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Variational Probabilistic Multi-Hypothesis Tracking

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SSRN

SSRN 2024年

作者： Shin, Hyo-Sang Xu, Shuoyuan Tsourdos, Antonios School of Aerospace Transport and Manufacturing Cranfield University CranfieldMK43 0AL United Kingdom Cho Chun Shik Graduate School of Mobility Korea Advanced Institute of Science and Technology Daejeon34141 Korea Republic of

This paper proposes a novel multi-target tracking (MTT) algorithm for scenarios with arbitrary numbers of measurements per target. We propose the variational probabilistic multi-hypothesis tracking (VPMHT) algorithm based on the variational Bayesian expectation-maximisation (VBEM) algorithm to overcome limitations in the classic probabilistic multi-hypothesis tracking (PMHT) algorithm. The introduction of variational inference allows VPMHT to handle track-loss much better than the conventional PMHT, while preserving a similar or even better tracking accuracy. Extensive numerical simulations are conducted to validate the proposed algorithm. © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Learning to Rank for Multiple Retrieval-Augmented Models through Iterative Utility maximization

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arXiv 2024年

作者： Salemi, Alireza Zamani, Hamed University of Massachusetts Amherst United States

This paper investigates the design of a unified search engine to serve multiple retrieval-augmented generation (RAG) agents, each with a distinct task, backbone large language model (LLM), and retrieval-augmentation strategy. We introduce an iterative approach where the search engine generates retrieval results for these RAG agents and gathers feedback on the quality of the retrieved documents during an offline phase. This feedback is then used to iteratively optimize the search engine using a novel expectation-maximization algorithm, with the goal of maximizing each agent’s utility function. Additionally, we adapt this approach to an online setting, allowing the search engine to refine its behavior based on real-time individual agents feedback to better serve the results for each of them. Experiments on diverse datasets from the Knowledge-Intensive Language Tasks (KILT) benchmark demonstrates that our approach significantly on average outperforms competitive baselines across 18 RAG models. We also demonstrate that our method effectively "personalizes" the retrieval process for each RAG agent based on the collected feedback. Finally, we provide a comprehensive ablation study to explore various aspects of our method. © 2024, CC BY.

关键词： expectation maximization algorithm

Estimation and imputation of missing data in longitudinal models with Zero-Inflated Poisson response variable

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arXiv 2024年

作者： Martinez-Lobo, D.S. Martinez, Oscar Orlando Melo Gutierrez, Nelson Alirio Cruz Universidad del Bosque Colombia Departamento de Estadistica Facultad de Ciencias Universidad Nacional de Colombia Colombia Universitat de les Illes Balears Departament de Matemàtiques i Informàtica Spain

This research deals with the estimation and imputation of missing data in longitu- dinal models with a Poisson response variable inflated with zeros. A methodology is proposed that is based on the use of maximum likelihood, assuming that data is missing at random and that there is a correlation between the response vari- ables. In each of the times, the expectation maximization (EM) algorithm is used: in step E, a weighted regression is carried out, conditioned on the previous times that are taken as covariates. In step M, the estimation and imputation of the missing data are performed. The good performance of the methodology in dif- ferent loss scenarios is demonstrated in a simulation study comparing the model only with complete data, and estimating missing data using the mode of the data of each individual. Furthermore, in a study related to the growth of corn, it is tested on real data to develop the algorithm in a practical scenario. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm

Cross-Entropy Optimization for Hyperparameter Optimization in Stochastic Gradient-based Approaches to Train Deep Neural Networks

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arXiv 2024年

作者： Li, Kevin Li, Fulu

In this paper, we present a cross-entropy optimization method for hyperparameter optimization in stochastic gradient-based approaches to train deep neural networks. The value of a hyperparameter of a learning algorithm often has great impact on the performance of a model such as the convergence speed, the generalization performance metrics, etc. While in some cases the hyperparameters of a learning algorithm can be part of learning parameters, in other scenarios the hyperparameters of a stochastic optimization algorithm such as Adam [5] and its variants are either fixed as a constant or are kept changing in a monotonic way over time. We give an in-depth analysis of the presented method in the framework of expectation maximization (EM). The presented algorithm of cross-entropy optimization for hyperparameter optimization of a learning algorithm (CEHPO) can be equally applicable to other areas of optimization problems in deep learning. We hope that the presented methods can provide different perspectives and offer some insights for optimization problems in different areas of machine learning and beyond. © 2024, CC BY.

关键词： expectation maximization algorithm

Fairness in Social Influence maximization via Optimal Transport

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arXiv 2024年

作者： Chowdhary, Shubham De Pasquale, Giulia Lanzetti, Nicolas Stoica, Ana-Andreea Dörfler, Florian ETH Zürich Switzerland Eindhoven University of Technology Netherlands Max Planck Institute Tübingen Germany

We study fairness in social influence maximization, whereby one seeks to select seeds that spread a given information throughout a network, ensuring balanced outreach among different communities (e.g. demographic groups). In the literature, fairness is often quantified in terms of the expected outreach within individual communities. In this paper, we demonstrate that such fairness metrics can be misleading since they overlook the stochastic nature of information diffusion processes. When information diffusion occurs in a probabilistic manner, multiple outreach scenarios can occur. As such, outcomes such as "In 50% of the cases, no one in group 1 gets the information, while everyone in group 2 does, and in the other 50%, it is the opposite", which always results in largely unfair outcomes, are classified as fair by a variety of fairness metrics in the literature. We tackle this problem by designing a new fairness metric, mutual fairness, that captures variability in outreach through optimal transport theory. We propose a new seed-selection algorithm that optimizes both outreach and mutual fairness, and we show its efficacy on several real datasets. We find that our algorithm increases fairness with only a minor decrease (and at times, even an increase) in efficiency. © 2024, CC BY.

