Fast marginal likelihood estimation of penalties for group-adaptive elastic net

Nowadays, clinical research routinely uses omics data, such as gene expression, for predicting clinical outcomes or selecting markers. Additionally, so-called co-data are often available, providing complementary information on the covariates, like p-values from previously published studies or groups of genes corresponding to pathways. Elastic net penalisation is widely used for prediction and covariate selection. Group-adaptive elastic net penalisation learns from co-data to improve the prediction and covariate selection, by penalising important groups of covariates less than other groups. Existing methods are, however, computationally expensive. Here we present a fast method for marginal likelihood estimation of group-adaptive elastic net penalties for generalised linear models. We first derive a low-dimensional representation of the Taylor approximation of the marginal likelihood and its first derivative for group-adaptive ridge penalties, to efficiently estimate these penalties. Then we show by using asymptotic normality of the linear predictors that the marginal likelihood for elastic net models may be approximated well by the marginal likelihood for ridge models. The ridge group penalties are then transformed to elastic net group penalties by using the variance function. The method allows for overlapping groups and unpenalised variables. We demonstrate the method in a model-based simulation study and an application to cancer genomics. The method substantially decreases computation time and outperforms or matches other methods by learning from co-data.Comment: 16 pages, 6 figures, 1 tabl

Fast cross-validation for multi-penalty ridge regression

High-dimensional prediction with multiple data types needs to account for potentially strong differences in predictive signal. Ridge regression is a simple model for high-dimensional data that has challenged the predictive performance of many more complex models and learners, and that allows inclusion of data type specific penalties. The largest challenge for multi-penalty ridge is to optimize these penalties efficiently in a cross-validation (CV) setting, in particular for GLM and Cox ridge regression, which require an additional estimation loop by iterative weighted least squares (IWLS). Our main contribution is a computationally very efficient formula for the multi-penalty, sample-weighted hat-matrix, as used in the IWLS algorithm. As a result, nearly all computations are in low-dimensional space, rendering a speed-up of several orders of magnitude. We developed a flexible framework that facilitates multiple types of response, unpenalized covariates, several performance criteria and repeated CV. Extensions to paired and preferential data types are included and illustrated on several cancer genomics survival prediction problems. Moreover, we present similar computational shortcuts for maximum marginal likelihood and Bayesian probit regression. The corresponding R-package, multiridge, serves as a versatile standalone tool, but also as a fast benchmark for other more complex models and multi-view learners

Gate-tunable band structure of the LaAlO3_3-SrTiO3_3 interface

The 2-dimensional electron system at the interface between LaAlO$_{3}$ and SrTiO$_{3}$ has several unique properties that can be tuned by an externally applied gate voltage. In this work, we show that this gate-tunability extends to the effective band structure of the system. We combine a magnetotransport study on top-gated Hall bars with self-consistent Schr\"odinger-Poisson calculations and observe a Lifshitz transition at a density of $2.9\times10^{13}$ cm$^{-2}$. Above the transition, the carrier density of one of the conducting bands decreases with increasing gate voltage. This surprising decrease is accurately reproduced in the calculations if electronic correlations are included. These results provide a clear, intuitive picture of the physics governing the electronic structure at complex oxide interfaces.Comment: 14 pages, 4 figure

Electronic transport through a parallel--coupled triple quantum dot molecule: Fano resonances and bound states in the continuum

The electronic transport through a triple quantum dot molecule attached in parallel to leads in presence of a magnetic flux is studied. Analytical expressions of the linear conductance and density of states for the molecule in equilibrium at zero temperature are obtained. As a consequence of quantum interference, the conductance exhibits in general a Breit--Wigner and two Fano resonances, the positions and widths of which are controlled by the magnetic field. Every two flux quanta, there is an inversion of roles of the bonding and antibonding states. For particular values of the magnetic flux and dot-lead couplings, one or even both Fano resonances collapse and bound states in the continuum (BIC's) are formed. The line broadenings of the molecular states are examined as a function of the Aharonov--Bohm phase around the condition for the formation of BIC's, finding resonances extremely narrow and robust against variations of the magnetic field.Comment: 15 pages, 7 figure

Josephson supercurrent in a topological insulator without a bulk shunt

A Josephson supercurrent has been induced into the three-dimensional topological insulator Bi1.5Sb0.5Te1.7Se1.3. We show that the transport in Bi1.5Sb0.5Te1.7Se1.3 exfoliated flakes is dominated by surface states and that the bulk conductivity can be neglected at the temperatures where we study the proximity induced superconductivity. We prepared Josephson junctions with widths in the order of 40 nm and lengths in the order of 50 to 80 nm on several Bi1.5Sb0.5Te1.7Se1.3 flakes and measured down to 30 mK. The Fraunhofer patterns unequivocally reveal that the supercurrent is a Josephson supercurrent. The measured critical currents are reproducibly observed on different devices and upon multiple cooldowns, and the critical current dependence on temperature as well as magnetic field can be well explained by diffusive transport models and geometric effects