Partial Information Decomposition via Normalizing Flows in Latent Gaussian Distributions

• URL: http://arxiv.org/abs/2510.04417v1
• Date: Mon, 06 Oct 2025 01:08:34 GMT
• Title: Partial Information Decomposition via Normalizing Flows in Latent Gaussian Distributions
• Authors: Wenyuan Zhao, Adithya Balachandran, Chao Tian, Paul Pu Liang,
• Abstract summary: We propose a new gradient-based algorithm that substantially improves the computational efficiency of Gaussian PID (GPID)<n>We show that our proposed method provides more accurate and efficient PID estimates than existing baselines.<n>We evaluate a series of large-scale multimodal benchmarks to show its utility in real-world applications of quantifying PID in multimodal datasets.
• Score: 24.013410583573318
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The study of multimodality has garnered significant interest in fields where the analysis of interactions among multiple information sources can enhance predictive modeling, data fusion, and interpretability. Partial information decomposition (PID) has emerged as a useful information-theoretic framework to quantify the degree to which individual modalities independently, redundantly, or synergistically convey information about a target variable. However, existing PID methods depend on optimizing over a joint distribution constrained by estimated pairwise probability distributions, which are costly and inaccurate for continuous and high-dimensional modalities. Our first key insight is that the problem can be solved efficiently when the pairwise distributions are multivariate Gaussians, and we refer to this problem as Gaussian PID (GPID). We propose a new gradient-based algorithm that substantially improves the computational efficiency of GPID based on an alternative formulation of the underlying optimization problem. To generalize the applicability to non-Gaussian data, we learn information-preserving encoders to transform random variables of arbitrary input distributions into pairwise Gaussian random variables. Along the way, we resolved an open problem regarding the optimality of joint Gaussian solutions for GPID. Empirical validation in diverse synthetic examples demonstrates that our proposed method provides more accurate and efficient PID estimates than existing baselines. We further evaluate a series of large-scale multimodal benchmarks to show its utility in real-world applications of quantifying PID in multimodal datasets and selecting high-performing models.

Related papers

• An Elementary Approach to Scheduling in Generative Diffusion Models [55.171367482496755]
  An elementary approach to characterizing the impact of noise scheduling and time discretization in generative diffusion models is developed.<n> Experiments across different datasets and pretrained models demonstrate that the time discretization strategy selected by our approach consistently outperforms baseline and search-based strategies.
  arXiv  Detail & Related papers  (2026-01-20T05:06:26Z)
• Explainable Multimodal Regression via Information Decomposition [27.157278306251772]
  We propose a novel multimodal regression framework grounded in Partial Information Decomposition (PID)<n>Our framework outperforms state-of-the-art methods in both predictive accuracy and interpretability, while also enabling informed modality selection for efficient inference.
  arXiv  Detail & Related papers  (2025-12-26T18:07:18Z)
• Distributional encoding for Gaussian process regression with qualitative inputs [0.7342677574855652]
  We show that a generalization based on distributional encoding (DE) makes use of all samples of the target variable for a category.<n>Our approach is validated empirically, and we demonstrate state-of-the-art predictive performance on a variety of synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2025-06-05T09:35:02Z)
• Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling [22.256068524699472]
  In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. We combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence.
  arXiv  Detail & Related papers  (2024-08-13T08:09:05Z)
• DiffSG: A Generative Solver for Network Optimization with Diffusion Model [75.27274046562806]
  Generative diffusion models are popular in various cross-domain applications.<n>These models hold promise in tackling complex network optimization problems.<n>We propose a new framework for generative diffusion models called Diffusion Model-based Solution Generation.
  arXiv  Detail & Related papers  (2024-08-13T07:56:21Z)
• Rethinking Clustered Federated Learning in NOMA Enhanced Wireless Networks [60.09912912343705]
  This study explores the benefits of integrating the novel clustered federated learning (CFL) approach with non-independent and identically distributed (non-IID) datasets. A detailed theoretical analysis of the generalization gap that measures the degree of non-IID in the data distribution is presented. Solutions to address the challenges posed by non-IID conditions are proposed with the analysis of the properties.
  arXiv  Detail & Related papers  (2024-03-05T17:49:09Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)
• Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities [13.38077406934971]
  We derive a distributed provably-correct algorithm in the functional space of probability distributions over continuous variables.<n>We leverage these results to obtain new distributed estimators restricted to subsets of variables observed by individual agents.<n>This relates to applications such as cooperative localization and federated learning, where the data collected at any agent depends on a subset of all variables of interest.
  arXiv  Detail & Related papers  (2023-12-02T21:10:06Z)
• Heterogeneous Multi-Task Gaussian Cox Processes [61.67344039414193]
  We present a novel extension of multi-task Gaussian Cox processes for modeling heterogeneous correlated tasks jointly. A MOGP prior over the parameters of the dedicated likelihoods for classification, regression and point process tasks can facilitate sharing of information between heterogeneous tasks. We derive a mean-field approximation to realize closed-form iterative updates for estimating model parameters.
  arXiv  Detail & Related papers  (2023-08-29T15:01:01Z)
• Permutation Invariant Policy Optimization for Mean-Field Multi-Agent Reinforcement Learning: A Principled Approach [128.62787284435007]
  We propose the mean-field proximal policy optimization (MF-PPO) algorithm, at the core of which is a permutation-invariant actor-critic neural architecture. We prove that MF-PPO attains the globally optimal policy at a sublinear rate of convergence. In particular, we show that the inductive bias introduced by the permutation-invariant neural architecture enables MF-PPO to outperform existing competitors.
  arXiv  Detail & Related papers  (2021-05-18T04:35:41Z)
• Multi-Fidelity High-Order Gaussian Processes for Physical Simulation [24.033468062984458]
  High-fidelity partial differential equations (PDEs) are more expensive than low-fidelity ones. We propose Multi-Fidelity High-Order Gaussian Process (MFHoGP) that can capture complex correlations. MFHoGP propagates bases throughout fidelities to fuse information, and places a deep matrix GP prior over the basis weights.
  arXiv  Detail & Related papers  (2020-06-08T22:31:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.