In any given machine learning problem, there may be many models that could
explain the data almost equally well. However, most learning algorithms return
only one of these models, leaving practitioners with no practical way to
explore alternative models that might have desirable properties beyond what
could be expressed within a loss function. The Rashomon set is the set of these
all almost-optimal models. Rashomon sets can be extremely complicated,
particularly for highly nonlinear function classes that allow complex
interaction terms, such as decision trees. We provide the first technique for
completely enumerating the Rashomon set for sparse decision trees; in fact, our
work provides the first complete enumeration of any Rashomon set for a
non-trivial problem with a highly nonlinear discrete function class. This
allows the user an unprecedented level of control over model choice among all
models that are approximately equally good. We represent the Rashomon set in a
specialized data structure that supports efficient querying and sampling. We
show three applications of the Rashomon set: 1) it can be used to study
variable importance for the set of almost-optimal trees (as opposed to a single
tree), 2) the Rashomon set for accuracy enables enumeration of the Rashomon
sets for balanced accuracy and F1-score, and 3) the Rashomon set for a full
dataset can be used to produce Rashomon sets constructed with only subsets of
the data set. Thus, we are able to examine Rashomon sets across problems with a
new lens, enabling users to choose models rather than be at the mercy of an
algorithm that produces only a single model.

首次提供了一种完整枚举稀疏决策树中 Rashomon set 的技术，并通过特定的数据结构提供高效的查询和抽样，该技术可以使用户在精度相近的所有模型中实现无前提选择，并展示了三个应用，包括研究变量的重要性、平衡精度和 F1 得分的 Rashomon set 的枚举以及使用完整数据集产生只使用数据子集构建的 Rashomon set。

探究稀疏决策树的整个拉绍门集

Exploring the Whole Rashomon Set of Sparse Decision Trees

The causal structure of any system can be analyzed at a multitude of spatial
and temporal scales. It has long been thought that while higher scale (macro)
descriptions of causal structure may be useful to observers, they are at best a
compressed description and at worse leave out critical information. However,
recent research applying information theory to causal analysis has shown that
the causal structure of some systems can actually come into focus (be more
informative) at a macroscale (Hoel et al. 2013). That is, a macro model of a
system (a map) can be more informative than a fully detailed model of the
system (the territory). This has been called causal emergence. While causal
emergence may at first glance seem counterintuitive, this paper grounds the
phenomenon in a classic concept from information theory: Shannon's discovery of
the channel capacity. I argue that systems have a particular causal capacity,
and that different causal models of those systems take advantage of that
capacity to various degrees. For some systems, only macroscale causal models
use the full causal capacity. Such macroscale causal models can either be
coarse-grains, or may leave variables and states out of the model (exogenous)
in various ways, which can improve the model's efficacy and its informativeness
via the same mathematical principles of how error-correcting codes take
advantage of an information channel's capacity. As model choice increase, the
causal capacity of a system approaches the channel capacity. Ultimately, this
provides a general framework for understanding how the causal structure of some
systems cannot be fully captured by even the most detailed microscopic model.

通过信息学理论，本文探讨了一些系统的因果结构在宏观尺度上更具信息量，特定的因果模型能够更好地利用系统特定的因果能力。最终导致这些系统的因果结构无法被微观模型完全捕获。

地图胜于领土

When the map is better than the territory

In this chapter, we will first present the most standard computational
challenges met in Bayesian Statistics, focussing primarily on mixture
estimation and on model choice issues, and then relate these problems with
computational solutions. Of course, this chapter is only a terse introduction
to the problems and solutions related to Bayesian computations. For more
complete references, see Robert and Casella (2004, 2009), or Marin and Robert
(2007), among others. We also restrain from providing an introduction to
Bayesian Statistics per se and for comprehensive coverage, address the reader
to Robert (2007), (again) among others.

介绍了贝叶斯统计中的混合估计和模型选择问题，以及与之相关的计算解决方案，参考文献主要为 Robert 和 Casella (2004, 2009) 和 Marin 和 Robert (2007) 等。