关键词： expectation maximization algorithm

Probabilistic Targeted Factor Analysis

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arXiv 2024年

作者： Herculano, Miguel C. Montoya-Blandón, Santiago Adam Smith Business School University of Glasgow United Kingdom

We develop a probabilistic variant of Partial Least Squares (PLS) we call Probabilistic Targeted Factor Analysis (PTFA), which can be used to extract common factors in predictors that are useful to predict a set of predetermined target variables. Along with the technique, we provide an efficient expectation-maximization (EM) algorithm to learn the parameters and forecast the targets of interest. We develop a number of extensions to missing-at-random data, stochastic volatility, and mixed-frequency data for real-time forecasting. In a simulation exercise, we show that PTFA outperforms PLS at recovering the common underlying factors affecting both features and target variables delivering better in-sample fit, and providing valid forecasts under contamination such as measurement error or outliers. Finally, we provide two applications in Economics and Finance where PTFA performs competitively compared with PLS and Principal Component Analysis (PCA) at out-of-sample forecasting. © 2024, CC BY-NC-SA.

关键词： expectation maximization algorithm

FAST AND ACCURATE algorithmS TO CALCULATE EXPECTED MODULARITY IN PROBABILISTIC NETWORKS

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arXiv 2024年

作者： Shen, Xin Rohner, Christian Magnani, Matteo Skerman, Fiona InfoLab Department of Information Technology Centre of Natural Hazards and Disaster Science Uppsala University Uppsala75105 Sweden InfoLab Department of Information Technology Uppsala University Uppsala75105 Sweden Department of Mathematics Uppsala University Uppsala75105 Sweden

Modularity maximization is a widely used community detection technique for deterministic networks. However, little research has been performed to develop efficient modularity calculation algorithms for probabilistic networks. Particularly, it is challenging to efficiently calculate expected modularity when all possible worlds are considered. To address this problem, we propose two algorithms, namely PWPEMOD and APWPEMOD, partitioning the possible worlds based on their modularities to significantly reduce the number of probability calculations. We evaluate the accuracy and time efficiency of our algorithms through comprehensive experiments. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Improving Tree Probability Estimation with Stochastic Optimization and Variance Reduction

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arXiv 2024年

作者： Xie, Tianyu Yuan, Musu Deng, Minghua Zhang, Cheng School of Mathematical Sciences Peking University Beijing100871 China Center for Quantitative Biology Peking University Beijing100871 China Center for Quantitative Biology School of Mathematical Sciences Center for Statistical Science Peking University Beijing100871 China School of Mathematical Sciences Center for Statistical Science Peking University Beijing100871 China

Probability estimation of tree topologies is one of the fundamental tasks in phylogenetic inference. The recently proposed subsplit Bayesian networks (SBNs) provide a powerful probabilistic graphical model for tree topology probability estimation by properly leveraging the hierarchical structure of phylogenetic trees. However, the expectation maximization (EM) method currently used for learning SBN parameters does not scale up to large data sets. In this paper, we introduce several computationally efficient methods for training SBNs and show that variance reduction could be the key for better performance. Furthermore, we also introduce the variance reduction technique to improve the optimization of SBN parameters for variational Bayesian phylogenetic inference (VBPI). Extensive synthetic and real data experiments demonstrate that our methods outperform previous baseline methods on the tasks of tree topology probability estimation as well as Bayesian phylogenetic inference using SBNs. © 2024, CC BY.

关键词： expectation maximization algorithm

Fast algorithms to improve fair information access in networks

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arXiv 2024年

作者： Windham, Dennis Robert Wendt, Caroline J. Crane, Alex Warr, Madelyn J. Shi, Freda Friedler, Sorelle A. Sullivan, Blair D. Clauset, Aaron Department of Computer Science University of Colorado United States University of Utah United States Haverford College United States BioFrontiers Institute University of Colorado United States Santa Fe Institute United States

We consider the problem of selecting k seed nodes in a network to maximize the minimum probability of activation under an independent cascade beginning at these seeds. The motivation is to promote fairness by ensuring that even the least advantaged members of the network have good access to information. Our problem can be viewed as a variant of the classic influence maximization objective, but it appears somewhat more difficult to solve: only heuristics are known. Moreover, the scalability of these methods is sharply constrained by the need to repeatedly estimate access probabilities. We design and evaluate a suite of 10 new scalable algorithms which crucially do not require probability estimation. To facilitate comparison with the state-of-the-art, we make three more contributions which may be of broader interest. We introduce a principled method of selecting a pairwise information transmission parameter used in experimental evaluations, as well as a new performance metric which allows for comparison of algorithms across a range of values for the parameter k. Finally, we provide a new benchmark corpus of 174 networks drawn from 6 domains. Our algorithms retain most of the performance of the state-of-the-art while reducing running time by orders of magnitude. Specifically, a meta-learner approach is on average only 20% less effective than the state-of-the-art on held-out data, but about 75 − 130 times faster. Further, the meta-learner’s performance exceeds the state-of-the-art on about 20% of networks, and the magnitude of its running time advantage is maintained on much larger networks. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm