Stability revisited: new generalisation bounds for the Leave-one-Out
This work addresses the need for theoretical guarantees in machine learning for a broad class of algorithms, offering incremental improvements over existing bounds that were limited to uniform stability.
The paper tackles the problem of deriving non-asymptotic generalization bounds for the Leave-one-Out procedure in learning algorithms, achieving new PAC exponential bounds under mild assumptions by introducing the concept of L^q stability and using moment inequalities.
The present paper provides a new generic strategy leading to non-asymptotic theoretical guarantees on the Leave-one-Out procedure applied to a broad class of learning algorithms. This strategy relies on two main ingredients: the new notion of $L^q$ stability, and the strong use of moment inequalities. $L^q$ stability extends the ongoing notion of hypothesis stability while remaining weaker than the uniform stability. It leads to new PAC exponential generalisation bounds for Leave-one-Out under mild assumptions. In the literature, such bounds are available only for uniform stable algorithms under boundedness for instance. Our generic strategy is applied to the Ridge regression algorithm as a first step.