy are newly constructed for optimizing the selecting of seed nodes. Third, we develop a balance index to evaluate the performance of different methods in striking the tradeoff between time complexity and the accuracy of influential nodes identification. Finally, we demonstrate the approach performance over ten public datasets. The extensive experiments show that the proposed approach outperforms 16 state-of-the-art techniques on the balance between time complexity and accuracy of influential nodes identification. Compared with the method with the second highest value of the balance index, our approach can be improved by at most 9.29%. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Probability, Statistics, and Computational Science

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Probability, Statistics, and Computational Science

作者： Niko Beerenwinkel Juliane Siebourg

In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent *** this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.

关键词： Statistical Calculation Genomics Statistical Modeling Bayesian inference Hidden Markov models Maximum likelihood Bayesian networks Statistical models Dynamic programming Markov chains expectation maximization algorithm