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Quantization Of Probability Measures In Maximum Mean Discrepancy Distance

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arXiv 2025年

作者： Mehraban, Zahra Pichler, Alois Faculty of Mathematics University of Technology ChemnitzD-09111 Germany

Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate optimal approximations by determining the best weights, followed by addressing the problem of optimal facility locations. To facilitate efficient computation, we reformulate the nonlinear objective as expectations over a product space, enabling the use of stochastic approximation methods. For the Gaussian kernel, we derive closed-form expressions to develop a deterministic optimization approach. By integrating stochastic approximation with deterministic techniques, our framework achieves precise and efficient quantization of continuous distributions, with significant implications for machine learning and signal processing applications. © 2025, CC BY.

关键词： expectation maximization algorithm

Allocating Variance to Maximize expectation

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arXiv 2025年

作者： Leme, Renato Purita Paes Stein, Cliff Teng, Yifeng Worah, Pratik Google Inc United States Google Inc. Columbia University United States

We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let OPT:= maxσ1,···,σn E ∑mj=1 maxi∈Sj Xi, where Xi are Gaussian, Sj ⊂ [n] and ∑ i σi2 = 1, then our theoretical results include: • We characterize the optimal variance allocation – it concentrates on a small subset of variables as |Sj| increases, • A polynomial time approximation scheme (PTAS) for computing OPT when m = 1, and • An O(log n) approximation algorithm for computing OPT for general m > 1. Such expectation maximization problems occur in diverse applications, ranging from utility maximization in auctions markets to learning mixture models in quantitative genetics. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Reasoning-Enhanced Self-Training for Long-Form Personalized Text Generation

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arXiv 2025年

作者： Salemi, Alireza Li, Cheng Zhang, Mingyang Mei, Qiaozhu Kong, Weize Chen, Tao Li, Zhuowan Bendersky, Michael Zamani, Hamed University of Massachusetts Amherst United States Google DeepMind United Kingdom University of Michigan United States

Personalized text generation requires a unique ability of large language models (LLMs) to learn from context that they often do not encounter during their standard training. One way to encourage LLMs to better use personalized context for generating outputs that better align with the user's expectations is to instruct them to reason over the user's past preferences, background knowledge, or writing style. To achieve this, we propose Reasoning-Enhanced Self-Training for Personalized Text Generation (REST-PG), a framework that trains LLMs to reason over personal data during response generation. REST-PG first generates reasoning paths to train the LLM's reasoning abilities and then employs expectation-maximization Reinforced Self-Training to iteratively train the LLM based on its own high-reward outputs. We evaluate REST-PG on the LongLaMP benchmark, consisting of four diverse personalized long-form text generation tasks. Our experiments demonstrate that REST-PG achieves significant improvements over state-of-the-art baselines, with an average relative performance gain of 14.5% on the benchmark. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Neural Parameter Estimation with Incomplete Data

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arXiv 2025年

作者： Sainsbury-Dale, Matthew Zammit-Mangion, Andrew Cressie, Noel Huser, Raphaël Saudi Arabia School of Mathematics and Applied Statistics University of Wollongong Australia

Advancements in artificial intelligence (AI) and deep learning have led to neural networks being used to generate lightning-speed answers to complex questions, to paint like Monet, or to write like Proust. Leveraging their computational speed and flexibility, neural networks are also being used to facilitate fast, likelihood-free statistical inference. However, it is not straightforward to use neural networks with data that for various reasons are incomplete, which precludes their use in many applications. A recently proposed approach to remedy this issue inputs an appropriately padded data vector and a vector that encodes the missingness pattern to a neural network. While computationally efficient, this "masking" approach can result in statistically inefficient inferences. Here, we propose an alternative approach that is based on the Monte Carlo expectation-maximization (EM) algorithm. Our EM approach is likelihood-free, substantially faster than the conventional EM algorithm as it does not require numerical optimization at each iteration, and more statistically efficient than the masking approach. This research represents a prototype problem that indicates how improvements could be made in AI by introducing Bayesian statistical thinking. We compare the two approaches to missingness using simulated incomplete data from two models: a spatial Gaussian process model, and a spatial Potts model. The utility of the methodology is shown on Arctic sea-ice data and cryptocurrency data. © 2025, CC BY.

关键词： expectation maximization algorithm

Missing data: A comparison of neural network and expectation maximization techniques

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CURRENT SCIENCE 2007年第11期93卷 1514-1521页

作者： Nelwamondo, Fulufhelo V. Mohamed, Shakir Marwala, Tshilidzi Univ Witwatersrand Sch Elect & Informat Engn ZA-2050 Johannesburg South Africa

Two techniques have emerged from the recent literature as candidate solutions to the problem of missing data imputation. These are the expectation maximization (EM) algorithm and the auto-associative neural network and genetic algorithm (GA) combination. Both these techniques have been discussed individually and their merits discussed at length in the available literature. However, they have not been compared with each other. This article provides a comparison of the two techniques using datasets of an industrial power plant, an industrial winding process and HIV seroprevalence survey data. Results show that the EM algorithm is more suitable and performs better in cases where there is little or no interdependency between the input variables, whereas the auto-associative neural network and GA combination is suitable when there are inherent nonlinear relationships between some of the given variables.

