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Optimal investment and consumption under g- expected utility and general constraints in incomplete market

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arXiv 2025年

作者： Faidi, Wahid Department of Mathematics College of Science and Humanities Shaqra University Al Quwayiyah Saudi Arabia University of Tunis El Manar LAMSIN Tunis Tunisia

This article studies the problem of utility maximization in an incomplete market under a class of nonlinear expectations and general constraints on trading strategies. Using a g-martingale method, we provide an explicit solution to our optimization problem for different utility functions and characterize an optimal investment-consumption strategy through the solutions to quadratic BSDEs. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Fenchel-Young Variational Learning

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arXiv 2025年

作者： Sklaviadis, Sophia Agrawal, Sweta Farinhas, Antonio Martins, Andre Figueiredo, Mario Instituto de Telecomunicacoes Lisbon Portugal Instituto Superior Técnico Universidade de Lisboa Lisbon Portugal Unbabel Lisbon Portugal Lisbon Portugal

From a variational perspective, many statistical learning criteria involve seeking a distribution that balances empirical risk and regularization. In this paper, we broaden this perspective by introducing a new general class of variational methods based on Fenchel-Young (FY) losses, treated as divergences that generalize (and encompass) the familiar Kullback-Leibler divergence at the core of classical variational learning. Our proposed formulation—FY variational learning—includes as key ingredients new notions of FY free energy, FY evidence, FY evidence lower bound, and FY posterior. We derive alternating minimization and gradient backpropagation algorithms to compute (or lower bound) the FY evidence, which enables learning a wider class of models than previous variational formulations. This leads to generalized FY variants of classical algorithms, such as an FY expectation-maximization (FYEM) algorithm, and latent-variable models, such as an FY variational autoencoder (FYVAE). Our new methods are shown to be empirically competitive, often outperforming their classical counterparts, and most importantly, to have qualitatively novel features. For example, FYEM has an adaptively sparse E-step, while the FYVAE can support models with sparse observations and sparse posteriors. © 2025, CC BY.

关键词： expectation maximization algorithm

A generalized approach to label shift: the Conditional Probability Shift Model

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arXiv 2025年

作者： Teisseyre, Pawel Mielniczuk, Jan Institute of Computer Science Polish Academy of Sciences Jana Kazimierza 5 Warsaw01-248 Poland Faculty of Mathematics and Information Science Warsaw University of Technology Koszykowa 75 Warsaw00-662 Poland

In many practical applications of machine learning, a discrepancy often arises between a source distribution from which labeled training examples are drawn and a target distribution for which only unlabeled data is observed. Traditionally, two main scenarios have been considered to address this issue: covariate shift (CS), where only the marginal distribution of features changes, and label shift (LS), which involves a change in the class variable’s prior distribution. However, these frameworks do not encompass all forms of distributional shift. This paper introduces a new setting, Conditional Probability Shift (CPS), which captures the case when the conditional distribution of the class variable given some specific features changes while the distribution of remaining features given the specific features and the class is preserved. For this scenario we present the Conditional Probability Shift Model (CPSM) based on modeling the class variable’s conditional probabilities using multinomial regression. Since the class variable is not observed for the target data, the parameters of the multinomial model for its distribution are estimated using the expectation-maximization algorithm. The proposed method is generic and can be combined with any probabilistic classifier. The effectiveness of CPSM is demonstrated through experiments on synthetic datasets and a case study using the MIMIC medical database, revealing its superior balanced classification accuracy on the target data compared to existing methods, particularly in situations situations of conditional distribution shift and no apriori distribution shift, which are not detected by LS-based methods. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Multipath Component Power Delay Profile Based Joint Range and Doppler Estimation for AFDM-ISAC Systems

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arXiv 2025年

作者： Xiao, Fangqing Li, Zunqi Slock, Dirk Communication Systems Department Eurecom France

Integrated Sensing and Communication (ISAC) systems combine sensing and communication functionalities within a unified framework, enhancing spectral efficiency and reducing costs by utilizing shared hardware components. This paper investigates multipath component power delay profile (MPCPDP)-based joint range and Doppler estimation for Affine Frequency Division Multiplexing (AFDM)-ISAC systems. The path resolvability of the equivalent channel in the AFDM system allows the recognition of Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) paths within a single pilot symbol in fast time-varying channels. We develop a joint estimation model that leverages multipath Doppler shifts and delays information under the AFDM waveform. Utilizing the MPCPDP, we propose a novel ranging method that exploits the range-dependent magnitude of the MPCPDP across its delay spread by constructing a Nakagami-m statistical fading model for MPC channel fading and correlating the distribution parameters with propagation distance in AFDM systems. This method eliminates the need for additional time synchronization or extra hardware. We also transform the nonlinear Doppler estimation problem into a bilinear estimation problem using a First-order Taylor expansion. Moreover, we introduce the expectation maximization algorithm to estimate the hyperparameters and leverage the expectation Consistent algorithm to cope with high-dimensional integration challenges. Extensive numerical simulations demonstrate the effectiveness of our MPCPDP-based joint range and Doppler estimation in ISAC systems. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Generalized Tree-Informed Mixed Model Regression

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arXiv 2025年

作者： Allis, Jeremiah Jin, Xin Ghosh, Riddhi Pratim Department of Mathematics and Statistics Bowling Green State University United States Department of Mathematics The University of Tampa United States

