[cs-talks] Upcoming CS Seminars: PhD Proposal (Tues)
fgreen1 at bu.edu
Wed Oct 21 16:02:53 EDT 2015
A Differential Geometric Approach to Classification
Qinxun Bai, Boston University
Tuesday, October 27, 2015 at 5pm in MCS 180- Hariri Seminar Room
Abstract: In this thesis we study the classification problem from a geometric perspective. In particular, we propose a unified geometric setup for learning both binary and multiclass plug-in classifiers, which estimates the class probability P(y=l|x) by fitting a submanifold corresponding to the estimator of P(y=l|x). We propose a geometric regularization technique where the regularization term measures the volume of this submanifold, based on the intuition that overfitting produces fast oscillations and hence large volume of the estimator. We use gradient flow methods to move from an initial estimator towards a minimizer of a penalty function that penalizes both the deviation of the submanifold from the training data and large volume. We establish universal Bayes consistency for our algorithm under mild initialization assumptions. In the feasibility study, a parametric implementation of this algorithm compares favorably to several widely used classification methods for both binary and multiclass classification. In the remaining work, we will analyze the convergence rate of our algorithm under certain ``small local oscillation" assumptions on P(y=l|x), and generalize our geometric regularization technique to regularize other widely-used classifiers, such as deep neural networks. We will evaluate our work on larger datasets, such as ImageNet, MNIST and Pascal VOC.
Primary Advisor: Stan Sclaroff
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