TASK DEFINITION: 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.
PROBLEM: Deep neural networks have led to a series of breakthroughs, dramatically improving the state-of-the-art in many domains. The techniques driving these advances, however, lack a formal method to account for model uncertainty. While the Bayesian approach to learning provides a solid theoretical framework to handle uncertainty, inference in Bayesian-inspired deep neural networks is difficult. In this paper, we provide a practical approach to Bayesian learning that relies on a regularization technique found in nearly every modern network, batch normalization. We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. Our approach is thoroughly validated in a series of empirical experiments on different tasks and using various measures, showing it to outperform baselines on a majority of datasets with strong statistical significance.

SOLUTION: We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty in conventional networks.

PROBLEM: Computing distances between examples is at the core of many learning algorithms for time series. Consequently, a great deal of work has gone into designing effective time series distance measures. We present Jiffy, a simple and scalable distance metric for multivariate time series. Our approach is to reframe the task as a representation learning problem---rather than design an elaborate distance function, we use a CNN to learn an embedding such that the Euclidean distance is effective. By aggressively max-pooling and downsampling, we are able to construct this embedding using a highly compact neural network. Experiments on a diverse set of multivariate time series datasets show that our approach consistently outperforms existing methods.

SOLUTION: Jiffy is a convolutional approach to learning a distance metric for multivariate time series that outperforms existing methods in terms of nearest-neighbor classification accuracy.

PROBLEM: Learning can be framed as trying to encode the mutual information between input and output while discarding other information in the input. Since the distribution between input and output is unknown, also the true mutual information is. To quantify how difficult it is to learn a task, we calculate a observed mutual information score by dividing the estimated mutual information by the entropy of the input. We substantiate this score analytically by showing that the estimated mutual information has an error that increases with the entropy of the data. Intriguingly depending on how the data is represented the observed entropy and mutual information can vary wildly. There needs to be a match between how data is represented and how a model encodes it. Experimentally we analyze image-based input data representations and demonstrate that performance outcomes of extensive network architectures searches are well aligned to the calculated score. Therefore to ensure better learning outcomes, representations may need to be tailored to both task and model to align with the implicit distribution of the model.

SOLUTION:
We take a step towards measuring learning task difficulty and demonstrate that in practice performance strongly depends on the match of the representation of the information and the model interpreting it.