Establishes sparsity-adaptive L_r-moment bounds for centered polynomials of degree at most D in independent sparse α-sub-exponential variables via partition norms of sparsity-weighted expected derivative tensors, recovering prior results in non-sparse and quadratic cases.
Bernstein-like Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case
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abstract
We show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\lambda$ is at most $e^{-\lambda^2 / (R^q Var(f))}$ for sufficiently small $\lambda$, where $R$ is an absolute constant. This matches (up to constants in the exponent) what one would expect from the central limit theorem. Our methods handle a variety of types of random variables including Gaussian, Boolean, exponential, and Poisson. Previous work by Kim-Vu and Schudy-Sviridenko gave bounds of the same form that involved less natural parameters in place of the variance.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Nonparametric inference for structural balance in dynamic signed networks via time-varying graphon model, kernel smoothing, and Edgeworth expansion for studentized statistics.
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Sparsity-adaptive concentration inequalities for random polynomials
Establishes sparsity-adaptive L_r-moment bounds for centered polynomials of degree at most D in independent sparse α-sub-exponential variables via partition norms of sparsity-weighted expected derivative tensors, recovering prior results in non-sparse and quadratic cases.
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Inference for Balance in Dynamic Signed Networks
Nonparametric inference for structural balance in dynamic signed networks via time-varying graphon model, kernel smoothing, and Edgeworth expansion for studentized statistics.