Function Approximation¶
Discretization - Non-Parametric¶
Can I go from unstructured data to structured data.
Unstructured —> Regular
- Histogram
- k-Nearest Neighbours
- Radius Neighbours
- Kernel Density Estimation Unstructured —> Irregular
- Voronoi
- Gaussian Mixture Model
- K-Means
- HDBScan Scale
- Parallelization
- Algorithm - Ball-Tree, KD-Tree, R-Tree - Overview
- Hardware - CUDA/GPU
Regression - Non-Parametric¶
- Nearest Neighbour Regression
- Radius Neighbour Regression
- Gaussian Process
Regression - Parametric¶
- Linear
- Basis Function - FFT, Splines, RBF
- Neural Fields
Spatial Encoders¶
- Splines
- Trigonometry
- Spherical Harmonics
- Scaling, e.g., Hashing
Temporal Encoders¶
- Linear
- Bounded
- Exponential
- Fourier Features, e.g., Sinusoidal Embedding
Neural Fields¶
- Why MLPs don’t work
- Parameterizations - FF, SIREN, MFN
- Connections
- 1 Layer - GP, RFF
- Multiple Layers - Deep GPs, Random Feature Expansions
- Modulation, aka, HyperNetworks
- Uncertainty
- Physics-Informed Loss Function
- Scaling
Examples
- Ocean Land Mask - Discrete
- Orography - Continuous
Examples
- Spatial Encoders
- Discretization