Abstract: 

The significance of high-dimensional data lies in its pervasive presence across numerous scientific, engineering, and business domains. 
As datasets grow in complexity and scale, the analysis of high-dimensional data becomes increasingly vital. In fields like genomics, health sciences, and finance, where intricate relationships and interactions abound, the ability to navigate and derive meaningful insights from large datasets is crucial. Whether it's understanding protein interactions, optimizing financial portfolios with thousands of assets, or interpreting high-resolution images, the capacity to handle and analyze data with a large number of correlated variables is at the forefront of advancements in research, technology, and innovation. In this talk we present a new modelling framework which allows for inference, variable selection, and dimension reduction in the most challenging purely-dimensional asymptotic regime, where the sample size is fixed and the number of observed variables grows without bound.