Research map / Learning theory and algorithms / Prediction and decision losses
On Computing Optimal Tree Ensembles
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use witness-guided refinements instead of the prior enumerative approach | Minimum decision tree size · Training data with parameters δ, D, and s | running time: prior function f is at least δ^s · (D^s2δ)^s · 2^{s^2}; new bound O((δ D s)^s · sdn) | Helped |
| Extend subset dynamic programming from one tree to an ensemble, tracking correct-classification counts | Minimum tree ensemble size · Training data with n examples and ℓ trees | running time: O(2^n · Ddn) -> (ℓ + 1)^n · Ddn | Helped |
| Use witness-tree search for ensemble optimization rather than enumerative decision-tree methods | Minimum tree ensemble size · Training data parameterized by total tree size S | running time: (4δDS)^S · Sℓdn | Helped |
| Increase the number of trees in an ensemble | Tree ensembles versus decision trees · Training data classifiable by ℓ trees of size at most s | size: decision tree upper bound (s + 1)^ℓ -1; lower bound \frac{(s+1)^\ell}{\ell (\frac{s+1}{2})^{\frac{\ell-1}{2}}}-1 | Mixed |
| Use dynamic programming over example subsets for decision-tree optimization | Minimum decision tree size · Training data with n examples | running time: O(3^n · Ddn) -> O(2^n · Ddn) | Helped |
| Reduce the exponential running-time exponent below S for MTES | MTES with D=2 and ℓ=1 · Training data | running time: (δ D S)^{o(S)} · poly | Hurt |
| Improve the example-count dependence below the stated base for MTES | MTES · Training data with n examples | running time: f(ℓ) · 2^{o(log ℓ)·n}· poly | Hurt |
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