Data assimilation refers to a set of algorithms designed to compute the
optimal estimate of a system's state by refining the prior prediction (known as
background states) using observed data. Variational assimilation methods rely
on the maximum likelihood approach to formulate a variational cost, with the
optimal state estimate derived by minimizing this cost. Although traditional
variational methods have achieved great success and have been widely used in
many numerical weather prediction centers, they generally assume Gaussian
errors in the background states, which limits the accuracy of these algorithms
due to the inherent inaccuracies of this assumption. In this paper, we
introduce VAE-Var, a novel variational algorithm that leverages a variational
autoencoder (VAE) to model a non-Gaussian estimate of the background error
distribution. We theoretically derive the variational cost under the VAE
estimation and present the general formulation of VAE-Var; we implement VAE-Var
on low-dimensional chaotic systems and demonstrate through experimental results
that VAE-Var consistently outperforms traditional variational assimilation
methods in terms of accuracy across various observational settings.

VAE-Var 是一种新的变分算法，利用变分自动编码器（VAE）对背景误差分布进行建模，理论推导了 VAE 估计下的变分成本，并提出了 VAE-Var 的一般公式；我们在低维混沌系统上实现了 VAE-Var，并通过实验结果证明了在不同观测设置下 VAE-Var 始终优于传统的变分同化方法。

VAE-Var：变分自编码增强的变分同化

VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilation

Weighted estimators are commonly used for estimating exposure effects in
observational settings to establish causal relations. These estimators have a
long history of development when the exposure of interest is binary and where
the weights are typically functions of an estimated propensity score. Recent
developments in optimization-based estimators for constructing weights in
binary exposure settings, such as those based on entropy balancing, have shown
more promise in estimating treatment effects than those methods that focus on
the direct estimation of the propensity score using likelihood-based methods.
This paper explores recent developments of entropy balancing methods to
continuous exposure settings and the estimation of population dose-response
curves using nonparametric estimation combined with entropy balancing weights,
focusing on factors that would be important to applied researchers in medical
or health services research. The methods developed here are applied to data
from a study assessing the effect of non-randomized components of an
evidence-based substance use treatment program on emotional and substance use
clinical outcomes.

本文研究了权重估计在连续曝光情况下的熵平衡优化估计方法，并结合熵平衡权重进行了非参数估计，聚焦于在医疗和健康服务研究中的实际应用和重要因素。该方法应用于评估基于证据的物质使用治疗程序的非随机组分对情感和物质使用临床结果的影响时的数据。