Approximate Bayesian Inference via Bitstring Representations

• URL: http://arxiv.org/abs/2508.13598v1
• Date: Tue, 19 Aug 2025 08:08:17 GMT
• Title: Approximate Bayesian Inference via Bitstring Representations
• Authors: Aleksanteri Sladek, Martin Trapp, Arno Solin,
• Abstract summary: We propose performing probabilistic inference in the quantized, discrete parameter space created by representations.<n>This work advances scalable, interpretable machine learning by utilizing discrete approximations for probabilistic computations.
• Score: 15.754246455963907
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these representations, effectively enabling us to learn a continuous distribution using discrete parameters. We consider both 2D densities and quantized neural networks, where we introduce a tractable learning approach using probabilistic circuits. This method offers a scalable solution to manage complex distributions and provides clear insights into model behavior. We validate our approach with various models, demonstrating inference efficiency without sacrificing accuracy. This work advances scalable, interpretable machine learning by utilizing discrete approximations for probabilistic computations.

Related papers

• On the Hardness of Approximating Distributions with Tractable Probabilistic Models [2.9726600487327093]
  We study approximating distributions with probabilistic circuits with guarantees based on $f$-divergences.<n>We show that approximating an arbitrary distribution with bounded $f$-divergence is $mathsfNP$-hard for any model that can tractably compute marginals.
  arXiv  Detail & Related papers  (2025-06-02T03:35:07Z)
• Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning [79.65014491424151]
  We propose a quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM)<n>It enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces.<n>This paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
  arXiv  Detail & Related papers  (2025-05-08T11:48:21Z)
• Efficient Fairness-Performance Pareto Front Computation [51.558848491038916]
  We show that optimal fair representations possess several useful structural properties. We then show that these approxing problems can be solved efficiently via concave programming methods.
  arXiv  Detail & Related papers  (2024-09-26T08:46:48Z)
• Sparse Variational Student-t Processes [7.165002658532572]
  Student-t Processes are used to model heavy-tailed distributions and datasets with outliers.<n>We propose a sparse representation framework to allow Student-t Processes to be more flexible for real-world datasets.<n>We evaluate two proposed approaches on various synthetic and real-world datasets from UCI and Kaggle.
  arXiv  Detail & Related papers  (2023-12-09T12:55:20Z)
• Implicit Variational Inference for High-Dimensional Posteriors [7.924706533725115]
  In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler.
  arXiv  Detail & Related papers  (2023-10-10T14:06:56Z)
• Kernel Density Matrices for Probabilistic Deep Learning [8.486487001779416]
  In quantum mechanics, a density matrix is the most general way to describe the state of a quantum system. This paper introduces a novel approach to probabilistic deep learning, kernel density matrices. It provides a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables.
  arXiv  Detail & Related papers  (2023-05-26T12:59:58Z)
• Invariant Causal Mechanisms through Distribution Matching [86.07327840293894]
  In this work we provide a causal perspective and a new algorithm for learning invariant representations. Empirically we show that this algorithm works well on a diverse set of tasks and in particular we observe state-of-the-art performance on domain generalization.
  arXiv  Detail & Related papers  (2022-06-23T12:06:54Z)
• Learning Structured Gaussians to Approximate Deep Ensembles [10.055143995729415]
  This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approxorimator for dense image prediction tasks. We capture the uncertainty and structured correlations in the predictions explicitly in a formal distribution, rather than implicitly through sampling alone. We demonstrate the merits of our approach on monocular depth estimation and show that the advantages of our approach are obtained with comparable quantitative performance.
  arXiv  Detail & Related papers  (2022-03-29T12:34:43Z)
• Bayesian Graph Contrastive Learning [55.36652660268726]
  We propose a novel perspective of graph contrastive learning methods showing random augmentations leads to encoders. Our proposed method represents each node by a distribution in the latent space in contrast to existing techniques which embed each node to a deterministic vector. We show a considerable improvement in performance compared to existing state-of-the-art methods on several benchmark datasets.
  arXiv  Detail & Related papers  (2021-12-15T01:45:32Z)
• Sampling from Arbitrary Functions via PSD Models [55.41644538483948]
  We take a two-step approach by first modeling the probability distribution and then sampling from that model. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models.
  arXiv  Detail & Related papers  (2021-10-20T12:25:22Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• Learned Factor Graphs for Inference from Stationary Time Sequences [107.63351413549992]
  We propose a framework that combines model-based algorithms and data-driven ML tools for stationary time sequences. neural networks are developed to separately learn specific components of a factor graph describing the distribution of the time sequence. We present an inference algorithm based on learned stationary factor graphs, which learns to implement the sum-product scheme from labeled data.
  arXiv  Detail & Related papers  (2020-06-05T07:06:19Z)
• Scalable Approximate Inference and Some Applications [2.6541211006790983]
  In this thesis, we propose a new framework for approximate inference. Our proposed four algorithms are motivated by the recent computational progress of Stein's method. Results on simulated and real datasets indicate the statistical efficiency and wide applicability of our algorithm.
  arXiv  Detail & Related papers  (2020-03-07T04:33:27Z)

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.