耦合变分自编码器：改进的变分自编码器的准确性和鲁棒性
Coupled VAE: Improved Accuracy and Robustness of a Variational Autoencoder
AI总结：
本文提出一种耦合变分自编码器，通过改进损失函数提升模型的准确性和鲁棒性。
摘要：
我们提出了一种耦合变分自编码器（VAE）方法，该方法提高了在表示数据上概率推断的准确性和鲁棒性。新的方法建模了输入特征向量（图像）之间的依赖关系，并通过将原始损失函数推广到耦合熵函数，对异常值施加更高的惩罚，利用非线性统计耦合的原则。我们使用MNIST数据集评估耦合VAE模型的性能。与传统VAE算法相比，耦合VAE方法生成的输出图像更清晰、更不模糊。输入图像嵌入到2D潜在变量空间中的可视化为具有耦合损失函数的新模型提供了更深入的见解：潜在变量的偏差更小，更紧凑的潜在空间生成输出值。我们分析了输入图像似然分布的直方图，使用广义均值来衡量模型的准确性作为相对风险的函数。中性准确性，即几何平均数，与香农交叉熵的度量一致，得到了提升。鲁棒准确性，通过-2/3广义均值测量，也得到了提升。
英文摘要：
We present a coupled Variational Auto-Encoder (VAE) method that improves the accuracy and robustness of the probabilistic inferences on represented data. The new method models the dependency between input feature vectors (images) and weighs the outliers with a higher penalty by generalizing the original loss function to the coupled entropy function, using the principles of nonlinear statistical coupling. We evaluate the performance of the coupled VAE model using the MNIST dataset. Compared with the traditional VAE algorithm, the output images generated by the coupled VAE method are clearer and less blurry. The visualization of the input images embedded in 2D latent variable space provides a deeper insight into the structure of new model with coupled loss function: the latent variable has a smaller deviation and a more compact latent space generates the output values. We analyze the histogram of the likelihoods of the input images using the generalized mean, which measures the model's accuracy as a function of the relative risk. The neutral accuracy, which is the geometric mean and is consistent with a measure of the Shannon cross-entropy, is improved. The robust accuracy, measured by the -2/3 generalized mean, is also improved.
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