Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
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This thesis describes the model class of convexified convolutional neural networks (CCNNs), a type of deep learning model introduced by Zhang, Liang & Wainwright [1]. First, steps towards the...Show moreThis thesis describes the model class of convexified convolutional neural networks (CCNNs), a type of deep learning model introduced by Zhang, Liang & Wainwright [1]. First, steps towards the convex relaxation are described, as well as all the steps required to implement the algorithm. To this end, the thesis describes the mathematical structure of the shallow networks, how the function class can be relaxed to the convex case, as well as the role of Reproducing Kernel Hilbert Spaces, the Nystrom method, and projected gradient descent on the nuclear norm ball. The main contribution of this work is the implementation and application to a new data set. The problems considered are a simulation study and an implementation on the classification problem of text data. The results of the CCNN implementation show that it can be successfully applied on text data through the use of vectorized word representations. Advantages and drawbacks compared to more mainstream approaches are discussed.Show less
