A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{argument stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which hypotheses are selected. The main result of the paper bounds the generalization error of…
We explore in some detail the notion of algorithmic stability as a viable framework for analyzing the generalization error of learning algorithms. We introduce the new notion of training stability of a learning algorithm and show that, in a general setting, it is sufficient for good bounds on generalization error. In t…
The paper relaxes the stability condition to boost confidence in generalization for randomized learning algorithms.
problem The tension between uniform stability and L2-stability in generalization bounds.
method Establishes in-expectation first moment generalization error bounds for L2-stable randomized learning algorithms and uses subbagging to achieve near-tight exponential bounds.
result Improves generalization bounds for convex and non-convex optimization problems with SGD.
This paper analyzes stability of decision trees and logistic regression.
problem Stability of decision trees and logistic regression is analyzed to understand their performance and sensitivity.
method Two stability notions (hypothesis and pointwise hypothesis stability) are derived for decision trees and logistic regression. The stability of decision trees depends on the number of leaves, while for logistic regression, it depends on the smallest eigenvalue of the Hessian matrix. Upper bounds on generalization error are constructed.
result Logistic regression is not a stable learning algorithm.
Stability is a general notion that quantifies the sensitivity of a learning algorithm's output to small change in the training dataset (e.g. deletion or replacement of a single training sample). Such conditions have recently been shown to be more powerful to characterize learnability in the general learning setting und…
This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning algorithm is if it is allowed a one-step look-ahead into the future. We show that given…
The study identifies conditions under which algorithmic stability explains generalization in interpolating learning systems.
problem Understanding when algorithmic stability explains generalization in interpolating learning systems.
method Modeling training as a function-space trajectory and measuring sensitivity to single-sample perturbations.
result There exist interpolating regimes with small risk where contractive sensitivity cannot hold, showing that stability is not a universal explanation.
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly handled by algorithmic stability. The machine learning community has a rich his…
Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world systems. As a consequence, learning algorithms are rarely applied on safety-crit…
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 Lq stability, and the strong use of moment inequalities. Lq stability e…
We establish novel generalization bounds for learning algorithms that converge to global minima. We do so by deriving black-box stability results that only depend on the convergence of a learning algorithm and the geometry around the minimizers of the loss function. The results are shown for nonconvex loss functions sa…
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional sparse data, however, the method suffers from slow convergence and high variance…
We are interested in understanding stability (almost sure boundedness) of stochastic approximation algorithms (SAs) driven by a `controlled Markov' process. Analyzing this class of algorithms is important, since many reinforcement learning (RL) algorithms can be cast as SAs driven by a `controlled Markov' process. In t…