arXiv:2511.04552v1 Announce Type: cross 
Abstract: Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to dynamic settings, enabling recursive posterior inference using simulation-based methods powered by deep neural networks. GBF does not require explicit density evaluations, making it particularly effective when observation or transition distributions are analytically intractable. To address parameter learning, we introduce the Generative-Gibbs sampler, which bypasses explicit density evaluation by iteratively sampling each variable from its implicit full conditional distribution. Such technique is broadly applicable and enables inference in hierarchical Bayesian models with intractable densities, including state-space models. We assess the performance of the proposed methodologies through both simulated and empirical studies, including the estimation of $\alpha$-stable stochastic volatility models. Our findings indicate that GBF significantly outperforms existing likelihood-free approaches in accuracy and robustness when dealing with intractable state-space models.

يُحدث تصفية بايزيان التوليد (GBF) ضجة في مجال النمذجة الإحصائية من خلال تقديم طريقة قوية ومرنة للاستدلال اللاحق في الأنظمة المعقدة. تعتمد هذه الطريقة المبتكرة على حساب بايزيان التوليد (GBC) وتستخدم الشبكات العصبية العميقة لتعزيز الاستدلال التكراري دون الحاجة إلى تقييمات كثافة صريحة. هذا مهم لأنه يفتح آفاقًا جديدة لتحليل النماذج غير الخطية وغير الغاوسية، والتي غالبًا ما تكون صعبة التعامل معها. مع استمرار الباحثين في استكشاف GBF، قد يؤدي ذلك إلى تحقيق إنجازات في تطبيقات متنوعة، من المالية إلى الهندسة.

El Filtrado Bayesiano Generativo (GBF) está causando revuelo en el campo de la modelización estadística al ofrecer un método robusto para la inferencia posterior en sistemas complejos. Este enfoque innovador se basa en el Cálculo Bayesiano Generativo (GBC) y utiliza redes neuronales profundas para mejorar la inferencia recursiva sin necesidad de evaluaciones de densidad explícitas. Esto es significativo porque abre nuevas posibilidades para analizar modelos no lineales y no gaussianos, que a menudo son difíciles de manejar. A medida que los investigadores continúan explorando el GBF, podría llevar a avances en diversas aplicaciones, desde finanzas hasta ingeniería.

Le filtrage bayésien génératif (GBF) fait sensation dans le domaine de la modélisation statistique en offrant une méthode robuste pour l'inférence postérieure dans des systèmes complexes. Cette approche innovante s'appuie sur le calcul bayésien génératif (GBC) et utilise des réseaux de neurones profonds pour améliorer l'inférence récursive sans avoir besoin d'évaluations de densité explicites. Cela est significatif car cela ouvre de nouvelles possibilités pour analyser des modèles non linéaires et non gaussiens, souvent difficiles à traiter. À mesure que les chercheurs continuent d'explorer le GBF, cela pourrait conduire à des percées dans diverses applications, de la finance à l'ingénierie.

Generative Bayesian Filtering (GBF) is making waves in the field of statistical modeling by offering a robust method for posterior inference in complex systems. This innovative approach builds on Generative Bayesian Computation (GBC) and utilizes deep neural networks to enhance recursive inference without the need for explicit density evaluations. This is significant because it opens up new possibilities for analyzing nonlinear and non-Gaussian models, which are often challenging to work with. As researchers continue to explore GBF, it could lead to breakthroughs in various applications, from finance to engineering.

Generative Bayesian Filtering and Parameter Learning

arXiv:2601.08100v1 Announce Type: new 
Abstract: Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to their data-dependent nature and their ability to capture algorithmic and geometric properties of learned models. However, most existing results rely on isotropic Gaussian posteriors, heavy use of spectral-norm concentration for weight perturbations, and largely architecture-agnostic analyses, which together limit both the tightness and practical relevance of the resulting bounds. To address these limitations, in this work, we propose a unified framework for PAC-Bayesian norm-based generalization by reformulating the derivation of generalization bounds as a stochastic optimization problem over anisotropic Gaussian posteriors. The key to our approach is a sensitivity matrix that quantifies the network outputs with respect to structured weight perturbations, enabling the explicit incorporation of heterogeneous parameter sensitivities and architectural structures. By imposing different structural assumptions on this sensitivity matrix, we derive a family of generalization bounds that recover several existing PAC-Bayesian results as special cases, while yielding bounds that are comparable to or tighter than state-of-the-art approaches. Such a unified framework provides a principled and flexible way for geometry-/structure-aware and interpretable generalization analysis in deep learning.

