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FAST DATA INVERSION FOR HIGH-DIMENSIONAL DYNAMICAL SYSTEMS FROM NOISY MEASUREMENTS

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arXiv 2025年

作者： Lin, Yizi Liu, Xubo Segall, Paul Gu, Mengyang Department of Statistics and Applied Probability University of California Santa Barbara United States Department of Geophysics Stanford University United States

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can be either fixed or estimated. We utilize an orthogonal factor loading matrix that avoids computing the inversion of the posterior covariance matrix at each time of the Kalman filter, and derive closed-form expressions in an expectation-maximization algorithm for parameter estimation, which substantially reduces the computational complexity without approximation. Our study is motivated by inversely estimating slow slip events from geodetic data, such as continuous GPS measurements. Extensive simulated studies illustrate higher accuracy and scalability of our approach compared to alternatives. By applying our method to geodetic measurements in the Cascadia region, our estimated slip better agrees with independently measured seismic data of tremor events. The substantial acceleration from our method enables the use of massive noisy data for geological hazard quantification and other applications. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

A mirror descent approach to maximum likelihood estimation in latent variable models

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arXiv 2025年

作者： Crucinio, Francesca Romana Department of Economics Social Studies Applied Mathematics and Statistics University of Turin Italy

We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the parameter space and the space of probability distributions and, contrary to other popular approaches, can be implemented when the latent variable takes values in discrete spaces. We provide a detailed theoretical analysis of both the mirror descent algorithm and its approximation via SMC. We experimentally show that the proposed algorithm outperforms standard expectation maximisation algorithms and is competitive with other popular methods for real-valued latent variables. © 2025, CC BY.

关键词： expectation maximization algorithm

Seal Your Backdoor with Variational Defense

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arXiv 2025年

作者： Sabolić, Ivan Grcić, Matej Šegvić, Siniša University of Zagreb Faculty of Electrical Engineering and Computing Unska 3 Zagreb10000 Croatia

We propose VIBE, a model-agnostic framework that trains classifiers resilient to backdoor attacks. The key concept behind our approach is to treat malicious inputs and corrupted labels from the training dataset as observed random variables, while the actual clean labels are latent. VIBE then recovers the corresponding latent clean label posterior through variational inference. The resulting training procedure follows the expectation-maximization (EM) algorithm. The E-step infers the clean pseudolabels by solving an entropy-regularized optimal transport problem, while the M-step updates the classifier parameters via gradient descent. Being modular, VIBE can seamlessly integrate with recent advancements in self-supervised representation learning, which enhance its ability to resist backdoor attacks. We experimentally validate the method effectiveness against contemporary backdoor attacks on standard datasets, a large-scale setup with 1k classes, and a dataset poisoned with multiple attacks. VIBE consistently outperforms previous defenses across all tested scenarios. © 2025, CC BY-NC-SA.

关键词： expectation maximization algorithm

Optimising expectation with guarantees for window mean payoff in Markov decision processes

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arXiv 2025年

作者： Gaba, Pranshu Guha, Shibashis Tata Institute of Fundamental Research Mumbai India

The window mean-payoff objective strengthens the classical mean-payoff objective by computing the mean-payoff over a finite window that slides along an infinite path. Two variants have been considered: in one variant, the maximum window length is fixed and given, while in the other, it is not fixed but is required to be bounded. In this paper, we look at the problem of synthesising strategies in Markov decision processes that maximise the window mean-payoff value in expectation, while also simultaneously guaranteeing that the value is above a certain threshold. We solve the synthesis problem for three different kinds of guarantees: sure (that needs to be satisfied in the worst-case, that is, for an adversarial environment), almost-sure (that needs to be satisfied with probability one), and probabilistic (that needs to be satisfied with at least some given probability p). We show that for fixed window mean-payoff objective, all the three problems are in PTIME, while for bounded window mean-payoff objective, they are in NP ∩ coNP, and thus have the same complexity as for maximising the expected performance without any guarantee. Moreover, we show that pure finite-memory strategies suffice for maximising the expectation with sure and almost-sure guarantees, whereas, for maximising expectation with a probabilistic guarantee, randomised strategies are necessary in general. © 2025, CC BY.

关键词： expectation maximization algorithm

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

Learning to quantify graph nodes

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arXiv 2025年

作者： Micheli, Alessio Moreo, Alejandro Podda, Marco Sebastiani, Fabrizio Simoni, William Tortorella, Domenico Dipartimento di Informatica Università di Pisa Largo Bruno Pontecorvo 3 Pisa56127 Italy Istituto di Scienza e Tecnologie dell’Informazione Consiglio Nazionale delle Ricerche Via Giuseppe Moruzzi 1 Pisa56124 Italy

Network Quantification is the problem of estimating the class proportions in unlabeled subsets of graph nodes. When prior probability shift is at play, this task cannot be effectively addressed by first classifying the nodes and then counting the class predictions. In addition, unlike non-relational quantification on i.i.d. datapoints, Network Quantification demands enhanced flexibility to capture a broad range of connectivity patterns, resilience to the challenge of heterophily, and efficiency to scale to larger networks. To meet these stringent requirements we introduce XNQ, a novel method that synergizes the flexibility and efficiency of the unsupervised node embeddings computed by randomized recursive Graph Neural Networks, with an expectation-maximization algorithm that provides a robust quantification-aware adjustment to the output probabilities of a calibrated node classifier. We validate the design choices underpinning our method through comprehensive ablation experiments. In an extensive evaluation, we find that our approach consistently and significantly improves on the best Network Quantification methods to date, thereby setting the new state of the art for this challenging task. Simultaneously, it provides a training speed-up of up to 10×–100× over other graph learning based methods. © 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