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It is shown how expectation maximization (EM) may be viewed as a message passing algorithm in factor graphs. In particular, a general EM message computation rule is identified. As a factor graph tool, EM may be used to break cycles in a…

Information Theory · Computer Science 2009-10-16 Justin Dauwels , Andrew Eckford , Sascha Korl , Hans-Andrea Loeliger

We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. ExpMsFEM…

Numerical Analysis · Mathematics 2023-02-07 Yifan Chen , Thomas Y. Hou , Yixuan Wang

Expectation maximisation (EM) is usually thought of as an unsupervised learning method for estimating the parameters of a mixture distribution, however it can also be used for supervised learning when class labels are available. As such, EM…

Machine Learning · Computer Science 2022-06-01 Graham W. Pulford

In this work, the development and implementation of the effective stochastic potential (ESP) method is presented to perform efficient conformational sampling of molecules. The overarching goal of this work is to alleviate the computational…

Chemical Physics · Physics 2018-08-01 Jeremy A. Scher , Michael G. Bayne , Amogh Srihari , Shikha Nangia , Arindam Chakraborty

The Expectation Maximization (EM) algorithm is the default algorithm for inference in latent variable models. As in any other field of machine learning, applications of latent variable models to very large datasets make the use of advanced…

Optimization and Control · Mathematics 2021-11-11 Aymeric Dieuleveut , Gersende Fort , Eric Moulines , Geneviève Robin

In various web applications like targeted advertising and recommender systems, the available categorical features (e.g., product type) are often of great importance but sparse. As a widely adopted solution, models based on Factorization…

Machine Learning · Computer Science 2019-11-19 Tong Chen , Hongzhi Yin , Quoc Viet Hung Nguyen , Wen-Chih Peng , Xue Li , Xiaofang Zhou

Mixture of linear regression is well studied in statistics and machine learning, where the data points are generated probabilistically using $k$ linear models. Algorithms like Expectation Maximization (EM) may be used to recover the ground…

Machine Learning · Computer Science 2026-04-08 Avishek Ghosh

Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual…

Machine Learning · Computer Science 2020-05-19 Emanuele Bugliarello , Swayambhoo Jain , Vineeth Rakesh

We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…

Numerical Analysis · Mathematics 2019-07-30 Yue Wu , Dimitris Kamilis , Nick Polydorides

Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…

Numerical Analysis · Mathematics 2021-10-12 Feng Wu , Kailing Zhang , Li Zhu , Jiayao Hu

A novel methodology for short-term energy forecasting using an Extreme Learning Machine ($\mathtt{ELM}$) is proposed. Using six years of hourly data collected in Corsica (France) from multiple energy sources (solar, wind, hydro, thermal,…

Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repeated passes over the full dataset. This has motivated…

Although personalized recommendation has been investigated for decades, the wide adoption of Latent Factor Models (LFM) has made the explainability of recommendations a critical issue to both the research community and practical application…

Information Retrieval · Computer Science 2017-08-23 Yongfeng Zhang

The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…

Statistics Theory · Mathematics 2022-05-03 Thomas Lartigue , Stanley Durrleman , Stéphanie Allassonnière

In the past decade, matrix factorization has been extensively researched and has become one of the most popular techniques for personalized recommendations. Nevertheless, the dot product adopted in matrix factorization based recommender…

Information Retrieval · Computer Science 2018-06-05 Shuai Zhang , Lina Yao , Yi Tay , Xiwei Xu , Xiang Zhang , Liming Zhu

Factorization machines (FMs) are machine learning predictive models based on second-order feature interactions and FMs with sparse regularization are called sparse FMs. Such regularizations enable feature selection, which selects the most…

Machine Learning · Statistics 2021-04-02 Kyohei Atarashi , Satoshi Oyama , Masahito Kurihara

In dealing with high-dimensional data, factor models are often used for reducing dimensions and extracting relevant information. The spectrum of covariance matrices from power data exhibits two aspects: 1) bulk, which arises from random…

Applications · Statistics 2019-10-22 Xin Shi , Robert Qiu

Several phenomena are available representing market activity: volumes, number of trades, durations between trades or quotes, volatility - however measured - all share the feature to be represented as positive valued time series. When…

Statistical Finance · Quantitative Finance 2021-07-14 Fabrizio Cipollini , Giampiero M. Gallo

We propose a novel exponentially-modified Gaussian (EMG) mixture residual model. The EMG mixture is well suited to model residuals that are contaminated by a distribution with positive support. This is in contrast to commonly used robust…

Machine Learning · Statistics 2019-02-18 Sebastian Ament , John Gregoire , Carla Gomes

Expected Shortfall (ES) is a coherent measure of tail risk that captures the average loss beyond a quantile threshold. Despite the growing literature on ES regression conditional on covariates, no existing work considers ES modeling in…

Methodology · Statistics 2026-04-15 Yujie Hou , Xinbing Kong , Yalin Wang , Bin Wu