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- W4317466387 abstract "This paper provides a framework to show the concentration of solutions $Y^*$ to convex minimizing problem where the objective function $phi(X)(Y)$ depends on some random vector $X$ satisfying concentration of measure hypotheses. More precisely, the convex problem translates into a contractive fixed point equation that ensure the transmission of the concentration from $X$ to $Y^*$. This result is of central interest to characterize many machine learning algorithms which are defined through implicit equations (e.g., logistic regression, lasso, boosting, etc.). Based on our framework, we provide precise estimations for the first moments of the solution $Y^*$, when $X= (x_1,ldots, x_n)$ is a data matrix of independent columns and $phi(X)(y)$ writes as a sum $frac{1}{n}sum_{i=1}^n h_i(x_i^TY)$. That allows to describe the behavior and performance (e.g., generalization error) of a wide variety of machine learning classifiers." @default.
- W4317466387 created "2023-01-20" @default.
- W4317466387 creator A5045532672 @default.
- W4317466387 date "2020-10-19" @default.
- W4317466387 modified "2023-09-25" @default.
- W4317466387 title "A Concentration of Measure Framework to study convex problems and other implicit formulation problems in machine learning" @default.
- W4317466387 doi "https://doi.org/10.48550/arxiv.2010.09877" @default.
- W4317466387 hasPublicationYear "2020" @default.
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