The standard regression tree method applied to observations within clusters poses both methodological and implementation challenges. Effectively leveraging these data requires methods that account for both individual-level and sample-level effects. We propose Generalized Tree-Informed Mixed Model (GTIMM), which replaces the linear fixed effect in a generalized linear mixed model (GLMM) with the output of a regression tree. Traditional parameter estimation and prediction techniques, such as the expectation-maximization algorithm, scale poorly in high-dimensional settings, creating a computational bottleneck. To address this, we employ a quasi-likelihood framework with stochastic gradient descent for optimized parameter estimation. Additionally, we establish a theoretical bound for the mean squared prediction error. The predictive performance of our method is evaluated through simulations and compared with existing approaches. Finally, we apply our model to predict country-level GDP based on trade, foreign direct investment, unemployment, inflation, and geographic region. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Mixture models for data with unknown distributions

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arXiv 2025年

作者： Newman, M.E.J. Center for the Study of Complex Systems University of Michigan Ann ArborMI48109 United States

We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions. Fits to these models give us a way to cluster data with distributions of unknown form, including strongly non-Gaussian or multimodal distributions, and return both a division of the data and an estimate of the distributions, effectively performing clustering and density estimation within each cluster at the same time. We describe two fitting methods, one using an expectation-maximization (EM) algorithm and the other a Bayesian nonparametric method using a collapsed Gibbs sampler. The former is numerically efficient, but gives only point estimates of the probability densities. The latter is more computationally demanding but returns a full Bayesian posterior and also an estimate of the number of components. We demonstrate our methods with a selection of illustrative applications and give code implementing both algorithms. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

On the limits of some Bayesian model evaluation statistics

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arXiv 2025年

作者： Nguyen, Hien Duy Gupta, Mayetri Westerhout, Jacob Nguyen, TrungTin Department of Mathematics and Physical Science La Trobe University Melbourne Australia Institute of Mathematics for Industry Kyushu University Fukuoka Japan School of Mathematics and Statistics University of Glasgow Glasgow United Kingdom School of Mathematics and Physics University of Queensland Brisbane Australia School of Mathematical Sciences Queensland University of Technology Brisbane Australia

Model selection and order selection problems frequently arise in statistical practice. A popular approach to addressing these problems in the frequentist setting involves information criteria based on penalized maxima of log-likelihoods for competing models. In the Bayesian context, similar criteria are employed, replacing the maxima of log-likelihoods with their posterior expectations. Despite their popularity in applications, the large-sample behavior of these criteria—such as the deviance information criterion (DIC), Bayesian predictive information criterion (BPIC), and widely-applicable Bayesian information criterion (WBIC)—has received relatively little attention. In this work, we investigate the almost sure limits of these criteria and establish novel results on posterior and generalized posterior consistency, which are of independent interest. The utility of our theoretical findings is demonstrated via illustrative technical and numerical examples. © 2025, CC BY.

关键词： expectation maximization algorithm

expectation maximization estimates of the offspring probabilities in a class of multitype branching processes with binary family trees

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MATHEMATICAL POPULATION STUDIES 2017年第4期24卷 246-256页

作者： Daskalova, Nina Sofia Univ St Kliment Ohridski Fac Math & Informat 5 James Bourchier Blvd Sofia 1164 Bulgaria

When proliferating cells are counted in several independent colonies at some time points, the maximum likelihood estimates of the parameters of the multitype branching process are obtained trough an expectation maximization algorithm. In the case of an offspring distribution governed by a Markov branching process with binary family trees, this method, relying then on a partial knowledge of the tree, yields the same estimates as those computed with the complete knowledge of the tree.

关键词： cell proliferation expectation maximization algorithm maximum likelihood estimation multitype branching processes offspring distribution

An expectation maximization approach to Joint Modeling of Multidimensional Ratings derived from Multiple Annotators 17

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An Expectation Maximization approach to Joint Modeling of Mu...

17th Annual Conference of the International-Speech-Communication-Association (INTERSPEECH 2016)

作者： Ramakrishna, Anil Gupta, Rahul Grossman, Ruth B. Narayanan, Shrikanth S. Univ Southern Calif Signal Anal & Interpretat Lab Los Angeles CA 90007 USA Emerson Coll Dept Commun Sci & Disorders Boston MA 02116 USA

ISBN: (纸本)9781510833135

Ratings from multiple human annotators are often pooled in applications where the ground truth is hidden. Examples include annotating perceived emotions and assessing quality metrics for speech and image. These ratings are not restricted to a single dimension and can be multidimensional. In this paper, we propose an expectation-maximization based algorithm to model such ratings. Our model assumes that there exists a latent multidimensional ground truth that can be determined from the observation features and that the ratings provided by the annotators are noisy versions of the ground truth. We test our model on a study conducted on children with autism to predict a four dimensional rating of expressivity, naturalness, pronunciation goodness and engagement. Our goal in this application is to reliably predict the individual annotator ratings which can be used to address issues of cognitive load on the annotators as well as the rating cost. We initially train a baseline directly predicting annotator ratings from the features and compare it to our model under three different settings assuming: (i) each entry in the multidimensional rating is independent of others, (ii) a joint distribution among rating dimensions exists, (iii) a partial set of ratings to predict the remaining entries is available.

关键词： Multiple Annotator Modeling expectation maximization algorithm