Balancing reconstruction error and Kullback-Leibler divergence in Variational Autoencoders

On the Importance of the Kullback-Leibler Divergence Term in Variational Autoencoders for Text Generation

Variational Autoencoders (VAEs) are known to suffer from learning uninformative latent representation of the input due to issues such as approximated posterior collapse, or entanglement of the latent space. We impose an explicit constraint on the Kullback-Leibler (KL) divergence term inside the VAE objective function. While the explicit constraint naturally avoids posterior collapse, we use it to further understand the significance of the KL term in controlling the information transmitted through the VAE channel. Within this framework, we explore different properties of the estimated posterior…

Learning in Variational Autoencoders with Kullback-Leibler and Renyi Integral Bounds

In this paper we propose two novel bounds for the log-likelihood based on Kullback-Leibler and the Rényi divergences, which can be used for variational inference and in particular for the training of Variational AutoEncoders. Our proposal is motivated by the difficulties encountered in training VAEs on continuous datasets with high contrast images, such as those with handwritten digits and characters, where numerical issues often appear unless noise is added, either to the dataset during training or to the generative model given by the decoder. The new bounds we propose, which are obtained fro…

通过双重Kullback-Leibler最小化实现潜在高斯过程的变分稀疏逆Cholesky近似

Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimization

本文提出双重KL最优高斯过程近似方法，利用稀疏逆Cholesky因子同时变分近似先验与后验，在相近计算成本下对平稳核取得显著优于诱导点和平均场方法的精度。

Kullback-Leibler and Renyi divergences in reproducing kernel Hilbert space and Gaussian process settings

In this work, we present formulations for regularized Kullback-Leibler and Rényi divergences via the Alpha Log-Determinant (Log-Det) divergences between positive Hilbert-Schmidt operators on Hilbert spaces in two different settings, namely (i) covariance operators and Gaussian measures defined on reproducing kernel Hilbert spaces (RKHS); and (ii) Gaussian processes with squared integrable sample paths. For characteristic kernels, the first setting leads to divergences between arbitrary Borel probability measures on a complete, separable metric space. We show that the Alpha Log-Det divergences …

Analysis of Discriminator in RKHS Function Space for Kullback-Leibler Divergence Estimation

Several scalable sample-based methods to compute the Kullback Leibler (KL) divergence between two distributions have been proposed and applied in large-scale machine learning models. While they have been found to be unstable, the theoretical root cause of the problem is not clear. In this paper, we study a generative adversarial network based approach that uses a neural network discriminator to estimate KL divergence. We argue that, in such case, high fluctuations in the estimates are a consequence of not controlling the complexity of the discriminator function space. We provide a theoretical …

On the Interventional Kullback-Leibler Divergence

Modern machine learning approaches excel in static settings where a large amount of i.i.d. training data are available for a given task. In a dynamic environment, though, an intelligent agent needs to be able to transfer knowledge and re-use learned components across domains. It has been argued that this may be possible through causal models, aiming to mirror the modularity of the real world in terms of independent causal mechanisms. However, the true causal structure underlying a given set of data is generally not identifiable, so it is desirable to have means to quantify differences between …