Related papers: Testing High Dimensional Covariance Matrices, with…

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are…

Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…

This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…

We develop a stochastic differential equation, called homogenized SGD, for analyzing the dynamics of stochastic gradient descent (SGD) on a high-dimensional random least squares problem with $\ell^2$-regularization. We show that homogenized…

Modern medicine requires generalised approaches to the synthesis and integration of multimodal data, often at different biological scales, that can be applied to a variety of evidence structures, such as complex disease analyses and…

Associating genetic markers with a multidimensional phenotype is an important yet challenging problem. In this work, we establish the equivalence between two popular methods: kernel-machine regression (KMR), and kernel distance covariance…

In this paper, we consider testing the correlation coefficient matrix between two subsets of high-dimensional variables. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of…

Standard statistical learning theory predicts that Large Language Models (LLMs) should overfit because their parameter counts vastly exceed the number of training tokens. Yet, in practice, they generalize robustly. We propose that the…

Differentially Private Stochastic Gradient Descent (DP-SGD) limits the amount of private information deep learning models can memorize during training. This is achieved by clipping and adding noise to the model's gradients, and thus…

Standard approaches to analysing data in genome-wide association studies (GWAS) ignore any potential functional relationships between genetic markers. In contrast gene pathways analysis uses prior information on functional structure within…

Based on a generalized cosine measure between two symmetric matrices, we propose a general framework for one-sample and two-sample tests of covariance and correlation matrices. We also develop a set of associated permutation algorithms for…

The research presents a machine learning (ML) classifier designed to differentiate between schizophrenia patients and healthy controls by utilising features extracted from electroencephalogram (EEG) data, specifically focusing on…

Schizophrenia is a serious psychiatric disorder. Its pathogenesis is not completely clear, making it difficult to treat patients precisely. Because of the complicated non-Euclidean network structure of the human brain, learning critical…

Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…

Schizophrenia is a globally prevalent psychiatric disorder that severely impairs daily life. Schizophrenia is caused by dopamine imbalances in the fronto-striatal pathways of the brain, which influences fine motor control in the cerebellum.…

Estimation of the high-dimensional banded covariance matrix is widely used in multivariate statistical analysis. To ensure the validity of estimation, we aim to test the hypothesis that the covariance matrix is banded with a certain…

Genome-wide association studies (GWAS) provide a means of examining the common genetic variation underlying a range of traits and disorders. In addition, it is hoped that GWAS may provide a means of differentiating affected from unaffected…

Sparse autoencoders (SAEs) are a useful tool for uncovering human-interpretable features in the activations of large language models (LLMs). While some expect SAEs to find the true underlying features used by a model, our research shows…

Schizophrenia (SCZ) is a brain disorder where different people experience different symptoms, such as hallucination, delusion, flat-talk, disorganized thinking, etc. In the long term, this can cause severe effects and diminish life…