We investigate the high-dimensional properties of robust regression estimators in the
presence of heavy-tailed contamination of both the covariates and response functions. In …

For a large class of feature maps we provide a tight asymptotic characterisation of the test
error associated with learning the readout layer, in the high-dimensional limit where the …

We establish an invariance principle for polynomial functions of $ n $ independent high-
dimensional random vectors, and also show that the obtained rates are nearly optimal. Both …

We characterise the learning of a mixture of two clouds of data points with generic centroids
via empirical risk minimisation in the high dimensional regime, under the assumptions of …

We consider the problem of fitting a centered ellipsoid to n standard Gaussian random
vectors in R d, as n, d→∞ with n/d 2→ α> 0. It has been conjectured that this problem is, with …

Random linear vector channels have been known to increase the transmission of
information in several communications systems. For Gaussian priors, the statistics of a key …

Deep linear networks have been extensively studied, as they provide simplified models of
deep learning. However, little is known in the case of finite-width architectures with multiple …

The generalized penalized constrained regression (G-PCR) is a penalized model for high-
dimensional linear inverse problems with structured features. This paper presents a sharp …

We investigate a quantum perceptron implemented on a quantum circuit using a repeat until
method. We evaluate this from the perspective of capacity, one of the performance …

We construct examples of degree-two U-and V-statistics of $ n $ iid~ heavy-tailed random
vectors in $\mathbb {R}^{d (n)} $, whose $\nu $-th moments exist for ${\nu> 2} $, and provide …