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- W2891597037 abstract "Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range bounded in $[0,1]$, the generalization error of $gamma$-uniformly stable learning algorithm on $n$ samples is known to be at most $O((gamma +1/n) sqrt{n log(1/delta)})$ with probability at least $1-delta$. Unfortunately, this bound does not lead to meaningful generalization bounds in many common settings where $gamma geq 1/sqrt{n}$. At the same time the bound is known to be tight only when $gamma = O(1/n)$. Here we prove substantially stronger generalization bounds for uniformly stable algorithms without any additional assumptions. First, we show that the generalization error in this setting is at most $O(sqrt{(gamma + 1/n) log(1/delta)})$ with probability at least $1-delta$. In addition, we prove a tight bound of $O(gamma^2 + 1/n)$ on the second moment of the generalization error. The best previous bound on the second moment of the generalization error is $O(gamma + 1/n)$. Our proofs are based on new analysis techniques and our results imply substantially stronger generalization guarantees for several well-studied algorithms." @default.
- W2891597037 created "2018-09-27" @default.
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- W2891597037 date "2018-01-01" @default.
- W2891597037 modified "2023-09-24" @default.
- W2891597037 title "Generalization Bounds for Uniformly Stable Algorithms" @default.
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