From the 1 of 103 linked papers with an AI index.
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Almost sure null bankruptcy of testing-by-betting strategies
Hongjian Wang, Shubhada Agrawal, Aaditya Ramdas
The bounded mean betting procedure serves as a crucial interface between the domains of (1) sequential, anytime-valid statistical inference, and (2) online learning and portfolio s…
A variational approach to dimension-free self-normalized concentration
Ben Chugg, Aaditya Ramdas
We study the self-normalized concentration of vector-valued stochastic processes. We focus on bounds for "sub-" processes, a well-known and quite general class of process that…
Time-uniform Chernoff bounds via nonnegative supermartingales
Steven R. Howard, Aaditya Ramdas, Jon McAuliffe +1
We develop a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fr…
Positive Semidefinite Matrix Supermartingales
Hongjian Wang, Aaditya Ramdas
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These a…
Nonasymptotic and distribution-uniform Komlós-Major-Tusnády approximation
Ian Waudby-Smith, Martin Larsson, Aaditya Ramdas
We present nonasymptotic concentration inequalities for sums of independent and identically distributed random variables that yield asymptotic strong Gaussian approximations of Kom…
Sharp Matrix Empirical Bernstein Inequalities
Hongjian Wang, Aaditya Ramdas
We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unk…