Vanishing empirical variance in randomly initialized networks

Neural networks are commonly initialized to keep the theoretical variance of the hidden pre-activations constant, in order to avoid the vanishing and exploding gradient problem. Though this condition is necessary to train very deep networks, numerous analyses showed that it is not sufficient. We explain this fact by analyzing the behavior of the...

PGP for portfolio optimization: application to ESG index family

The conventional portfolio design approach assumes Gaussian return distributions, but this is not accurate in practice. Asymmetric and heavy-tailed return distributions necessitate consideration of higher-order moments such as skewness and kurtosis, in addition to mean and variance. This study proposes a multi-objective approach using a mean...

Tensor decomposition for Independent Component Analysis: Through implicit cumulant tensor manipulation

Blind Source Separation (BSS), the separation of latent source components from observed mixtures, is relevant to many fields of expertise such as neuro-imaging, economics and machine learning. Reliable estimates of the sources can be obtained through diagonalization of the cumulant tensor, i.e., a fourth-order symmetric multi-linear array...

Anomalous wave statistics following sudden depth transitions: application of an alternative Boussinesq-type formulation

Recent studies of water waves propagating over sloping seabeds have shown that sudden transitions from deeper to shallower depths can produce significant increases in the skewness and kurtosis of the free surface elevation and hence in the probability of rogue wave occurrence. Gramstad et al. (Phys. Fluids 25 (12): 122103, 2013) have shown...

Diffusion Kurtosis Imaging with free water elimination: A Bayesian estimation approach

Purpose: Diffusion kurtosis imaging (DKI) is an advanced magnetic resonance imaging modality that is known to be sensitive to changes in the underlying microstructure of the brain. Image voxels in diffusion weighted images, however, are typically relatively large making them susceptible to partial volume effects, especially when part of the...

Evaluation of instrumental measures for the prediction of musical noise in enhanced noisy speech

To obtain the absolute truth about the performance of a noise reduction method one requires to perform a listening experiment. As listening experiments are often time consuming and expensive there exists a need to replace these experiments by instrumental measures. Consequently, research has provided various instrumental measures which can been...