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.

Input: Consider Input: Variational inference (VI) is a popular approach for approximate Bayesian inference that is particularly promising for highly parameterized models such as deep neural networks.   A key challenge of variational inference is to approximate the posterior over model parameters with a distribution that is simpler and tractable yet sufficiently expressive. In this work, we propose a method for training highly flexible variational distributions by starting with a coarse approximation and iteratively refining it. Each refinement step makes cheap, local adjustments and only requires optimization of simple variational families. We demonstrate theoretically that our method always improves a bound on the approximation (the Evidence Lower BOund) and observe this empirically across a variety of benchmark tasks.   In experiments, our method consistently outperforms recent variational inference methods for deep learning in terms of log-likelihood and the ELBO.   We see that the gains are further amplified on larger scale models, significantly outperforming standard VI and deep ensembles on residual networks on CIFAR10.

Output: The paper proposes an algorithm to increase the flexibility of the variational posterior in Bayesian neural networks through iterative optimization.


Input: Consider Input: Extracting relevant information, causally inferring and predicting the future states with high accuracy is a crucial task for modeling complex systems. The endeavor to address these tasks is made even more challenging when we have to deal with high-dimensional heterogeneous data streams. Such data streams often have higher-order inter-dependencies across spatial and temporal dimensions. We propose to perform a soft-clustering of the data and learn its dynamics to produce a compact dynamical model while still ensuring the original objectives of causal inference and accurate predictions. To efficiently and rigorously process the dynamics of soft-clustering, we advocate for an information theory inspired approach that incorporates stochastic calculus and seeks to determine a trade-off between the predictive accuracy and compactness of the mathematical representation. We cast the model construction as a maximization of the compression of the state variables such that the predictive ability and causal interdependence (relatedness) constraints between the original data streams and the compact model are closely bounded. We provide theoretical guarantees concerning the convergence of the proposed learning algorithm. To further test the proposed framework, we consider a high-dimensional Gaussian case study and describe an iterative scheme for updating the new model parameters. Using numerical experiments, we demonstrate the benefits on compression and prediction accuracy for a class of dynamical systems. Finally, we apply the proposed algorithm to the real-world dataset of multimodal sentiment intensity and show improvements in prediction with reduced dimensions.

Output: Compact perception of dynamical process


Input: Consider Input: REINFORCE can be used to train models in structured prediction settings to directly optimize the test-time objective. However, the common case of sampling one prediction per datapoint (input) is data-inefficient. We show that by drawing multiple samples (predictions) per datapoint, we can learn with significantly less data, as we freely obtain a REINFORCE baseline to reduce variance. Additionally we derive a REINFORCE estimator with baseline, based on sampling without replacement. Combined with a recent technique to sample sequences without replacement using Stochastic Beam Search, this improves the training procedure for a sequence model that predicts the solution to the Travelling Salesman Problem.


Output: We show that by drawing multiple samples (predictions) per input (datapoint), we can learn with less data as we freely obtain a REINFORCE baseline.