# Agnostic query learning of decision trees

Gopalan, Kalai, Klivans gave an algorithm https://dl.acm.org/citation.cfm?id=1374376.1374451 for agnostically learning decision trees $$h:\{0,1\}^n\to\{0,1\}$$ under the uniform distribution given black-box query access to a target function. They use discrete Fourier analysis. Question: How might one extend this to learning decision trees over $$\mathbb{R}^n$$? Obviously there is no "uniform distribution", unless we limit the domain to a (say) ball, which I'm perfectly happy to do.

• A hazy idea: their proof doesn't extend to the Gaussian measure, using Hermite instead of Fourier (and mimicking the argument)? – Clement C. Jun 4 '19 at 17:25
• Hmm, interesting idea, I'll give it some thought. – Aryeh Jun 4 '19 at 21:41