text: Unlike machines, humans learn through rapid, Abstract model-building. The role of a teacher is not simply to hammer home right or wrong answers, but rather to provide intuitive comments, comparisons, and explanations to a pupil. This is what the Learning Under Privileged Information (LUPI) paradigm endeavors to model by utilizing extra knowledge only available during training. We propose a new LUPI algorithm specifically designed for Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). We propose to use a heteroscedastic dropout (i.e. dropout with a varying variance) and make the variance of the dropout a function of privileged information. Intuitively, this corresponds to using the privileged information to control the uncertainty of the model output. We perform experiments using CNNs and RNNs for the tasks of image classification and machine translation. Our method significantly increases the sample efficiency during learning, resulting in higher accuracy with a large margin when the number of training examples is limited. We also theoretically justify the gains in sample efficiency by providing a generalization error bound decreasing with O(1 n), where n is the number of training examples, in an oracle case.
  @cite_36: Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.
  @cite_26: We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the mini-batch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments.
summary: We use multiplicative Gaussian dropout instead of Bernoulli dropout. Gaussian dropout is first introduced in @cite_36 . Its variational extension @cite_26 uses local re-parameterization to perform Bayesian learning.