Curse of Dimensionality
A central difficulty in high-dimensional data analysis: as dimensionality increases, the sample size required for nonparametric estimation grows exponentially, causing the convergence rates of methods such as kernel density estimation and kernel mean embedding to lose practical utility.
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The curse of dimensionality refers to the fact that as the covariate dimension d increases, the sample size required for non-parametric estimation grows exponentially, causing methods such as kernel density estimation and kernel mean embedding to lose practical convergence rates.
The paper proves that, under appropriate network depth and width configurations, the convergence rate of dense ReLU networks can overcome the curse of dimensionality, achieving polynomial-level sample complexity.
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The curse of dimensionality refers to the fact that as the covariate dimension d increases, the sample size required for non-parametric estimation grows exponentially, causing methods such as kernel density estimation and kernel mean embedding to lose practical convergence rates.
50%UnverifiedThe paper proves that, under appropriate network depth and width configurations, the convergence rate of dense ReLU networks can overcome the curse of dimensionality, achieving polynomial-level sample complexity.
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