Seeing the "curse of dimensionality" being applied to computer graphics and pictures here is really cool. This makes me think of the similarities between statistics and computer graphics, as sampling and averaging are both fundamental concepts in both. Therefore, I wonder how many statistics concepts can actually be applied into computer graphics, as common techniques for reducing dimension in statistics are SVD/PCA.
andrewdotwang
Why does Monte Carlo integration require fewer samples than quadrature-based numerical integration in high dimensions? Are there any tradeoffs?
abhi-n-anand
From what I've read online @andrewdotwang, it seems as if Monte Carlo Integration requires less samples because for quadrature-based numerical integration, as dimensionality increases, the rate at which it converges worsens. However, for Monte Carlo Integration, convergence rate seems to be independent of dimensionality.
Seeing the "curse of dimensionality" being applied to computer graphics and pictures here is really cool. This makes me think of the similarities between statistics and computer graphics, as sampling and averaging are both fundamental concepts in both. Therefore, I wonder how many statistics concepts can actually be applied into computer graphics, as common techniques for reducing dimension in statistics are SVD/PCA.
Why does Monte Carlo integration require fewer samples than quadrature-based numerical integration in high dimensions? Are there any tradeoffs?
From what I've read online @andrewdotwang, it seems as if Monte Carlo Integration requires less samples because for quadrature-based numerical integration, as dimensionality increases, the rate at which it converges worsens. However, for Monte Carlo Integration, convergence rate seems to be independent of dimensionality.