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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Deconvolution of arbitrary distribution functions and den...
[Submitted on 6 Oct 2025 (v1), last revised 10 Jul 2026 (this ve · 2025-10-06 · via stat updates on arXiv.org

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Abstract:In this article we propose a novel approach for the deconvolution of the distribution function associated with an arbitrary probability measure (and possibly existing density). We first show that the initial convolution equation always can be transformed to a convolution equation that involves a symmetric distribution function, whose characteristic function has its values in the unit interval. As a consequence, the characteristic function of the target measure turns out as the limit of a geometric series. By truncation of this series, approximations for distribution function and density are established. The convergence properties of these approximations are examined in detail across diverse setups.

Submission history

From: Henrik Kaiser Mr. [view email]
[v1] Mon, 6 Oct 2025 12:15:42 UTC (61 KB)
[v2] Fri, 10 Jul 2026 20:17:41 UTC (204 KB)