Density estimation
Estimate the probability density the data came from. Histograms and their fragile bins, kernel density estimation and the bandwidth as a bias–variance dial, Silverman's rule of thumb, parametric versus nonparametric models, and why all of this breaks down as dimensions grow.
45 min
After this lesson you can
- Explain why a histogram depends on bin width and bin placement
- Define the kernel density estimator and show that it is a valid density
- Derive the leading bias and variance of a KDE at a point, and read the bandwidth as a bias–variance trade-off
- Apply Silverman's rule of thumb and know when it misleads
- Explain why nonparametric density estimation suffers from the curse of dimensionality
In this lesson
- Histograms
- Kernel density estimation
- The bandwidth is a bias–variance dial
- The curse of dimensionality
This lesson is part of Descent Pro
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