This paper investigates the consequences of encoding a $K$-valued categorical
variable incorrectly as $K$ bits via one-hot encoding, when using a Na\"{\i}ve
Bayes classifier. This gives rise to a product-of-Bernoullis (PoB) assumption,
rather than the correct categorical Na\"{\i}ve Bayes classifier. The
differences between the two classifiers are analysed mathematically and
experimentally. In our experiments using probability vectors drawn from a
Dirichlet distribution, the two classifiers are found to agree on the maximum a
posteriori class label for most cases, although the posterior probabilities are
usually greater for the PoB case.

通过错误地将一个 $K$ 值分类变量编码为 $K$ 位二进制数，将其用于朴素贝叶斯分类器，本文研究了这种编码方式的后果，从而得出了一个伯努利乘积（PoB）假设，而不是正确的分类朴素贝叶斯分类器。通过数学和实验分析了两种分类器之间的差异。在从狄利克雷分布中抽取的概率向量实验中，大多数情况下，这两种分类器在最大后验类标签上达成一致，尽管 PoB 情况下的后验概率通常更大。

朴素贝叶斯分类器和分类变量的一位有效编码

Naive Bayes Classifiers and One-hot Encoding of Categorical Variables

Considering the case where the response variable is a categorical variable
and the predictor is a random function, two novel functional sufficient
dimensional reduction (FSDR) methods are proposed based on mutual information
and square loss mutual information. Compared to the classical FSDR methods,
such as functional sliced inverse regression and functional sliced average
variance estimation, the proposed methods are appealing because they are
capable of estimating multiple effective dimension reduction directions in the
case of a relatively small number of categories, especially for the binary
response. Moreover, the proposed methods do not require the restrictive linear
conditional mean assumption and the constant covariance assumption. They avoid
the inverse problem of the covariance operator which is often encountered in
the functional sufficient dimension reduction. The functional principal
component analysis with truncation be used as a regularization mechanism. Under
some mild conditions, the statistical consistency of the proposed methods is
established. It is demonstrated that the two methods are competitive compared
with some existing FSDR methods by simulations and real data analyses.

本文提出了两种基于互信息和平方损失互信息的新型功能性充分降维（FSDR）方法，能够在分类数目相对较小的情况下估计多个有效的降维方向，尤其是对于二元响应，而且不需要线性条件平均值和常数协方差假设。在一些温和的条件下，本文建立了所提出方法的统计一致性，并通过模拟和实际数据分析证明了这两种方法的竞争性。

通过信息最大化进行功能充分降维并应用于分类

Functional sufficient dimension reduction through information  maximization with application to classification

This paper proposes a neural sequence-to-sequence text-to-speech (TTS) model
which can control latent attributes in the generated speech that are rarely
annotated in the training data, such as speaking style, accent, background
noise, and recording conditions. The model is formulated as a conditional
generative model based on the variational autoencoder (VAE) framework, with two
levels of hierarchical latent variables. The first level is a categorical
variable, which represents attribute groups (e.g. clean/noisy) and provides
interpretability. The second level, conditioned on the first, is a multivariate
Gaussian variable, which characterizes specific attribute configurations (e.g.
noise level, speaking rate) and enables disentangled fine-grained control over
these attributes. This amounts to using a Gaussian mixture model (GMM) for the
latent distribution. Extensive evaluation demonstrates its ability to control
the aforementioned attributes. In particular, we train a high-quality
controllable TTS model on real found data, which is capable of inferring
speaker and style attributes from a noisy utterance and use it to synthesize
clean speech with controllable speaking style.

该研究提出了一种神经序列到序列的文本转语音模型，基于变分自动编码器（VAE）框架，通过两级分层潜变量，实现对生成语音中很少被训练数据标记的潜在属性的控制，包括口音、语速、噪声等，其中第一级为类别变量，第二级为多元高斯变量，通过高斯混合模型 (GMM) 实现。经广泛评估，该模型展现出控制这些潜在属性的能力。