Research Semester Programme Machine Learning TheorySeminar++

Overview

Seminar++ meetings consist of a one-hour lecture building up to an open problem, followed by an hour of brainstorming time. The meeting is intended for interested researchers including PhD students. These meetings are freely accessible without registration. Cookies and tea will be provided in the half-time break.

This lecture is part of a series of 8.

Sophie Langer
Assistant Professsor at the University of Twente.

Image classification: A (new) statistical viewpoint

Abstract: In this talk we consider a simple supervised classification problem for object recognition on grayscale images. There are two possible perspectives to solve this problem. Firstly, one can interpret object recognition as a high-dimensional classification problem, where every pixel is a variable. The task is then to map these pixel values to the conditional class probabilities or the labels. Increasing the dimension makes the problem considerably harder, leading to slow convergence rates due to the curse of dimensionality. Another perspective is to view images as two-dimensional objects. Increasing the number of pixels leads to higher resolution and therefore better performance is expected for large images. Following the second route, we present a new image deformation model, for which we propose and analyze two different classifiers. The first method estimates the image deformation by support alignment. Under a minimal separation condition, it is shown that perfect classification is possible. The second method fits a CNN to the data. We derive a rate for the misclassification error depending on the sample size and the number of pixels d². Both classifiers are empirically compared on images generated from the MNIST handwritten digit database.