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- W4221166431 abstract "Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $ell_1$ distance essentially at most a constant times larger than its closest $t$-piece degree-$d$ polynomial, where $tge1$ and $dge0$. Letting $c_{t,d}$ denote the smallest such factor, clearly $c_{1,0}=1$, and it can be shown that $c_{t,d}ge 2$ for all other $t$ and $d$. Yet current computationally efficient algorithms show only $c_{t,1}le 2.25$ and the bound rises quickly to $c_{t,d}le 3$ for $dge 9$. We derive a near-linear-time and essentially sample-optimal estimator that establishes $c_{t,d}=2$ for all $(t,d)ne(1,0)$. Additionally, for many practical distributions, the lowest approximation distance is achieved by polynomials with vastly varying number of pieces. We provide a method that estimates this number near-optimally, hence helps approach the best possible approximation. Experiments combining the two techniques confirm improved performance over existing methodologies." @default.
- W4221166431 created "2022-04-03" @default.
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- W4221166431 date "2022-02-14" @default.
- W4221166431 modified "2023-09-23" @default.
- W4221166431 title "TURF: A Two-factor, Universal, Robust, Fast Distribution Learning Algorithm" @default.
- W4221166431 doi "https://doi.org/10.48550/arxiv.2202.07172" @default.
- W4221166431 hasPublicationYear "2022" @default.
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