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• W3204251936 abstract "A $k$-decision tree $t$ (or $k$-tree) is a recursive partition of a matrix (2D-signal) into $kgeq 1$ block matrices (axis-parallel rectangles, leaves) where each rectangle is assigned a real label. Its regression or classification loss to a given matrix $D$ of $N$ entries (labels) is the sum of squared differences over every label in $D$ and its assigned label by $t$. Given an error parameter $varepsilonin(0,1)$, a $(k,varepsilon)$-coreset $C$ of $D$ is a small summarization that provably approximates this loss to emph{every} such tree, up to a multiplicative factor of $1pmvarepsilon$. In particular, the optimal $k$-tree of $C$ is a $(1+varepsilon)$-approximation to the optimal $k$-tree of $D$. We provide the first algorithm that outputs such a $(k,varepsilon)$-coreset for emph{every} such matrix $D$. The size $|C|$ of the coreset is polynomial in $klog(N)/varepsilon$, and its construction takes $O(Nk)$ time. This is by forging a link between decision trees from machine learning -- to partition trees in computational geometry. Experimental results on texttt{sklearn} and texttt{lightGBM} show that applying our coresets on real-world data-sets boosts the computation time of random forests and their parameter tuning by up to x$10$, while keeping similar accuracy. Full open source code is provided." @default.
• W3204251936 created "2021-10-11" @default.
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• W3204251936 date "2021-10-07" @default.
• W3204251936 modified "2023-09-27" @default.
• W3204251936 title "Coresets for Decision Trees of Signals" @default.
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• W3204251936 hasPublicationYear "2021" @default.
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