Regularization

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Regularization Techniques

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Kullback-Leibler Divergence

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Divergence

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Bregman Divergences

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Entropy-Regularized Equilibrium Selection

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Kullback-Leibler Regularization

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Quantitative Idea Divergence

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638 papers

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Estimating Mixture Distributions via Stochastic Mirror Descent
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SILSM: A Sustainable Interactive Level Set Method for Progressive Refinement
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Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating
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RADAR: Relative Angular Divergence Across Representations
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Human-Centered Learning Mechanics: A Dynamical Framework for Entropy-Regulated Representation Learning
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The Value of Covariance Matching in Gaussian DDPMs and the Lanczos Sampler
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Implicit Regularization of Mini-Batch Training in Graph Neural Networks
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One LR Doesn't Fit All: Heavy-Tail Guided Layerwise Learning Rates for LLMs
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Detecting Atypical Clients in Federated Learning via Representation-Level Divergence
May 21, 2026Cristian Pérez-Corral, Jose I. Mestre, Alberto Fernández-Hernández +2Federated Learning Quantitative Idea Divergence
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May 20, 2026Zheyuan Zhang, Kaiwen Shi, Han Bao +3Multi-Objective Policy Optimization Calibrated Uncertainty
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Towards Context-Invariant Safety Alignment for Large Language Models
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May 19, 2026Wei-Bin Kou, Guangxu Zhu, Ming Tang +4Federated Learning Heterogeneous Edge Devices
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May 19, 2026Nikhil Cherian Kurian, Victor Caquilpan Parra, Abin Shoby +6Fairness-Aware Learning Medical Image Classification
Reducing Diffusion Model Memorization with Higher Order Langevin Dynamics
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MANGO: Meta-Adaptive Network Gradient Optimization for Online Continual Learning
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A Unified Framework for Data-Free One-Step Sampling via Wasserstein Gradient Flows
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May 15, 2026Gurjeet Jagwani, Stephen Thorp, Sinan Deger +1Likelihood Normalizing Flows
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Beyond What to Select: A Plug-and-play Oscillatory Data-Volume Scheduling for Efficient Model Training
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FrontierSmith: Synthesizing Open-Ended Coding Problems at Scale
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Rethinking Generalization in Graph Neural Networks: A Structural Complexity Perspective
May 13, 2026Peiyao Wang, Liang Bai, Xian Yang +2Graph Neural Networks Model Complexity
ArcVQ-VAE: A Spherical Vector Quantization Framework with ArcCosine Additive Margin
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Shortcut Mitigation via Spurious-Positive Samples
May 13, 2026Phuong Quynh Le, Jörg Schlötterer, Sari Sadiya +2Training Data Attribution Mitigation
Proximal-Based Generative Modeling for Bayesian Inverse Problems
May 13, 2026Boyang Zhang, Zhiguo Wang, Ya-Feng LiuScore-Based Diffusion Model Ill-Posed Inverse Problem
Hybrid Quantum-MambaVision: A Quantum-enhanced State Space Model for Calibrated Mixed-type Wafer Defect Detection
May 13, 2026Satwik Sai Prakash Sahoo, Jyoti Prakash Sahoo, Ting Wang +1Hybrid Quantum Neural Networks Scalable Defect Detection
On the Generalization of Knowledge Distillation: An Information-Theoretic View
May 13, 2026Bingying Li, Haiyun HeKnowledge Distillation Ontology-Amplified Distillation

May 24, 2026 · stat.MLJ/K move · Enter open · S save

Estimating Mixture Distributions via Stochastic Mirror Descent

Mohammadreza Ahmadypour, Tara Javidi, Farinaz Koushanfar

Department of Electrical and Computer Engineering University of California San Diego, San Diego, CA, USA

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of

M

-component mixture distributions, we propose a family of estimators derived from the stochastic mirror descent (SMD) algorithm. This optimization-based approach provides a principled and flexible framework that generalizes traditional estimators and proposes a variety of novel estimators through the choice of Bregman divergences. A key advantage of our method is that it scales efficiently with the number of candidate components

f_i

; that is, one can employ a large set of basis distributions in the mixture model without incurring significant computational overhead. This enables richer approximations and improved estimation accuracy. Moreover, in the case of categorical distribution (discrete outcomes) our estimators do not require a strict lower bound, in other words our framework does not require the precise knowledge of the support of the distribution. We demonstrate that, under mild conditions, the proposed

\varphi

-SMD estimators achieve near-optimal convergence rates in both Kullback-Leibler (KL) divergence and

\ell_2

-norm and offer practical benefits when computation is expensive. Our numerical analysis highlights improved performance guaranties over classical estimators, particularly in terms of sample efficiency and scalability.

Mixture Models Estimators Mirror Descent Bregman Divergences Cross-Entropy Losses

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