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A GENERAL APPROACH TO FITTING MULTISTATE CURE MODELS BASED ON AN EXTENDED-LONG-FORMAT DATA STRUCTURE

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arXiv 2024年

作者： Jiang, Yilin van Tinteren, Harm Fiocco, Marta Leiden University Netherlands Princess Maxima Center Netherlands Leiden University Medical Center Netherlands

A multistate cure model is a statistical framework used to analyze and represent the transitions individuals undergo between different states over time, accounting for the possibility of being cured by initial treatment. This model is particularly useful in pediatric oncology where a proportion of the patient population achieves cure through treatment and therefore will never experience certain events. Despite its importance, no universal consensus exists on the structure of multistate cure models. Our study provides a novel framework for defining such models through a set of non-cure states. We develops a generalized algorithm based on the extended long data format, an extension of the traditional long data format, where a transition can be divided into two rows, each with a weight assigned reflecting the posterior probability of its cure status. The multistate cure model is built upon the current framework of multistate model and mixture cure model. The proposed algorithm makes use of the expectation-maximization (EM) algorithm and weighted likelihood representation such that it is easy to implement with standard packages. Additionally, it facilitates dynamic prediction. The algorithm is applied on data from the European Society for Blood and Marrow Transplantation (EBMT). Standard errors of the estimated parameters in the EM algorithm are obtained via a non-parametric bootstrap procedure, while the method involving the calculation of the second-derivative matrix of the observed log-likelihood is also presented. © 2024, CC BY.

关键词： expectation maximization algorithm

Symbolic Parameter Learning in Probabilistic Answer Set Programming

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arXiv 2024年

作者： Azzolini, Damiano Gentili, Elisabetta Riguzzi, Fabrizio Department of Environmental and Prevention Sciences University of Ferrara Ferrara Italy Department of Engineering University of Ferrara Ferrara Italy Department of Mathematics and Computer Science University of Ferrara Ferrara Italy

Parameter learning is a crucial task in the field of Statistical Relational Artificial Intelligence: given a probabilistic logic program and a set of observations in the form of interpretations, the goal is to learn the probabilities of the facts in the program such that the probabilities of the interpretations are maximized. In this paper, we propose two algorithms to solve such a task within the formalism of Probabilistic Answer Set Programming, both based on the extraction of symbolic equations representing the probabilities of the interpretations. The first solves the task using an off-the-shelf constrained optimization solver while the second is based on an implementation of the expectation maximization algorithm. Empirical results show that our proposals often outperform existing approaches based on projected answer set enumeration in terms of quality of the solution and in terms of execution time. The paper has been accepted at the ICLP2024 conference and is under consideration in Theory and Practice of Logic Programming (TPLP). © 2024, CC BY.

关键词： expectation maximization algorithm

The Log Private Company Valuation Model

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arXiv 2022年

作者： Gankhuu, Battulga Department of Applied Mathematics National University of Mongolia Ulaanbaatar Mongolia

For a public company, pricing and hedging models of options and equity–linked life insurance products have been sufficiently developed. However, for a private company, because of unobserved prices, pricing and hedging models of the European options and life insurance products are in their early stages of development. For this reason, this paper introduces a log private company valuation model, which is based on the dynamic Gordon growth model. In this paper, we obtain closed–form pricing and hedging formulas of the European options and equity–linked life insurance products for private companies. Also, the paper provides Maximum Likelihood (ML) estimations of our model, expectation maximization (EM) algorithm, and valuation formula for private companies. © 2022, CC BY.

关键词： expectation maximization algorithm

Identification and Uncertainty Quantification of Hybrid Models with Incomplete Data for Chemometric Applications

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SSRN

SSRN 2024年

作者： Cong, Hongri Wang, Bo Chen, Tao School of Computing and Mathematical Sciences University of Leicester LeicesterLE1 7RH United Kingdom School of Chemistry and Chemical Engineering University of Surrey GuildfordGU2 7XH United Kingdom

Hybrid models, which integrate multiple modelling approaches, are crucial in accurately capturing complex systems in chemical engineering. The identification and quantification of uncertainties in these models significantly influence their predictive performance and generalizability. In this paper, we introduce a novel hybrid model framework designed to work with incomplete datasets, a common scenario in chemometrics. For model identification and uncertainty quantification, two methods, namely the Monte Carlo expectation-maximization (MCEM) algorithm and the Plug-in method, are discussed and compared. Through extensive simulations and a real experimental data in modelling partition coefficients of chemicals, we demonstrate the usefulness of the model and the effectiveness of the proposed methods for model identification and uncertainty quantification, providing valuable insights into their practical applications in chemometrics. © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Functional Clustering for Longitudinal Associations between Social Determinants of Health and Stroke Mortality in the US

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arXiv 2024年

作者： Luo, Fangzhi Tan, Jianbin Zhang, Donglan Huang, Hui Shen, Ye Department of Epidemiology and Biostatistics College of Public Health University of Georgia AthensGA United States Department of Biostatistics and Bioinformatics School of Medicine Duke University DurhamNC United States Department of Foundations of Medicine NYU Grossman Long Island School of Medicine MineolaNY United States Center for Applied Statistics School of Statistics Renmin University of China Beijing China

