Finding and describing sub-populations that are exceptional regarding a
target property has important applications in many scientific disciplines, from
identifying disadvantaged demographic groups in census data to finding
conductive molecules within gold nanoparticles. Current approaches to finding
such subgroups require pre-discretized predictive variables, do not permit
non-trivial target distributions, do not scale to large datasets, and struggle
to find diverse results.
To address these limitations, we propose Syflow, an end-to-end optimizable
approach in which we leverage normalizing flows to model arbitrary target
distributions, and introduce a novel neural layer that results in easily
interpretable subgroup descriptions. We demonstrate on synthetic and real-world
data, including a case study, that Syflow reliably finds highly exceptional
subgroups accompanied by insightful descriptions.

使用 Syflow 方法和正则化流来寻找和描述具有异常目标特性的子群，并提供易于解释的子群描述。

通过端到端最大化 KL 散度学习异常子群

Learning Exceptional Subgroups by End-to-End Maximizing KL-divergence

Classical epidemiological models assume homogeneous populations. There have
been important extensions to model heterogeneous populations, when the identity
of the sub-populations is known, such as age group or geographical location.
Here, we propose two new methods to model the number of people infected with
COVID-19 over time, each as a linear combination of latent sub-populations --
i.e., when we do not know which person is in which sub-population, and the only
available observations are the aggregates across all sub-populations. Method #1
is a dictionary-based approach, which begins with a large number of pre-defined
sub-population models (each with its own starting time, shape, etc), then
determines the (positive) weight of small (learned) number of sub-populations.
Method #2 is a mixture-of-$M$ fittable curves, where $M$, the number of
sub-populations to use, is given by the user. Both methods are compatible with
any parametric model; here we demonstrate their use with first (a)~Gaussian
curves and then (b)~SIR trajectories. We empirically show the performance of
the proposed methods, first in (i) modeling the observed data and then in (ii)
forecasting the number of infected people 1 to 4 weeks in advance. Across 187
countries, we show that the dictionary approach had the lowest mean absolute
percentage error and also the lowest variance when compared with classical SIR
models and moreover, it was a strong baseline that outperforms many of the
models developed for COVID-19 forecasting.

该研究提出了两种新的模型方法来预测 COVID-19 感染人数，分别为基于字典的方法和可拟合曲线的混合方法，通过子人群的线性组合进行建模，对 187 个国家的数据进行了实证研究，发现该字典方法在预测中表现最优。