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New paper precisely maps tail probability under bounded kurtosis

By PulseAugur Editorial · [3 sources] ·

Researchers have determined the precise worst-case tail probability for random variables with bounded kurtosis. This analysis defines a four-regime map that details how kurtosis bounds affect one-sided tail control, revealing that information from fourth moments can negate improvements offered by two-moment bounds. The findings also establish the minimal degree of sum-of-squares proofs required for these bounds and provide explicit dual certificates and extremal distributions. AI

IMPACT This research provides a theoretical framework that could inform the design and analysis of AI algorithms, particularly in understanding the robustness and predictability of their outputs under uncertainty.

RANK_REASON The cluster contains an academic paper published on arXiv detailing a new mathematical finding.

Read on arXiv stat.ML →

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New paper precisely maps tail probability under bounded kurtosis

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COVERAGE [3]

  1. arXiv stat.ML TIER_1 English(EN) · Xiaoyu Li, Andi Han, Jiaojiao Jiang, Junbin Gao ·

    The Exact Worst-Case Tail Probability under Bounded Kurtosis

    arXiv:2607.05226v1 Announce Type: cross Abstract: We determine exactly what a kurtosis bound buys for one-sided tail control. For the class $\mathcal{C}(\kappa)$ of real random variables with mean $0$, variance $1$, and fourth moment at most $\kappa$, the skewness left free, we c…

  2. arXiv stat.ML TIER_1 English(EN) · Junbin Gao ·

    The Exact Worst-Case Tail Probability under Bounded Kurtosis

    We determine exactly what a kurtosis bound buys for one-sided tail control. For the class $\mathcal{C}(κ)$ of real random variables with mean $0$, variance $1$, and fourth moment at most $κ$, the skewness left free, we compute the worst-case tail probability $V_1(t,κ)=\sup_{X\in\…

  3. arXiv stat.ML TIER_1 English(EN) · Junbin Gao ·

    The Exact Worst-Case Tail Probability under Bounded Kurtosis

    We determine exactly what a kurtosis bound buys for one-sided tail control. For the class $\mathcal{C}(κ)$ of real random variables with mean $0$, variance $1$, and fourth moment at most $κ$, the skewness left free, we compute the worst-case tail probability $V_1(t,κ)=\sup_{X\in\…

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