Derives the first empirical Bennett and Bernstein inequalities for bounded compact self-adjoint operators that use intrinsic dimension and empirical variance estimates to achieve dimension-free guarantees.
Sharp empirical Bernstein bounds for the variance of bounded random variables
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The paper supplies computable KMT-type bounds for bounded i.i.d. sums that depend only on range and variance (or an empirical estimate), plus a moderate-deviation byproduct.
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Intrinsic-dimension empirical Bernstein inequalities for bounded self-adjoint operators
Derives the first empirical Bennett and Bernstein inequalities for bounded compact self-adjoint operators that use intrinsic dimension and empirical variance estimates to achieve dimension-free guarantees.
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Computable Bounds for Strong Approximations with Applications
The paper supplies computable KMT-type bounds for bounded i.i.d. sums that depend only on range and variance (or an empirical estimate), plus a moderate-deviation byproduct.