Specifically,we propose to construct amatrix-variate normal prior (on weights) whose covariance matrix hasaKroneckerproduct structure. Thisstructure is designed to capture the correlations in neurons through backpropagation.

We study how the word usage of U.S. Congressional speeches varies across states and party affiliation, how words are used differently across sections of the ArXiv, and how the co-purchase patterns of groceries can vary across seasons.

Neural Information Processing Systems http://nips.cc/

Statistical Strength Throughoutt the paper, you refer to the concept of'statistical strength' without describing what it actually means. I expect it means that if two things are correlated, you can estimate properties of them with better sample efficiency if you take this correlation into account, since you're effectively getting more data. Given that two features are correlated, optimization will be improved if you do some sort of preconditioning that accounts for this structure. In other words, given that features are correlated, you want to'share statistical strength.' However, it is less clear to me why you want to regularize the model such that things become correlated/anti-correlated.

Although deep neural networks have been widely applied in various domains [19, 25, 27], usually its parameters are learned via the principle of maximum likelihood, hence its success crucially hinges on the availability of large scale datasets. When training rich models on small datasets, explicit regularization techniques are crucial to alleviate overfitting. Previous works have explored various regularization [39] and data augmentation [19, 38] techniques to learn diversified representations. In this paper, we look into an alternative direction by proposing an adaptive and data-dependent regularization method to encourage neurons of the same layer to share statistical strength. The goal of our method is to prevent overfitting when training (large) networks on small dataset. Our key insight stems from the famous argument by Efron [8] in the literature of the empirical Bayes method: It is beneficial to learn from the experience of others. From an algorithmic perspective, we argue that the connection weights of neurons in the same layer (row/column vectors of the weight matrix) will be correlated with each other through the backpropagation learning. Hence, by learning the correlations of the weight matrix, a neuron can "borrow statistical strength" from other neurons in the same layer.

While label fusion from multiple noisy annotations is a well understood concept in data wrangling (tackled for example by the Dawid-Skene (DS) model), we consider the extended problem of carrying out learning when the labels themselves are not consistently annotated with the same schema. We show that even if annotators use disparate, albeit related, label-sets, we can still draw inferences for the underlying full label-set. We propose the Inter-Schema AdapteR (ISAR) to translate the fully-specified label-set to the one used by each annotator, enabling learning under such heterogeneous schemas, without the need to re-annotate the data. We apply our method to a mouse behavioural dataset, achieving significant gains (compared with DS) in out-of-sample log-likelihood (-3.40 to -2.39) and F1-score (0.785 to 0.864).

Word embeddings are a powerful approach for analyzing language, and exponential family embeddings (EFE) extend them to other types of data. Here we develop structured exponential family embeddings (S-EFE), a method for discovering embeddings that vary across related groups of data. We study how the word usage of U.S. Congressional speeches varies across states and party affiliation, how words are used differently across sections of the ArXiv, and how the co-purchase patterns of groceries can vary across seasons. Key to the success of our method is that the groups share statistical information. We develop two sharing strategies: hierarchical modeling and amortization. We demonstrate the benefits of this approach in empirical studies of speeches, abstracts, and shopping baskets. We show how SEFE enables group-specific interpretation of word usage, and outperforms EFE in predicting held-out data.

Common statistical practice has shown that the full power of Bayesian methods is not realized until hierarchical priors are used, as these allow for greater "robustness" and the ability to "share statistical strength." Yet it is an ongoing challenge to provide a learning-theoretically sound formalism of such notions that: offers practical guidance concerning when and how best to utilize hierarchical models; provides insights into what makes for a good hierarchical prior; and, when the form of the prior has been chosen, can guide the choice of hyperparameter settings. We present a set of analytical tools for understanding hierarchical priors in both the online and batch learning settings. We provide regret bounds under log-loss, which show how certain hierarchical models compare, in retrospect, to the best single model in the model class. We also show how to convert a Bayesian log-loss regret bound into a Bayesian risk bound for any bounded loss, a result which may be of independent interest. Risk and regret bounds for Student's $t$ and hierarchical Gaussian priors allow us to formalize the concepts of "robustness" and "sharing statistical strength." Priors for feature selection are investigated as well. Our results suggest that the learning-theoretic benefits of using hierarchical priors can often come at little cost on practical problems.