It has been observed that the performances of many high-dimensional estimation problems
are universal with respect to underlying sensing (or design) matrices. Specifically, matrices …

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

Recent years have been marked with the fast-pace diversification and increasing ubiquity of
machine learning applications. Yet, a firm theoretical understanding of the surprising …

When can the input of a ReLU neural network be inferred from its output? In other words,
when is the network injective? We consider a single layer, x↦ ReLU (W x), with a random …

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 consider the problem of fitting a centered ellipsoid to n standard Gaussian random
vectors in, as with. It has been conjectured that this problem is, with high probability …

Since its use in the Lottery Ticket Hypothesis, iterative magnitude pruning (IMP) has become
a popular method for extracting sparse subnetworks that can be trained to high performance …

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 …