Simulation-based inference (SBI) enables amortized Bayesian inference for
simulators with implicit likelihoods. But when we are primarily interested in
the quality of predictive simulations, or when the model cannot exactly
reproduce the observed data (i.e., is misspecified), targeting the Bayesian
posterior may be overly restrictive. Generalized Bayesian Inference (GBI) aims
to robustify inference for (misspecified) simulator models, replacing the
likelihood-function with a cost function that evaluates the goodness of
parameters relative to data. However, GBI methods generally require running
multiple simulations to estimate the cost function at each parameter value
during inference, making the approach computationally infeasible for even
moderately complex simulators. Here, we propose amortized cost estimation (ACE)
for GBI to address this challenge: We train a neural network to approximate the
cost function, which we define as the expected distance between simulations
produced by a parameter and observed data. The trained network can then be used
with MCMC to infer GBI posteriors for any observation without running
additional simulations. We show that, on several benchmark tasks, ACE
accurately predicts cost and provides predictive simulations that are closer to
synthetic observations than other SBI methods, especially for misspecified
simulators. Finally, we apply ACE to infer parameters of the Hodgkin-Huxley
model given real intracellular recordings from the Allen Cell Types Database.
ACE identifies better data-matching parameters while being an order of
magnitude more simulation-efficient than a standard SBI method. In summary, ACE
combines the strengths of SBI methods and GBI to perform robust and
simulation-amortized inference for scientific simulators.

本研究提出了一种基于神经网络的 ACE 方法，通过代替可能过于严格的贝叶斯后验分布，使用适应数据的成本函数来进行科学模拟器的仿真推断，从而同时减少了计算成本和提高了精度。

通过摊销费用估算实现科学模拟器的一般化贝叶斯推断

Generalized Bayesian Inference for Scientific Simulators via Amortized  Cost Estimation

We study generalized Bayesian inference under misspecification, i.e. when the
model is 'wrong but useful'. Generalized Bayes equips the likelihood with a
learning rate $\eta$. We show that for generalized linear models (GLMs),
$\eta$-generalized Bayes concentrates around the best approximation of the
truth within the model for specific $\eta \neq 1$, even under severely
misspecified noise, as long as the tails of the true distribution are
exponential. We derive MCMC samplers for generalized Bayesian lasso and
logistic regression and give examples of both simulated and real-world data in
which generalized Bayes substantially outperforms standard Bayes.

该研究探讨了广义贝叶斯推断在错配模型下的应用，包括广义线性模型，通过 MCMC 抽样来实现广义贝叶斯 Lasso 和 Logistic 回归，并在模拟和真实数据中展示了广义贝叶斯在表现上超过标准贝叶斯的优点。

安全贝叶斯广义线性回归

Safe-Bayesian Generalized Linear Regression

We present new excess risk bounds for general unbounded loss functions
including log loss and squared loss, where the distribution of the losses may
be heavy-tailed. The bounds hold for general estimators, but they are optimized
when applied to $\eta$-generalized Bayesian, MDL, and empirical risk
minimization estimators. In the case of log loss, the bounds imply convergence
rates for generalized Bayesian inference under misspecification in terms of a
generalization of the Hellinger metric as long as the learning rate $\eta$ is
set correctly. For general loss functions, our bounds rely on two separate
conditions: the $v$-GRIP (generalized reversed information projection)
conditions, which control the lower tail of the excess loss; and the newly
introduced witness condition, which controls the upper tail. The parameter $v$
in the $v$-GRIP conditions determines the achievable rate and is akin to the
exponent in the Tsybakov margin condition and the Bernstein condition for
bounded losses, which the $v$-GRIP conditions generalize; favorable $v$ in
combination with small model complexity leads to $\tilde{O}(1/n)$ rates. The
witness condition allows us to connect the excess risk to an "annealed" version
thereof, by which we generalize several previous results connecting Hellinger
and R\'enyi divergence to KL divergence.

本文提出了一种适用于广义无界损失函数的新型超额风险界限，并探讨了该界限对于广义贝叶斯推断在错误设置下具有的收敛速率以及其与赫林格度量的关系。