<ul><li>Researchers have explored joint learning in the Gaussian Single Index Model to simultaneously learn a one-dimensional projection and a univariate function in high-dimensional Gaussian models.</li><li>The study focuses on predictors of the form f(x)=ϕ∗(⟨w∗,x⟩), where the direction w∗ and the function ϕ∗ are learned from Gaussian data.</li><li>The research delves into a non-convex problem at the intersection of representation learning and nonlinear regression, analyzing gradient flow dynamics and proving convergence with a rate controlled by the information exponent signifying the Gaussian regularity of the function ϕ∗.</li><li>Despite initial negative correlation between the direction and the target, the analysis demonstrates convergence. Practical implementation using a Reproducing Kernel Hilbert Space (RKHS) tailored to the problem's structure allows efficient and flexible estimation of the univariate function, offering theoretical insights and practical methodologies for learning low-dimensional structures in high-dimensional scenarios.</li></ul>

Joint Learning in the Gaussian Single Index Model

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