Mean-Square Analysis of Discretized Itô Diffusions for Heavy-tailed Sampling

Bounding the error of discretized Langevin algorithms for non-strongly log-concave targets

In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the Langevin Monte Carlo (LMC) algorithm, the Euler discretization of the Langevin diffusion. The second and the third schemes are, respectively, the kinetic Langevin Monte Carlo (KLMC) for differentiable potentials and the kinetic Langevin Monte Carlo for twice-differentiable potentials (KLMC2). The main focus is on the target densities that are smooth and log-concave on $\mathbb R^p$, but not necessarily strongly log-…

Heavy tailed priors: an alternative to non-informative priors in the estimation of proportions on small areas

We explore the Cauchy and a new heavy tailed (Fuquene, Perez and Pericchi (2011)) priors to estimate proportions on small areas. Hierarchical models and the Binomial likelihood in the exponential family form are used. We believe that the heavy tailed priors in survey sampling settings could be more effective than the choice of noninformative priors to eliminate antipathy towards methods that involve subjective elements or assumptions. To illustrate the robust Bayesian approach, we apply this methodology in a popular example: "the clement problem". Finally, we recommend to use the Cauchy prior …

具有重尾权重的深度神经网络的后验和变分推断

Posterior and variational inference for deep neural networks with heavy-tailed weights

本文在贝叶斯框架下提出基于重尾权重和ReLU激活的深度学习先验，证明其后验分布在多场景中达到近最优极小极大收缩率且无需超参数采样，还给出变分贝叶斯对应结果支持平均场近似的理论最优性。

在流形上使用兰格vin扩散进行采样和估计

Sampling and estimation on manifolds using the Langevin diffusion

本文提出了一种在流形上使用兰格vin扩散进行采样和估计的方法，推导了误差界并验证了其在不同曲率流形上的实用性。

从重尾噪声中恢复隐藏的周期性

Recovery of periodicities hidden in heavy-tailed noise

本文研究了离散信号在重尾噪声下的参数联合检测估计问题，提出基于反导数奇异性检测和两级选择过程的估计器构造方法，证明了参数估计的渐近一致性。

稳定相位恢复：Poisson模型与重尾模型下的最优速率

Stable Phase Retrieval: Optimal Rates in Poisson and Heavy-tailed Models

本文研究Poisson与重尾噪声模型下的相位恢复稳定保证，分析凸与非凸最小二乘估计器的最优误差率，构建统一分析框架并推广至稀疏相位恢复等相关问题。

再探切片采样的Wasserstein收缩与谱间隙

Wasserstein contraction and spectral gap of slice sampling revisited

本研究提出$k$-极切片采样（$k$-PSS）新方法，通过分析其Wasserstein收缩率与谱间隙，推进了对均匀和极切片采样的理论理解，还揭示了两类方法在重尾分布下的维度相关性能差异。

Safe and adaptive importance sampling: a mixture approach

This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous particles), and a "safe" heavy-tailed density. When the share of samples generated according to the safe density goes to zero but not too quickly, two results are established: (i) uniform convergence rates are derived for the policy toward the target density; (ii) a central limit theorem is obtained for the resulting integral estimates. The fact that the asy…

Schrödinger-Föllmer扩散的弱逼近

Weak approximation of Schrödinger-Föllmer diffusion

本文研究了Schrödinger-Föllmer扩散的Euler-Maruyama逼近的弱收敛性，证明了在温和正则性条件下，时间离散化过程的终端随机变量分布弱收敛于目标分布，为从给定分布采样提供了理论支撑。

On Set Size Distribution Estimation and the Characterization of Large Networks via Sampling

In this work we study the set size distribution estimation problem, where elements are randomly sampled from a collection of non-overlapping sets and we seek to recover the original set size distribution from the samples. This problem has applications to capacity planning, network theory, among other areas. Examples of real-world applications include characterizing in-degree distributions in large graphs and uncovering TCP/IP flow size distributions on the Internet. We demonstrate that it is hard to estimate the original set size distribution. The recoverability of original set size distributi…

陡势下随机游走Metropolis算法的鲁棒性

Robustness of random-walk Metropolis for steep potentials

本研究针对轻尾目标分布的采样问题，分析无梯度的随机游走Metropolis算法的鲁棒性，证明其接受概率稳定并可推导混合时间估计。