In this paper, we propose a density estimation algorithm called
\textit{Gradient Boosting Histogram Transform} (GBHT), where we adopt the
\textit{Negative Log Likelihood} as the loss function to make the boosting
procedure available for the unsupervised tasks. From a learning theory
viewpoint, we first prove fast convergence rates for GBHT with the smoothness
assumption that the underlying density function lies in the space
$C^{0,\alpha}$. Then when the target density function lies in spaces
$C^{1,\alpha}$, we present an upper bound for GBHT which is smaller than the
lower bound of its corresponding base learner, in the sense of convergence
rates. To the best of our knowledge, we make the first attempt to theoretically
explain why boosting can enhance the performance of its base learners for
density estimation problems. In experiments, we not only conduct performance
comparisons with the widely used KDE, but also apply GBHT to anomaly detection
to showcase a further application of GBHT.

本文提出一种密度估计算法 GBHT，采用负对数似然作为损失函数，使 Boosting 方法适用于无监督任务，在学习理论的角度，我们首先证明 GBHT 的收敛速率快，然后将目标密度函数定义在空间 C ^ {1，α} 中，GBHT 的收敛速率的上界小于其对应基学习者的下界，并尝试从理论上解释为什么 Boosting 可以提高密度估计问题的基学习者的性能。在实验中，我们不仅与广泛使用的 KDE 进行性能比较，而且将 GBHT 应用于异常检测，以展示 GBHT 的进一步应用。

GBHT: 梯度增强直方图变换用于密度估计

GBHT: Gradient Boosting Histogram Transform for Density Estimation

Binary classifiers are often employed as discriminators in GAN-based
unsupervised style transfer systems to ensure that transferred sentences are
similar to sentences in the target domain. One difficulty with this approach is
that the error signal provided by the discriminator can be unstable and is
sometimes insufficient to train the generator to produce fluent language. In
this paper, we propose a new technique that uses a target domain language model
as the discriminator, providing richer and more stable token-level feedback
during the learning process. We train the generator to minimize the negative
log likelihood (NLL) of generated sentences, evaluated by the language model.
By using a continuous approximation of discrete sampling under the generator,
our model can be trained using back-propagation in an end- to-end fashion.
Moreover, our empirical results show that when using a language model as a
structured discriminator, it is possible to forgo adversarial steps during
training, making the process more stable. We compare our model with previous
work using convolutional neural networks (CNNs) as discriminators and show that
our approach leads to improved performance on three tasks: word substitution
decipherment, sentiment modification, and related language translation.

本研究提出了一种新的方法，使用目标域语言模型作为辨别器，为生成模型提供更丰富和更稳定的令牌级反馈，以便用于二进制分类器在 GAN-based 无监督风格转换系统中。该模型可使用从生成模型下的连续近似离散采样而训练，且相较于以前使用卷积神经网络（CNN）作为辨别器的先前工作，我们的方法在单词替换解密、情感修改和相关语言翻译三项任务上表现出了更好的性能，同时可以省略训练期间的对抗步骤，使过程更加稳定。