Categorical features are present in about 40% of real world problems,
highlighting the crucial role of encoding as a preprocessing component. Some
recent studies have reported benefits of the various target-based encoders over
classical target-agnostic approaches. However, these claims are not supported
by any statistical analysis, and are based on a single dataset or a very small
and heterogeneous sample of datasets. The present study explores the encoding
effects in an exhaustive sample of classification problems from OpenML
repository. We fitted linear mixed-effects models to the experimental data,
treating task ID as a random effect, and the encoding scheme and the various
characteristics of categorical features as fixed effects. We found that in
multiclass tasks, one-hot encoding and Helmert contrast coding outperform
target-based encoders. In binary tasks, there were no significant differences
across the encoding schemes; however, one-hot encoding demonstrated a
marginally positive effect on the outcome. Importantly, we found no significant
interactions between the encoding schemes and the characteristics of
categorical features. This suggests that our findings are generalizable to a
wide variety of problems across domains.

在一个来自 OpenML 仓库的大规模分类问题样本中，通过对实验数据拟合线性混合效应模型，我们发现在多类别任务中，独热编码和 Helmert 对比编码优于基于目标的编码器。在二分类任务中，不同的编码方案之间没有显著差异；然而，独热编码对结果有一定积极影响。重要的是，我们发现编码方案与分类特征的特性之间没有显著交互作用，这说明我们的发现适用于不同领域的各种问题。

编码分类数据：除了一位有效编码，还有更热门的编码方式吗？

Encoding categorical data: Is there yet anything 'hotter' than one-hot  encoding?

Maximum likelihood or restricted maximum likelihood (REML) estimates of the
parameters in linear mixed-effects models can be determined using the lmer
function in the lme4 package for R. As for most model-fitting functions in R,
the model is described in an lmer call by a formula, in this case including
both fixed- and random-effects terms. The formula and data together determine a
numerical representation of the model from which the profiled deviance or the
profiled REML criterion can be evaluated as a function of some of the model
parameters. The appropriate criterion is optimized, using one of the
constrained optimization functions in R, to provide the parameter estimates. We
describe the structure of the model, the steps in evaluating the profiled
deviance or REML criterion, and the structure of classes or types that
represents such a model. Sufficient detail is included to allow specialization
of these structures by users who wish to write functions to fit specialized
linear mixed models, such as models incorporating pedigrees or smoothing
splines, that are not easily expressible in the formula language used by lmer.

使用 R 语言的 lme4 包中的 lmer 函数可以使用最大似然或受限制的最大似然估计线性混合效应模型中的参数。该论文描述了模型的结构，评估剖面偏差或 REML 准则的步骤，以及表示这种模型的类或类型的结构。

使用 lme4 拟合线性混合效应模型

Fitting Linear Mixed-Effects Models using lme4

We propose an $\ell_1$-penalized estimation procedure for high-dimensional
linear mixed-effects models. The models are useful whenever there is a grouping
structure among high-dimensional observations, i.e. for clustered data. We
prove a consistency and an oracle optimality result and we develop an algorithm
with provable numerical convergence. Furthermore, we demonstrate the
performance of the method on simulated and a real high-dimensional data set.

本研究提出了一种针对高维线性混合效应模型的 $\ell_1$- 惩罚估计过程，该模型对于高维观测中存在分组结构的数据非常有用。我们证明了一致性和优化性结果，并开发了一种具有可证明数值收敛性的算法。此外，我们还在模拟和实际高维数据集上展示了该方法的性能。