Empirical Risk Minimization
A fundamental learning paradigm in statistical learning in which a hypothesis is selected by minimizing the empirical error on training samples. It is the theoretical basis for many learning algorithms.
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On the corresponding truncated network class, empirical risk minimization (ERM) achieves the minimax regression rate n^{-2s/(2s+D)} with no additional logarithmic factor.
The paper does not address whether ERM on the truncated network class is easy to find in practical optimization (the optimization landscape problem), nor whether the conclusions can be extended to non-uniform error or more general function spaces.
Previous ERM analyses based on neural networks typically had an extra log n factor, which could only be removed with more refined model selection or early stopping strategies.
On non-degenerate classes, every consistent learner (no matter how it breaks ties) achieves the optimal realizable sample complexity, with the gap only within a constant factor.
The study adopts an empirical risk minimization perspective to decompose PFN deployment error into three sources: prior error, context error, and amortization error.
The theoretical foundations of empirical risk minimization can be traced back to the work of Vapnik and Chervonenkis in the 1970s, who proved that under conditions such as finite VC dimension of the hypothesis space, empirical risk minimizers can converge to true risk minimizers at a controllable rate.
The theoretical foundations of Empirical Risk Minimization (ERM) can be traced back to the pioneering work of Vapnik and Chervonenkis in the 1970s.
All Facts (7)
On the corresponding truncated network class, empirical risk minimization (ERM) achieves the minimax regression rate n^{-2s/(2s+D)} with no additional logarithmic factor.
50%UnverifiedThe paper does not address whether ERM on the truncated network class is easy to find in practical optimization (the optimization landscape problem), nor whether the conclusions can be extended to non-uniform error or more general function spaces.
50%UnverifiedPrevious ERM analyses based on neural networks typically had an extra log n factor, which could only be removed with more refined model selection or early stopping strategies.
50%UnverifiedOn non-degenerate classes, every consistent learner (no matter how it breaks ties) achieves the optimal realizable sample complexity, with the gap only within a constant factor.
50%UnverifiedThe study adopts an empirical risk minimization perspective to decompose PFN deployment error into three sources: prior error, context error, and amortization error.
50%UnverifiedThe theoretical foundations of empirical risk minimization can be traced back to the work of Vapnik and Chervonenkis in the 1970s, who proved that under conditions such as finite VC dimension of the hypothesis space, empirical risk minimizers can converge to true risk minimizers at a controllable rate.
50%UnverifiedThe theoretical foundations of Empirical Risk Minimization (ERM) can be traced back to the pioneering work of Vapnik and Chervonenkis in the 1970s.
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