There is a growing gap between the impressive results of deep image
generative models and classical algorithms that offer theoretical guarantees.
The former suffer from mode collapse or memorization issues, limiting their
application to scientific data. The latter require restrictive assumptions such
as log-concavity to escape the curse of dimensionality. We partially bridge
this gap by introducing conditionally strongly log-concave (CSLC) models, which
factorize the data distribution into a product of conditional probability
distributions that are strongly log-concave. This factorization is obtained
with orthogonal projectors adapted to the data distribution. It leads to
efficient parameter estimation and sampling algorithms, with theoretical
guarantees, although the data distribution is not globally log-concave. We show
that several challenging multiscale processes are conditionally log-concave
using wavelet packet orthogonal projectors. Numerical results are shown for
physical fields such as the $\varphi^4$ model and weak lensing convergence maps
with higher resolution than in previous works.

介绍了条件强对数凹模型的概念，该模型将数据分布因子化为强对数凹条件概率分布的乘积，并使用适应于数据分布的正交投影器来实现因子化，从而实现了有效的参数估计和抽样算法，并在物理字段等多个领域展示了该模型的实用性。

有条件强对数凹生成模型

Conditionally Strongly Log-Concave Generative Models

Scattering moments provide nonparametric models of random processes with
stationary increments. They are expected values of random variables computed
with a nonexpansive operator, obtained by iteratively applying wavelet
transforms and modulus nonlinearities, which preserves the variance. First- and
second-order scattering moments are shown to characterize intermittency and
self-similarity properties of multiscale processes. Scattering moments of
Poisson processes, fractional Brownian motions, L\'{e}vy processes and
multifractal random walks are shown to have characteristic decay. The
Generalized Method of Simulated Moments is applied to scattering moments to
estimate data generating models. Numerical applications are shown on financial
time-series and on energy dissipation of turbulent flows.

本文探讨了散射矩提供了随机过程的非参数模型，散射矩通过应用小波变换和非线性模量来计算随机变量的期望值，能够揭示多尺度过程的间歇性和自相似性属性，是数据生成模型的重要参数估计方式。