Research map / Probabilistic and scientific modeling / Variational and generative sampling
Demystifying Orthogonal Monte Carlo and Beyond
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use orthogonal samples instead of iid samples | Monte Carlo estimation for isotropic distributions and F1 functions · General nonlinear objectives | mean squared error | Helped |
| Use orthogonal samples instead of iid samples | Monte Carlo estimation for isotropic distributions and F1 functions · General nonlinear objectives | concentration bound | Helped |
| Extend OMC concentration analysis to all RBF kernels, including Matérn kernels | OMC random-feature kernel approximation · All RBF kernels | concentration guarantee | Helped |
| Apply the uniform-convergence guarantee to OMC kernel ridge regression | OMC kernel ridge regression · Arbitrary RBF kernels | failure-probability guarantee | Helped |
| Use NOMC instead of MC, QMC, or B-OMC | Random-feature kernel approximation · Letter Recognition Data Set, 8 tested kernel classes | mean squared error | Mixed |
| Use NOMC instead of MC, QMC, or B-OMC | Sliced Wasserstein distance estimation · 8 tested distribution classes | mean squared error | Helped |
| Construct globally near-orthogonal ensembles for sample counts greater than dimension | Monte Carlo estimation with s > d · Kernel approximation and sliced Wasserstein estimation | accuracy | Helped |
| Use the algebraic construction rather than optimizing sample locations | NOMC · Near-orthogonal ensemble construction | accuracy | No clear effect |
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