Bayesian probabilistic models provide a nimble and expressive framework for modeling "small-world" data. In contrast, deep learning offers a more rigid yet much more powerful framework for modeling data of massive size. Edward is a probabilistic programming library that bridges this gap: "black-box" variational inference enables us to fit extremely flexible Bayesian models to large-scale data. Furthermore, these models themselves may take advantage of classic deep-learning architectures of arbitrary complexity. Edward uses TensorFlow for symbolic gradients and data flow graphs.
Variational auto-encoders (VAE) are scalable and powerful generative models. However, the choice of the variational posterior determines tractability and flexibility of the VAE. Commonly, latent variables are modeled using the normal distribution with a diagonal covariance matrix. This results in computational efficiency but typically it is not flexible enough to match the true posterior distribution. One fashion of enriching the variational posterior distribution is application of normalizing flows, i.e., a series of invertible transformations to latent variables with a simple posterior. In this paper, we follow this line of thinking and propose a volume-preserving flow that uses a series of Householder transformations. We show empirically on MNIST dataset and histopathology data that the proposed flow allows to obtain more flexible variational posterior and competitive results comparing to other normalizing flows.
This article follows my previous one on Bayesian probability & probabilistic programming that I published few months ago on LinkedIn. And for the purpose of this article, I am going to assume that most this article readers have some idea what a Neural Network or Artificial Neural Network is. Neural Network is a non-linear function approximator. We can think of it as a parameterized function where the parameters are the weights & biases of Neural Network through which we will be typically passing our data (inputs), that will be converted to a probability between 0 and 1, to some kind of non-linearity such as a sigmoid function and help make our predictions or estimations. These non-linear functions can be composed together hence Deep Learning Neural Network with multiple layers of this function compositions.
Modern deep neural network models suffer from adversarial examples, i.e. confidently misclassified points in the input space. It has been shown that Bayesian neural networks are a promising approach for detecting adversarial points, but careful analysis is problematic due to the complexity of these models. Recently Gilmer et al. (2018) introduced adversarial spheres, a toy set-up that simplifies both practical and theoretical analysis of the problem. In this work, we use the adversarial sphere set-up to understand the properties of approximate Bayesian inference methods for a linear model in a noiseless setting. We compare predictions of Bayesian and non-Bayesian methods, showcasing the advantages of the former, although revealing open challenges for deep learning applications.
However Deep neural networks recently have achieved impressive results for different tasks, they suffer from poor uncertainty prediction. Temperature Scaling (TS) is an efficient post-processing method for calibrating DNNs toward to have more accurate uncertainty prediction. TS relies on a single parameter T which softens the logit layer of a DNN and the optimal value of it is found by minimizing on Negative Log Likelihood (NLL) loss function. In this paper, we discuss about weakness of NLL loss function, especially for DNNs with high accuracy and propose a new loss function called Attended-NLL which can improve TS calibration ability significantly.