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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)

Style Guide

• First derivatives are named using the pattern function_d* and second derivatives function_d*d*. For example, kernel_dxdy. Since the name of a function does not change when it is differentiated with respect to a variable, it is redundant to write something like 'function_dfunction_dxdy'
• Line lengths are variable - aim to keep lines of code under 80 characters but allow the definition of a function to be as long as needed as julia often has long function names/definitions

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.
• When scanning an array, ensure that the innermost loop corresponds to the leftmost index when accessing an array - Julia's arrays are in column-major order
• When a function contains two or more loops in succession (not composition) or some set-up code, try to break these into separate functions
• Avoid operating on multiple arrays at once in Julia (eg. attempt to use BLAS where possible)
• more?

Notes

• LaTeX Notes