In statistics, KDE/KDC is a type of non-parametric regression to estimate the density function of a random variable(s)
KDE/KDC - How it Works & Compared to Histogram
Must See: Histogram vs KDE
- 𝐏ˆ(𝑋=𝑥) = 1/[ℎ·𝑛]・𝛴𝑥𝑖∊𝑎𝑙𝑙-𝑠𝑎𝑚𝑝𝑙𝑒𝑠𝑘(𝑥𝑖,𝑥)
- 𝐏ˆ(𝑋=𝑥|𝑌=𝑦) = 1/[ℎ·𝑐𝑜𝑢𝑛𝑡(𝑌=𝑦)]・𝛴(𝑥𝑖,𝑦𝑖)∊𝑎𝑙𝑙-𝑠𝑎𝑚𝑝𝑙𝑒𝑠𝑘[(𝑥𝑖,𝑦𝑖),(𝑥,𝑦)]
where:
- ℎ > 0 - bandwidth
- 𝑘() - the kernel function
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Kernel Function (𝑘) |
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Kernel Density Estimate (KDE) with different bandwidths of a random sample of 100 points from a standard normal distribution:
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KDE/KDC - Types
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