تشير دراسة جديدة إلى إطار موحد لـ PAC-Bayes للحدود العامة المعتمدة على المعايير، حيث تتناول التحديات المتعلقة بفهم سلوك التعميم في الشبكات العصبية العميقة. تعيد هذه الدراسة صياغة اشتقاق هذه الحدود كمشكلة تحسين عشوائي على توزيعات غاوسية غير متساوية، بهدف تعزيز الصلة العملية للنتائج.

Un nuevo estudio propone un marco PAC-Bayes unificado para los límites de generalización basados en normas, abordando los desafíos de comprender el comportamiento de generalización de las redes neuronales profundas. La investigación reformula la derivación de estos límites como un problema de optimización estocástica sobre posteriors gaussianos anisotrópicos, con el objetivo de mejorar la relevancia práctica de los resultados.

Une nouvelle étude propose un cadre PAC-Bayésien unifié pour les bornes de généralisation basées sur les normes, abordant les défis de la compréhension du comportement de généralisation des réseaux de neurones profonds. La recherche reformule la dérivation de ces bornes comme un problème d'optimisation stochastique sur des postérieurs gaussiens anisotropes, visant à améliorer la pertinence pratique des résultats.

A new study proposes a unified PAC-Bayesian framework for norm-based generalization bounds, addressing the challenges of understanding deep neural networks' generalization behavior. The research reformulates the derivation of these bounds as a stochastic optimization problem over anisotropic Gaussian posteriors, aiming to enhance the practical relevance of the results.

Towards A Unified PAC-Bayesian Framework for Norm-based Generalization Bounds

arXiv:2601.07944v1 Announce Type: new 
Abstract: Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural networks and foundation models has now given rise to a new paradigm in statistical modeling, in which Bayesian inference can be amortized through large-scale learned predictors. In amortized inference, substantial computation is invested upfront to train a neural network that can subsequently produce approximate posterior or predictions at negligible marginal cost across a wide range of tasks. At deployment, amortized inference offers substantial computational savings compared with traditional Bayesian procedures, which generally require repeated likelihood evaluations or Monte Carlo simulations for predictions for each new dataset.
  Despite the growing popularity of amortized inference, its statistical interpretation and its role within Bayesian inference remain poorly understood. This paper presents statistical perspectives on the working principles of several major neural architectures, including feedforward networks, Deep Sets, and Transformers, and examines how these architectures naturally support amortized Bayesian inference. We discuss how these models perform structured approximation and probabilistic reasoning in ways that yield controlled generalization error across a wide range of deployment scenarios, and how these properties can be harnessed for Bayesian computation. Through simulation studies, we evaluate the accuracy, robustness, and uncertainty quantification of amortized inference under varying signal-to-noise ratios and distributional shifts, highlighting both its strengths and its limitations.

أظهرت دراسة حديثة فعالية الاستدلال المدعوم في الإحصاءات البايزية، خاصة تحت تغيرات نسبة الإشارة إلى الضوضاء وتحولات التوزيع. تستخدم هذه الطريقة الشبكات العصبية العميقة لتبسيط عملية الاستدلال، مما يسمح بتوفير كبير في الحوسبة مقارنة بالأساليب البايزية التقليدية التي تتطلب تقييمات واسعة لاحتمالية.

Un estudio reciente ha evaluado la efectividad de la inferencia amortizada en estadísticas bayesianas, particularmente bajo variaciones en la relación señal-ruido y cambios en la distribución. Este método aprovecha redes neuronales profundas para agilizar el proceso de inferencia, permitiendo ahorros computacionales significativos en comparación con los enfoques bayesianos tradicionales que requieren evaluaciones extensas de verosimilitud.

Une étude récente a évalué l'efficacité de l'inférence amortie dans les statistiques bayésiennes, en particulier sous des variations de rapport signal-bruit et des changements de distribution. Cette méthode utilise des réseaux de neurones profonds pour rationaliser le processus d'inférence, permettant des économies computationnelles significatives par rapport aux approches bayésiennes traditionnelles qui nécessitent des évaluations de vraisemblance étendues.

A recent study has assessed the effectiveness of amortized inference in Bayesian statistics, particularly under varying signal-to-noise ratios and distribution shifts. This method leverages deep neural networks to streamline the inference process, allowing for significant computational savings compared to traditional Bayesian approaches that require extensive likelihood evaluations.

A Statistical Assessment of Amortized Inference Under Signal-to-Noise Variation and Distribution Shift

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Generative Bayesian Filtering and Parameter Learning

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