关键词： expectation maximization algorithm genetic algorithm missing data neural network

Design and analysis of direction of arrival using hybrid expectation-maximization and MUSIC for wireless communication

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OPTIK 2018年 170卷 48-55页

作者： Malla, Prince Priya Mukherjee, Amrit Routray, Sidheswar Palai, G. KL Univ Dept Elect & Commun Engn Guntur Andhra Prades India KIIT Univ Sch Elect Engn Bhubaneswar Odisha India GITA Dept Elect & Commun Engn Bhubaneswar Odisha India

As multiple signal classification (MUSIC) algorithm is unable to estimate the direction of arrival (DOA) of highly correlated or coherent signal, based on array processing and decomposition of covariance matrix of incident signals due to its lack of source identification. In the proposed hybrid model, we have considered expectation maximization (EM) algorithm for precise identification of the DOA of highly correlated signals in wireless communication applications. The proposed model is analysed, simulated and verified using two different source signals. The mathematical analysis shows substantial closeness with the simulated results. The robustness of the proposed algorithm is further verified by adding noise to the incident signals. The utilization of the EM algorithm in the proposed hybrid approach reduces the time requirement and mathematical complexity of MUSIC algorithm for DOA estimation. By exploiting the EM algorithm, the original transmitted signal and its arriving angle on the antenna element are estimated from the mixture of interferer's signal, transmitted signal, multipath component and noise. Hence it is straightforward to recognise the desired signal.

关键词： Direction of arrival Music algorithm expectation maximization algorithm Wireless communication

HYPERGRAPH LINK PREDICTION VIA HYPEREDGE COPYING

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arXiv 2025年

作者： He, Xie Chodrow, Philip S. Mucha, Peter J. Microsoft Research United States Middlebury College United States Dartmouth College United States

We propose a generative model of temporally-evolving hypergraphs in which hyperedges form via noisy copying of previous hyperedges. Our proposed model reproduces several stylized facts from many empirical hypergraphs, is learnable from data, and defines a likelihood over a complete hypergraph rather than ego-based or other sub-hypergraphs. Analyzing our model, we derive descriptions of node degree, edge size, and edge intersection size distributions in terms of the model parameters. We also show several features of empirical hypergraphs which are and are not successfully captured by our model. We provide a scalable stochastic expectation maximization algorithm with which we can fit our model to hypergraph data sets with millions of nodes and edges. Finally, we assess our model on a hypergraph link prediction task, finding that an instantiation of our model with just 11 parameters can achieve competitive predictive performance with large neural networks. © 2025, CC BY.

关键词： expectation maximization algorithm

Cluster weighted models for functional data

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arXiv 2025年

作者： Anton, Cristina Smith, Iain Department of Mathematics and Statistics MacEwan University 10700 – 104 Avenue EdmontonABT5J 4S2 Canada

We propose a method, funWeightClust, based on a family of parsimonious models for clustering heterogeneous functional linear regression data. These models extend cluster weighted models to functional data, and they allow for multivariate functional responses and predictors. The proposed methodology follows the approach used by the the functional high dimensional data clustering (funHDDC) method. We construct an expectation maximization (EM) algorithm for parameter estimation. Using simulated and benchmark data we show that funWeightClust outperforms funHDDC and several two-steps clustering methods. We also use funWeightClust to analyze traffic patterns in Edmonton, Canada. © 2025, CC BY-NC-ND.

关键词： expectation maximization algorithm

Priority-Based Weighted Constrained Crowd Judgement Analysis with Quantum Genetic algorithm 4th

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Priority-Based Weighted Constrained Crowd Judgement Analysis...

4th International Conference on Advanced Network Technologies and Intelligent Computing, ANTIC 2024

作者： Mandal, Suraj Chatterjee, Sujoy Mukhopadhyay, Anirban University of Kalyani Kalyani India University of Campinas Sao Paulo Brazil Indian Institute of Technology Kanpur Kanpur India

ISBN: (纸本)9783031837920

Crowdsourcing has already obtained a lot of attention from researchers due to the enormous power of solving complex problems in less time and at a minimal cost. Most of the research considers finding aggregated judgment from multiple diverse opinions of workers, and several algorithms such as majority-voting, weighted majority voting, and expectation-maximization (EM) algorithms are widely accepted. Recently, a relatively unexplored area of judgement analysis algorithm was introduced in the literature, and each crowd worker provides their opinions that comprise multiple components for a single question, and there is a constraint for each pair of components. However, in state-of-the-art approaches, the weight of the opinions is not considered. In this work, a new variant of the problem is introduced, while the weights between the components are considered. More importantly, the weights are not predefined, rather they are collected from the crowd workers. Thus, it can help us to explore many other solutions based on the users’ preferences which is very difficult to obtain from decision-makers if the crowdsourcing technique is not employed. Quantum computing has been a new approach to computer science that explores the idea of parallelism in computing. In this work, we have introduced a quantum genetic algorithm that explores solving the multiple objective-based weighted constrained crowd judgment analysis. In addition to that, we have introduced a new variant of constrained crowd judgment analysis that not only explores the solution to the multiple opinion-based solutions but also makes a better interpretation of the solutions by including textual information and additional weight parameters. The algorithm is applied to a real-life crowdsourced dataset obtained from the campus of the University of Kalyani. The experimental results demonstrate the applicability of the proposed method while providing a better solution compared to the traditional method. © The Author(s),

关键词： expectation maximization algorithm