Overview

GauProS is a lightweight, memory-friendly implementation of Gaussian Processes for Scala and ScalaJS.
Aside from the Scala Standard Library there are no deployment dependencies, particularly no native
dependencies. An interactive example of GauProS running in the Browser can be found here.

GP without Hyperparameters

The Kernel function is a functional trait of type (xi: A, xj: A) => Double. If the Kernel only has fixed/known
hyperparameters, it can simply be instantiated using a lambda expression.

import gps.regression._
// SOURCE: https://data.bls.gov/timeseries/APU0000711211
val banana_prices = Vec(
  0.629, 0.641, 0.634, 0.629, 0.622, 0.617, 0.616, 0.611, 0.605, 0.598, 0.561, 0.571, 0.586, 0.587, 0.575, 0.580, 0.571, 0.577, 0.583, 0.576, 0.573, 0.580, 0.581, 0.587,
  0.596, 0.625, 0.621, 0.621, 0.617, 0.614, 0.611, 0.606, 0.607, 0.607, 0.598, 0.599, 0.604, 0.603, 0.607, 0.603, 0.599, 0.605, 0.604, 0.595, 0.597, 0.602, 0.600, 0.606,
  0.609, 0.611, 0.609, 0.597, 0.603, 0.603, 0.602, 0.595, 0.601, 0.586, 0.587, 0.592, 0.595, 0.599, 0.597, 0.597, 0.603, 0.607, 0.606, 0.608, 0.606, 0.582, 0.592, 0.585,
  0.583, 0.591, 0.593, 0.597, 0.582, 0.574, 0.581, 0.580, 0.580, 0.577, 0.575, 0.580, 0.581, 0.573, 0.586, 0.574, 0.570, 0.569, 0.567, 0.562, 0.575, 0.570, 0.573, 0.576,
  0.573, 0.573, 0.571, 0.571, 0.564, 0.572, 0.565, 0.561, 0.544, 0.548, 0.551, 0.558, 0.568, 0.574, 0.582, 0.578, 0.575, 0.575, 0.575, 0.569, 0.573, 0.574, 0.566, 0.577,
  0.576
)
val months = Array.tabulate(banana_prices.length)(-banana_prices.length + 1.0 + _)
val σ_f = 1.0 / 64
val l   = 1.0
val mean_price = banana_prices.sum / banana_prices.length
val kernel: Kernel[Double] = (xi,xj) => σ_f*σ_f * Math.exp( -(xi-xj)*(xi-xj) / (2*l*l) )
val gpr = GPR( x=months, y=banana_prices, y_shift=mean_price, kernel=kernel )
gps.regression.gpr.plot1d(gpr, Vec(months: _*), banana_prices, marginAbs=0.5, marginRel=0.0)

GP Regression with Hyperparameter Optimization

GauProS allows the easy composition and training of kernels with hyperparameters.
Trainable parameters are identified by a Symbol. GauProS uses an (un)boxed variant
of a BFGS optimizer. Said optimizer does not yet support starting from the box borders.
The initial hyperparameter values have to be well inside and not on the boundary of
the box.

// http://www.gaussianprocess.org/gpml/chapters/RW2.pdf#page=13
val kernel = Noise('σ_n * 'σ_n)  +  'σ_f * 'σ_f * Exp( - AbsDelta.pow(2.0) / (2 * 'l * 'l) )
val gpr = GPR.fit_shifted(
  x=months       ,
  y=banana_prices,
  y_shift = 'y_shift,
  kernel=kernel,
  likelihood_fn = GPR.logp_loo[Double], // <- The loss/likelihood function used for optimization.
                                        //    Built-in: GPR.logp_marginal and GPR.logp_loo
  param_init = Map(
    'σ_n -> 1,
    'σ_f -> 1,
    'l -> 4
  ),
  param_min = Map.empty[Symbol,Double] withDefaultValue Double.NegativeInfinity,
  param_max = Map.empty[Symbol,Double] withDefaultValue Double.PositiveInfinity
)
println(gpr.params) // <- the trained hyperparameter values
gps.regression.gpr.plot1d(gpr, Vec(months: _*), banana_prices, marginAbs=0.5, marginRel=0.0)