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However, optimizing of tree regularized classifier is challenging, since both of tree regularizer and hinge loss function in the proposed tree regularized classifier are non-differentiable.
In Section 3, we first illustrate the hierarchical structure in feature vector generated by the baseline method, then we adopt the tree regularizer to encode the hierarchical structure information of feature vector, and solve the optimization problem using ADMM method.
Hence by focusing on the prediction performance with suitably chosen regularizer, such as fixed low-rank in our model, it induces sparse decomposition of the signal which corresponds to conventional feature extraction.
where F([theta]) is the regularizer and [lambda] is the balancing parameter.
Based on the definition of IPM (3), empirical risk (4), and learning principle (11), we formally propose the framework of domain adaptation combining the source and the target data by replacing the regularizer.
Among these solvers, total variation (TV) regularizer is of great importance since it can efficiently deal with noisy signals that have sparse derivatives (or gradients).
The Regularizer and Dictionary Customization Problem
Considering the distance induced by the Frobenius norm, this leads directly to a regularizer [[parallel]D - [D.
Recovering an image from a degraded image is usually an ill-posed inverse problem and it should be dealt with through selecting a suitable regularizer.
ii) As to be seen in the next subsection, the minimum of this regularizer is a set of tight frames.
3RD IEEE Int'l Workshop on Privacy Aspects Data Mining 643 (describing a model in which two types of regularizers were adopted to enforce fair classification).
A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers.