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We give an $n^{O(loglog n)}$-time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over ${pm 1}^n$. Even in the realizable setting, the previous fastest runtime was $n^{O(log n)}$, a consequence of a classic algorithm of Ehrenfeucht and Haussler. Our algorithm shares similarities with practical heuristics for learning decision trees, which we augment with additional ideas to circumvent known lower bounds against these heuristics. To analyze our algorithm, we prove a new structural result for decision trees that strengthens a theorem of ODonnell, Saks, Schramm, and Servedio. While the OSSS theorem says that every decision tree has an influential variable, we show how every decision tree can be pruned so that every variable in the resulting tree is influential.
We study sublinear and local computation algorithms for decision trees, focusing on testing and reconstruction. Our first result is a tester that runs in $mathrm{poly}(log s, 1/varepsilon)cdot nlog n$ time, makes $mathrm{poly}(log s,1/varepsilon)cdot
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real
We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form $mathbf{x} mapsto max(0, mathbf{w} cdot mathbf{x})$ with $mathbf{w} in mathbb{S}^{n-1}$. Our algorithm works in the challeng
In this paper, we present a new methodology to evaluate whether a business process model is fully compliant with a regulatory framework composed of a set of conditional obligations. The methodology is based failure delta-constraints that are evaluate
We give a quasipolynomial-time algorithm for learning stochastic decision trees that is optimally resilient to adversarial noise. Given an $eta$-corrupted set of uniform random samples labeled by a size-$s$ stochastic decision tree, our algorithm run