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math.ST2026
How Many Samples Are Needed to Determine Causal Direction? Sharp Minimax Bounds for Bivariate LiNGAM
Jikai Jin
We study how many observations are needed to determine the causal direction between two linearly related variables. Classical LiNGAM theory shows that independent non-Gaussian dist…
math.OC2026
A Tight Lower Bound for Smooth Nonconvex Stochastic Optimization with Bounded Gradient Noise
Jikai Jin
We prove a sharp lower bound for smooth nonconvex stochastic optimization with uniformly bounded gradient noise. In the \(K=1\) fresh-sample model, every randomized adaptive algori…