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Statistical Finite Elements via Interacting Particle Langevin Dynamics

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arXiv 2024年

作者： Glyn-Davies, Alex Duffin, Connor Kazlauskaite, Ieva Girolami, Mark Akyildiz, Ö. Deniz

In this paper, we develop a class of interacting particle Langevin algorithms to solve inverse problems for partial differential equations (PDEs). In particular, we leverage the statistical finite elements (statFEM) formulation to obtain a finite-dimensional latent variable statistical model where the parameter is that of the (discretised) forward map and the latent variable is the statFEM solution of the PDE which is assumed to be partially observed. We then adapt a recently proposed expectation-maximisation like scheme, interacting particle Langevin algorithm (IPLA), for this problem and obtain a joint estimation procedure for the parameters and the latent variables. We consider three main examples: (i) estimating the forcing for linear Poisson PDE, (ii) estimating the forcing for nonlinear Poisson PDE, and (iii) estimating diffusivity for linear Poisson PDE. We provide computational complexity estimates for forcing estimation in the linear case. We also provide comprehensive numerical experiments and preconditioning strategies that significantly improve the performance, showing that the proposed class of methods can be the choice for parameter inference in PDE models. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

MGM: Global Understanding of Audience Overlap Graphs for Predicting the Factuality and the Bias of News Media

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arXiv 2024年

作者： Manzoor, Muhammad Arslan Zeng, Ruihong Azizov, Dilshod Nakov, Preslav Liang, Shangsong Mohamed bin Zayed University of Artificial Intelligence United Arab Emirates Sun Yat-sen University China

In the current era of rapidly growing digital data, evaluating the political bias and factuality of news outlets has become more important for seeking reliable information online. In this work, we study the classification problem of profiling news media from the lens of political bias and factuality. Traditional profiling methods, such as Pre-trained Language Models (PLMs) and Graph Neural Networks (GNNs) have shown promising results, but they face notable challenges. PLMs focus solely on textual features, causing them to overlook the complex relationships between entities, while GNNs often struggle with media graphs containing disconnected components and insufficient labels. To address these limitations, we propose Me-diaGraphMind (MGM), an effective solution within a variational expectation-maximization (EM) framework. Instead of relying on limited neighboring nodes, MGM leverages features, structural patterns, and label information from globally similar nodes. Such a framework not only enables GNNs to capture long-range dependencies for learning expressive node representations but also enhances PLMs by integrating structural information and therefore improving the performance of both models. The extensive experiments demonstrate the effectiveness of the proposed framework and achieve new state-of-the-art results. Further, we share our repository1 which contains the dataset, code, and documentation. © 2024, CC BY.

关键词： expectation maximization algorithm

Computing Experiment-Constrained D-Optimal Designs

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arXiv 2024年

作者： Pillai, Aditya Ponte, Gabriel Fampa, Marcia Lee, Jon Singh, Mohit Xie, Weijun H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology AtlantaGA30332 United States IOE Dept. University of Michigan Federal University of Rio de Janeiro Brazil COPPE Federal University of Rio de Janeiro Brazil IOE Dept. University of Michigan Ann ArborMI United States

In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing for nonlinear relationships in factor levels. We develop scalable algorithms suitable for cases where the number of candidate experiments grows exponentially with the factor dimension, focusing on both first- and second-order models under design constraints. Particularly, our approach integrates convex relaxation with pricing-based local search techniques, which can provide upper bounds and performance guarantees. Unlike traditional local search methods, such as the "Fedorov exchange" and its variants, our method effectively accommodates arbitrary side constraints in the design space. Furthermore, it yields both a feasible solution and an upper bound on the optimal value derived from the convex relaxation. Numerical results highlight the efficiency and scalability of our algorithms, demonstrating superior performance compared to the state-of-the-art commercial software, JMP. © 2024, CC BY.

关键词： expectation maximization algorithm

Towards Efficient Recommendation for Films

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Towards Efficient Recommendation for Films

2017 5th International Conference on Mechatronics,Materials,Chemistry and Computer Engineering(ICMMCCE 2017)

作者： Qiong Jia Jing Zhou School of Computer Science Communication University of China

We first examine the techniques,development,and application future of the current recommender systems in the film *** recommendation techniques in current applications and the K-nearest neighbor（***） algorithm,in particular,is then introduced in *** is followed by an introduction to the expectation maximization（***） algorithm based on the Bayesian classifier,which has been applied to the classification and similarity calculations of ***,the movieeviews data in the NLTK（Natural Language Toolkit）library is used to facilitate *** evaluate the classification accuracy of the KNN algorithm and the EM algorithm based on the Bayesian *** experimental results demonstrate that,the classification accuracy of the EM algorithm for films is higher than that of the KNN algorithm and it is feasible and useful to apply the EM algorithm to films classification.

关键词： Classification Accuracy Collaborative Filtering expectation maximization algorithm K-nearest Neighbour Personalized Recommendation

Learning Robust Treatment Rules for Censored Data

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arXiv 2024年

作者： Cui, Yifan Liu, Junyi Shen, Tao Qi, Zhengling Chen, Xi Zhejiang University China Tsinghua University China National University of Singapore Singapore George Washington University United States New York University United States

There is a fast-growing literature on estimating optimal treatment rules directly by maximizing the expected outcome. In biomedical studies and operations applications, censored survival outcome is frequently observed, in which case the restricted mean survival time and survival probability are of great interest. In this paper, we propose two robust criteria for learning optimal treatment rules with censored survival outcomes;the former one targets at an optimal treatment rule maximizing the restricted mean survival time, where the restriction is specified by a given quantile such as median;the latter one targets at an optimal treatment rule maximizing buffered survival probabilities, where the predetermined threshold is adjusted to account the restricted mean survival time. We provide theoretical justifications for the proposed optimal treatment rules and develop a sampling-based difference-of-convex algorithm for learning them. In simulation studies, our estimators show improved performance compared to existing methods. We also demonstrate the proposed method using AIDS clinical trial data. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Computationally Efficient Estimation of Large Probit Models