Understanding the longitudinally changing associations between Social Determinants of Health (SDOH) and stroke mortality is essential for effective stroke management. Previous studies have uncovered significant regional disparities in the associations between SDOH and stroke mortality. However, existing studies have not utilized longitudinal associations to develop data-driven methods for regional division in stroke control. To fill this gap, we propose a novel clustering method to analyze SDOH-stroke mortality associations across US counties. To enhance the interpretability of the clustering outcomes, we introduce a novel regularized expectation-maximization algorithm equipped with sparsity- and smoothness-pursued penalties, aiming at simultaneous clustering and variable selection in longitudinal associations. As a result, we can identify key SDOH that contributes to longitudinal changes in stroke mortality. This facilitates the clustering of US counties based on the associations between these SDOH and stroke mortality. The effectiveness of our proposed method is demonstrated through extensive numerical studies. By applying our method to longitudinal data on SDOH and stroke mortality at the county level, we identify 18 important SDOH for stroke mortality and divide the US counties into two clusters based on these selected SDOH. Our findings unveil complex regional heterogeneity in the longitudinal associations between SDOH and stroke mortality, providing valuable insights into region-specific SDOH adjustments for mitigating stroke mortality. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm

Many Hands Make Light Work: Group Influence maximization in Evolving Social Networks

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IEEE Transactions on Big Data 2024年

作者： Ma, Yuliang Chen, Yu Wei, Peng Yuan, Ye Wang, Guoren Jiang, Zhong-Zhong Northeastern University College of Information Science and Engineering Shenyang110167 China Northeastern University College of Information Science and Engineering Shenyang110189 China Shandong Branch Industrial and Commercial Bank of China Jinan250001 China Beijing Institute of Technology School of Computer Science and Technology Beijing100081 China Northeastern University School of Business Administration The Institute of Behavioral and Service Operations Management Shenyang110167 China

As the adage 'many hands make light work' suggests, collaborative influence often surpasses individual influence. Inspired by this insight, we undertook a study on group influence maximization in evolving social networks, which is applicable to domains such as social media marketing and financial risk management. Our goal is to reveal how collaborative influence propagates in dynamic settings. Existing research concentrates predominantly on static networks and overlooks the dynamics of evolving social structures. Recognizing the limitations of current influence propagation models for our specific issue, we introduce an innovative model rooted in user behaviors. It considers temporal aspects, and we also suggest a methodology for assessing influence propagation probabilities based on both user behaviors and duration. We introduce an algorithm for extracting user groups using community search, improving efficiency through supergraph construction. Additionally, we present an influence maximization algorithm based on group dynamics with a 3-degree propagation framework. Recognizing diminishing influence, a 3-degree truncation strategy effectively enhances the group influence propagation efficiency. This approach efficiently captures the influence spread and accelerates convergence, boosting the search efficiency. Finally, we conducted comprehensive experiments on real-world and synthetic datasets. The results distinctly highlight the superiority of the proposed algorithms. © 2015 IEEE.

关键词： expectation maximization algorithm

High-dimensional variable clustering based on maxima of a weakly dependent random process

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arXiv 2023年

作者： Boulin, Alexis Di Bernardino, Elena Laloë, Thomas Toulemonde, Gwladys Université Côte d’Azur CNRS LJAD France Univ Montpellier CNRS Montpellier France Inria Lemon France

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random process among clusters. This class of models is identifiable, meaning that there exists a maximal element with a partial order between partitions, allowing for statistical inference. We also present an algorithm depending on a tuning parameter that recovers the clusters of variables without specifying the number of clusters a priori. Our work provides some theoretical insights into the consistency of our algorithm, demonstrating that under certain conditions it can effectively identify clusters in the data with a computational complexity that is polynomial in the dimension. A data-driven selection method for the tuning parameter is also proposed. To further illustrate the significance of our work, we applied our method to neuroscience and environmental real-datasets. These applications highlight the potential and versatility of the proposed *** Codes 60G70, 62H05, 62M99 © 2023, CC BY.

关键词： expectation maximization algorithm

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Geometric Sampling

arXiv 2023年

作者： Panahbehagh, Bardia Faculty of Mathematical Sciences and Computer Kharazmi University Tehran Iran

This paper introduces an innovative and intuitive finite population sampling method that have been developed using a unique geometric framework. In this approach, I represent first-order inclusion probabilities as bars on a two-dimensional graph. By manipulating the positions of these bars, researchers can create a wide range of different sampling designs. This geometric visualization of sampling designs not only leads to increased creativity for researchers to provide new efficient designs but also eliminates the need for complex mathematical algorithms. This novel approach holds significant promise for tackling complex challenges in sampling, such as maximizing entropy and achieving an optimal design. By applying a version of the greedy best-first search algorithm to this geometric approach for finding an optimal design, I have demonstrated the potential for integrating intelligent algorithms into finite population sampling. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Extending Cluster-Weighted Factor Analyzers for multivariate prediction and high-dimensional interpretability

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arXiv 2024年

作者： Qin, Xiaoke Martella, Francesca Subedi, Sanjeena School of Mathematics and Statistics Carleton University ON Canada Department of Statistical Sciences Sapienza University of Rome Italy

Cluster-weighted factor analyzers (CWFA) are a versatile class of mixture models designed to estimate the joint distribution of a random vector that includes a response variable along with a set of explanatory variables. They are particularly valuable in situations involving high dimensionality. This paper enhances CWFA models in two notable ways. First, it enables the prediction of multiple response variables while considering their potential interactions. Second, it identifies factors associated with disjoint groups of explanatory variables, thereby improving interpretability. This development leads to the introduction of the multivariate cluster-weighted disjoint factor analyzers (MCWDFA) model. An alternating expectation-conditional maximization algorithm is employed for parameter estimation. The effectiveness of the proposed model is assessed through an extensive simulation study that examines various scenarios. The proposal is applied to crime data from the United States, sourced from the UCI Machine Learning Repository, with the aim of capturing potential latent heterogeneity within communities and identifying groups of socioeconomic features that are similarly associated with factors predicting crime rates. Results provide valuable insights into the underlying structures influencing crime rates which may potentially be helpful for effective cluster-specific policymaking and social *** Codes 62H30 © 2024, CC BY.

关键词： expectation maximization algorithm