3 problems
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Rudelson–Vershynin logarithmic metric-entropy conjecture
Let a bounded real-valued function class have finite -fat-shattering dimension, and consider the covering-number or metric-entropy bound obtained at the relevant scale. **R…
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Alon et al.'s metric-entropy logarithm conjecture
Let and let -fat-shattering dimension of a bounded real-valued function class be finite. Consider the metric entropy of the class at the relevant scale, measu…
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Phil Long's conjecture that the factor-of-two gap is unavoidable
In real-valued statistical learning, the -fat-shattering dimension controls learnability and uniform convergence only up to a possible factor of in the scale. Phil Long'…