In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

[EX Q]: In classic papers, Zellner (1988, 2002) demonstrated that Bayesian inference could be derived as the solution to an information theoretic functional.   Below we derive a generalized form of this functional as a variational lower bound of a predictive information bottleneck objective.   This generalized functional encompasses most modern inference procedures and suggests novel ones.
[EX A]: Rederive a wide class of inference procedures from an global information bottleneck objective.

[EX Q]: A distinct commonality between HMMs and RNNs is that they both learn hidden representations for sequential data. In addition, it has been noted that the backward computation of the Baum-Welch algorithm for HMMs is a special case of the back-propagation algorithm used for neural networks (Eisner (2016)). Do these observations suggest that, despite their many apparent differences, HMMs are a special case of RNNs? In this paper, we show that that is indeed the case, and investigate a series of architectural transformations between HMMs and RNNs, both through theoretical derivations and empirical hybridization. In particular, we investigate three key design factors—independence assumptions between the hidden states and the observation, the placement of softmaxes, and the use of non-linearities—in order to pin down their empirical effects. We present a comprehensive empirical study to provide insights into the interplay between expressivity and interpretability in this model family with respect to language modeling and parts-of-speech induction.
[EX A]: Are HMMs a special case of RNNs? We investigate a series of architectural transformations between HMMs and RNNs, both through theoretical derivations and empirical hybridization and provide new insights.

[EX Q]: We propose a method for quantifying uncertainty in neural network regression models when the targets are real values on a $d$-dimensional simplex, such as probabilities. We show that each target can be modeled as a sample from a Dirichlet distribution, where the parameters of the Dirichlet are provided by the output of a neural network, and that the combined model can be trained using the gradient of the data likelihood. This approach provides interpretable predictions in the form of multidimensional distributions, rather than point estimates, from which one can obtain confidence intervals or quantify risk in decision making. Furthermore, we show that the same approach can be used to model targets in the form of empirical counts as samples from the Dirichlet-multinomial compound distribution. In experiments, we verify that our approach provides these benefits without harming the performance of the point estimate predictions on two diverse applications: (1) distilling deep convolutional networks trained on CIFAR-100, and (2) predicting the location of particle collisions in the XENON1T Dark Matter detector.
[EX A]:
Neural network regression should use Dirichlet output distribution when targets are probabilities in order to quantify uncertainty of predictions.