Deep Learning techniques for classification of data with missing values

Two deep learning techniques for classification on corrupt data are investigated and compared by performance. A simple imputation before classification is compared to imputation using a Variational Autoencoder (VAE). Both single and multiple imputation using the VAE are considered and compared in classification performance for different types and levels of corruption, and for different sample sizes for the multiple imputation. Two main corruption methods are implemented, designed to test the classifiers for the cases of data missing at random or data missing not at random. The MNIST data set is used for evaluating performance of the different techniques. It is shown that a Multilayer Perceptron (MLP) trained on VAE imputations outperform a MLP using a simple imputation for all tested levels of corruption. A Convolutional Neural Network (CNN) classifier trained with the simple imputation outperforms both the MLP and the VAE classifier on MNIST. This is expected since it is designed to perform well on data sets with high local correlation, like image data sets, whereas the MLP and the VAE classifiers can generalize to other types of data. The reasons for the observed performance of the different techniques and possible implications are discussed.Imagine you find a puzzle in a bag in your attic. You don't know who left it there and the box is missing, so you have no idea what it should depict. Being an amateur detective, this only intrigues you more, and you try to piece it together to see what it resembles. After hard work you come to the conclusion that almost half of the pieces are missing. Can you still guess what the picture might be depicting? It should depend on how many and which pieces that are missing, but in many cases, you could probably do a decent job. Take a look at this picture: You could probably tell that it shows a cup of coffee, even though half of it is missing. Human vision and object recognition is very good, indeed. In recent years, computers using artificial neural networks (abbreviated ANN), a technique inspired by how the human brain works, have shown good performance when it comes to recognizing objects in images – sometimes even on par with human performance - but if the object is seen from an unfamiliar angle, or just part of the object is shown, the task is much more difficult. The way humans and computers are able to relate new objects to familiar objects is through the process of abstraction. We find similar features and repeating patterns, and classify objects or impressions according to abstract categories. A certain kind of ANN, called an autoencoder, forces the computer to ”think abstractly”. That way it performs much better when classifying objects (a sheep doesn't have to have four legs, it might be enough that it's woolly). But what to do when some pixels in the image are missing (or pieces in the puzzle)? Should it try to classify it anyway or should it try to first fill in the blanks, and then determine the object? I work with a particular kind of autoencoder, a ”variational autoencoder”, that is able to not only recognize general features but also be ”creative”. After showing it many pictures of sheep, it can draw a picture that it hasn't seen before, but that still looks like a sheep. In a sense, the computer dreams of sheep. With such an imaginative tool, I intend to determine how puzzle-solving should be done even when pieces are missing. We humans are good at solving puzzles, often better than computers, but we lack something that computers have, endurance. Even the most persistent human puzzle solver would get tired after trying to classify thousands of images, but once an ANN has been properly trained for the task, it can run day and night without a break and give a systematic answer every time