Counterfactual explanations utilize feature perturbations to analyze the
outcome of an original decision and recommend an actionable recourse. We argue
that it is beneficial to provide several alternative explanations rather than a
single point solution and propose a probabilistic paradigm to estimate a
diverse set of counterfactuals. Specifically, we treat the perturbations as
random variables endowed with prior distribution functions. This allows
sampling multiple counterfactuals from the posterior density, with the added
benefit of incorporating inductive biases, preserving domain specific
constraints and quantifying uncertainty in estimates. More importantly, we
leverage Bayesian hierarchical modeling to share information across different
subgroups of a population, which can both improve robustness and measure
fairness. A gradient based sampler with superior convergence characteristics
efficiently computes the posterior samples. Experiments across several datasets
demonstrate that the counterfactuals estimated using our approach are valid,
sparse, diverse and feasible.

本文提出一个新的概率模型，用于计算模型的多个对抗性解释。该模型可以共享群体分组的信息，并保留领域特定的约束条件，同时评估不确定性，并得出合理、稀疏、多样和可行的结果。

贝叶斯分层模型用于反事实估计

Bayesian Hierarchical Models for Counterfactual Estimation

Meta-learning allows an intelligent agent to leverage prior learning episodes
as a basis for quickly improving performance on a novel task. Bayesian
hierarchical modeling provides a theoretical framework for formalizing
meta-learning as inference for a set of parameters that are shared across
tasks. Here, we reformulate the model-agnostic meta-learning algorithm (MAML)
of Finn et al. (2017) as a method for probabilistic inference in a hierarchical
Bayesian model. In contrast to prior methods for meta-learning via hierarchical
Bayes, MAML is naturally applicable to complex function approximators through
its use of a scalable gradient descent procedure for posterior inference.
Furthermore, the identification of MAML as hierarchical Bayes provides a way to
understand the algorithm's operation as a meta-learning procedure, as well as
an opportunity to make use of computational strategies for efficient inference.
We use this opportunity to propose an improvement to the MAML algorithm that
makes use of techniques from approximate inference and curvature estimation.

本文探讨了如何使用 Bayesian 模型和梯度下降进行 meta-learning，通过 MAML 算法应用到复杂的函数逼近器上，进一步提升了算法的性能，并利用近似推断和曲率估计技术提出了改进措施。

基于层次贝叶斯的梯度元学习重建

Recasting Gradient-Based Meta-Learning as Hierarchical Bayes

Linear regression is common in astronomical analyses. I discuss a Bayesian
hierarchical modeling of data with heteroscedastic and possibly correlated
measurement errors and intrinsic scatter. The method fully accounts for time
evolution. The slope, the normalization, and the intrinsic scatter of the
relation can evolve with the redshift. The intrinsic distribution of the
independent variable is approximated using a mixture of Gaussian distributions
whose means and standard deviations depend on time. The method can address
scatter in the measured independent variable (a kind of Eddington bias),
selection effects in the response variable (Malmquist bias), and departure from
linearity in form of a knee. I tested the method with toy models and
simulations and quantified the effect of biases and inefficient modeling. The
R-package LIRA (LInear Regression in Astronomy) is made available to perform
the regression.

本文介绍了一种贝叶斯分层建模方法，能够对异方差性和可能相关的测量误差以及内在离散度进行建模，同时完全考虑时间演化，并且该方法可处理独立变量的波动，选择效应和非线性偏离等问题；通过仿真模型测试了该方法并提供了 R 软件包 LIRA 用以进行回归分析。