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arXiv 2024年

作者： Ding, Patrick Imbens, Guido Qu, Zhaonan Ye, Yinyu Microsoft Corporation United States Stanford University Department of Economics Graduate School of Business United States Columbia University Data Science Institute United States Stanford University Department of Management Science and Engineering United States

Probit models are useful for modeling correlated discrete responses in many disciplines, including consumer choice data in economics and marketing. However, the Gaussian latent variable feature of probit models coupled with identification constraints pose significant computational challenges for its estimation and inference, especially when the dimension of the discrete response variable is large. In this paper, we propose a computationally efficient expectation-maximization (EM) algorithm for estimating large probit models. Our work is distinct from existing methods in two important aspects. First, instead of simulation or sampling methods, we apply and customize expectation propagation (EP), a deterministic method originally proposed for approximate Bayesian inference, to estimate moments of the truncated multivariate normal (TMVN) in the E (expectation) step. Second, we take advantage of a symmetric identification condition to transform the constrained optimization problem in the M (maximization) step into a one-dimensional problem, which is solved efficiently using Newton’s method instead of off-the-shelf solvers. Our method enables the analysis of correlated choice data in the presence of more than 100 alternatives, which is a reasonable size in modern applications, such as online shopping and booking platforms, but has been difficult in practice with probit models. We apply our probit estimation method to study ordering effects in hotel search results on Expedia’s online booking platform. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Preference Optimization as Probabilistic Inference

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arXiv 2024年

作者： Abdolmaleki, Abbas Piot, Bilal Shahriari, Bobak Springenberg, Jost Tobias Hertweck, Tim Joshi, Rishabh Oh, Junhyuk Bloesch, Michael Lampe, Thomas Heess, Nicolas Buchli, Jonas Riedmiller, Martin Google DeepMind United Kingdom

Existing preference optimization methods are mainly designed for directly learning from human feedback with the assumption that paired examples (preferred vs. dis-preferred) are available. In contrast, we propose a method that can leverage unpaired preferred or dis-preferred examples, and works even when only one type of feedback (positive or negative) is available. This flexibility allows us to apply it in scenarios with varying forms of feedback and models, including training generative language models based on human feedback as well as training policies for sequential decision-making problems, where learned (value) functions are available. Our approach builds upon the probabilistic framework introduced in (Dayan and Hinton, 1997), which proposes to use expectation-maximization (EM) to directly optimize the probability of preferred outcomes (as opposed to classic expected reward maximization). To obtain a practical algorithm, we identify and address a key limitation in current EM-based methods: when applied to preference optimization, they solely maximize the likelihood of preferred examples, while neglecting dis-preferred samples. We show how one can extend EM algorithms to explicitly incorporate dis-preferred outcomes, leading to a novel, theoretically grounded, preference optimization algorithm that offers an intuitive and versatile way to learn from both positive and negative feedback. © 2024, CC BY.

关键词： expectation maximization algorithm

Improvements on Scalable Stochastic Bayesian Inference Methods for Multivariate Hawkes Process

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arXiv 2023年

作者： Jiang, Alex Ziyu Rodriguez, Abel Department of Statistics University of Washington United States

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which, while widely used in the context of Bayesian inference, have rarely been applied in the context of MHPs: stochastic gradient expectation-maximization, stochastic gradient variational inference and stochastic gradient Langevin Monte Carlo. An important contribution of this paper is a novel approximation to the likelihood function that allows us to retain the computational advantages associated with conjugate settings while reducing approximation errors associated with the boundary effects. The comparisons are based on various simulated scenarios as well as an application to the study of risk dynamics in the Standard & Poor’s 500 intraday index prices among its 11 sectors. © 2023, CC BY.

关键词： expectation maximization algorithm

IMPROVING UNSUPERVISED CONSTITUENCY PARSING VIA MAXIMIZING SEMANTIC INFORMATION

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arXiv 2024年

作者： Chen, Junjie He, Xiangheng Miyao, Yusuke Bollegala, Danushka Department of Computer Science the University of Tokyo Japan GLAM – Group on Language Audio & Music Imperial College London United Kingdom Department of Computer Science the University of Liverpool United Kingdom

Unsupervised constituency parsers organize phrases within a sentence into a tree-shaped syntactic constituent structure that reflects the organization of sentence semantics. However, the traditional objective of maximizing sentence log-likelihood (LL) does not explicitly account for the close relationship between the constituent structure and the semantics, resulting in a weak correlation between LL values and parsing accuracy. In this paper, we introduce a novel objective for training unsupervised parsers: maximizing the information between constituent structures and sentence semantics (SemInfo). We introduce a bag-of-substrings model to represent the semantics and apply the probability-weighted information metric to estimate the SemInfo. Additionally, we develop a Tree Conditional Random Field (TreeCRF)-based model to apply the SemInfo maximization objective to Probabilistic Context-Free Grammar (PCFG) induction, the state-of-the-art non-ensemble method for unsupervised constituency parsing. Experiments demonstrate that SemInfo correlates more strongly with parsing accuracy than LL. Our algorithm significantly enhances parsing accuracy by an average of 7.85 points across five PCFG variants and in four languages, achieving state-of-the-art level results in three of the four languages. © 2024, CC BY-SA.

关键词： expectation maximization algorithm