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Outstanding Features

• Kernels

  • Add Kernels
    • Periodic kernel: exp(-2sin(π*(x-y)/k.p)^2 / k.ell^2)
    • Automatic Relevance Determination Kernel: one for each euclidean distance and scalar product kernel - can we implement this orthogonal to the scalar kernelize()?
      • Derivatives w.r.t. elements of the weight vector
  • Expand derivatives to the other kernels
    • Laplacian Kernel
    • Rational Quadratic Kernel
    • Multi-Quadratic Kernel
    • Inverse Multi-Quadratic Kernel
    • Power Kernel
    • Log Kernel
    • Linear Kernel
    • Polynomial Kernel
    • Sigmoid Kernel
    • Mercer Sigmoid Kernel
  • Composites of composite kernels
    • Derivatives w.r.t. parameters of subkernels

• Methods

  • Efficient computation of weighted squared norms/scalar products
    • Efficient computation of derivatives w.r.t. the weights
  • Efficient computation of kernel derivatives
  • Efficient computation of weighted gramians
  • Efficient kernel matrix approximation (this should be last and it's not a hurry)

Optimisation Strategies

• Don't construct intermediate objects (vectors, matrices) inside loops - this leads to a lot of memory allocation and then the GC slows everything down. Instead, need to write functions such that everything is done in-place.
• ...
• more?

LaTeX Notes