In this work, we investigate Batch Normalization technique and propose its probabilistic interpretation. We propose a probabilistic model and show that Batch Normalization maximazes the lower bound of its marginalized log-likelihood. Then, according to the new probabilistic model, we design an algorithm which acts consistently during train and test. However, inference becomes computationally inefficient. To reduce memory and computational cost, we propose Stochastic Batch Normalization -an efficient approximation of proper inference procedure. This method provides us with a scalable uncertainty estimation technique. We demonstrate the performance of Stochastic Batch Normalization on popular architectures (including deep convolutional architectures: VGG-like and ResNets) for MNIST and CIFAR-10 datasets.

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Bayesian inference is known to provide a general framework for incorporating prior knowledge or specific properties into machine learning models via carefully choosing a prior distribution. In this work, we propose a new type of prior distributions for convolutional neural networks, deep weight prior (dwp), that exploit generative models to encourage a specific structure of trained convolutional filters e.g., spatial correlations. We define dwp in a form of an implicit distribution and propose a method for variational inference with such type of implicit priors. In experiments, we show that dwp improves the performance of Bayesian neural networks when training data are limited, and initialization of weights with samples from dwp accelerates training of conventional convolutional neural networks.

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Transfer learning has witnessed remarkable progress in recent years, for example, with the introduction of augmentation-based contrastive self-supervised learning methods. While a number of large-scale empirical studies on the transfer performance of such models have been conducted, there is not yet an agreed-upon set of control baselines, evaluation practices, and metrics to report, which often hinders a nuanced and calibrated understanding of the real efficacy of the methods. We share an evaluation standard that aims to quantify and communicate transfer learning performance in an informative and accessible setup. This is done by baking a number of simple yet critical control baselines in the evaluation method, particularly the 'blind-guess' (quantifying the dataset bias), 'scratchmodel' (quantifying the architectural contribution), and 'maximal-supervision' (quantifying the upper-bound). To demonstrate how the evaluation standard can be employed, we provide an example empirical study investigating a few basic questions about self-supervised learning. For example, using this standard, the study shows the effectiveness of existing self-supervised pre-training methods is skewed towards image classification tasks versus dense pixel-wise predictions. In general, we encourage using/reporting the suggested control baselines in evaluating transfer learning in order to gain a more meaningful and informative understanding.

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