Recently, L1 regularization have been attracted extensive attention and successfully applied in mean-variance portfolio selection for promoting out-of-sample properties and decreasing transaction costs. However, L1 regularization approach is ineffective in promoting sparsity and selecting regularization parameter on index tracking with the budget and no-short selling constraints, since the 1-no...

The technical reports of the CVGPR Group are listed under Abstract Most scale-space concepts have been expressed as parabolic or hyperbolic partial diierential equations (PDEs). In this paper we extend our work on scale-space properties of elliptic PDEs arising from regularization methods: we study linear and nonlinear regularization methods that are applied iteratively and with different regul...

We propose a Bayesian framework for learning the optimal regularization parameter in the L1-norm penalized least-mean-square (LMS) problem, also known as LASSO [1] or basis pursuit [2]. The setting of the regularization parameter is critical for deriving a correct solution. In most existing methods, the scalar regularization parameter is often determined in a heuristic manner; in contrast, our ...

In previous lectures, we saw how regularization can be used to restore the well-posedness of the empirical risk minimization (ERM) problem. We also derived algorithms that use regularization to impose smoothness assumptions on the solution space (as in the case of Tikhonov regularization) or introduce additional structure by confining the solution space to low dimensional manifolds (manifold re...

The arti…cial neural network (ANN) test of Lee, White and Granger (LWG, 1993) uses the ability of the ANN activation functions in the hidden layer to detect neglected functional misspeci…cation. As the estimation of the ANN model is often quite di¢ cult, LWG suggested activate the ANN hidden units based on randomly drawn activation parameters. To be robust to the random activations, a large num...