Algorithms

Applies the OAVI feature transformation to X_test.

Creates OAVI feature transformation fitted to X_train

Arguments

• 'X_train::Matrix{Float64}': training data
• 'max_degree::Int64': max degree of polynomials computed (default 10)
• 'psi::Float64': vanishing extent (default 0.1)
• 'epsilon::Float64': accuracy for convex optimizer (default 1.0e-7)
• 'tau::Union{Float64, Int64}': upper bound on norm of coefficient vector
• 'lambda::Float64': regularization parameter
• 'oracle::Union{String, <:Function}': string denoting which predefined constructor to use OR constructor function. (external constructor function MUST have 'data' and 'labels' as varargs)
• 'max_iters::Int64': max number of iterations in oracle
• 'inversehessianboost::String': whether or not to use IHB. Choose from "false", "weak" or "full".
• 'oracle_kwargs::Vector': Array containing keyword arguments for external constructor functions

Returns

• 'Xtraintransformed::Matrix{Float64}': transformed X_train
• 'sets::SetsOandG': instance of 'SetsOandG' keeping track of important sets

This function creates and applies a VCA transformation fitted to X.

Arguments

• 'X::Matrix{Float64}': data, stored row-wise
• 'psi::Float64': vanishing parameter
• 'max_degree::Int64': maximum degree to consider

Returns

• 'Xtraintransformed::Matrix{Float64}': X transformed according to transformation found by VCA
• 'sets_vca::SetsVCA': instance of SetsVCA containing relevant sets for VCA

Performs FindRangeNull (using SVD) for VCA. Reference: https://proceedings.mlr.press/v28/livni13.html

Arguments

• 'F::Matrix{Float64}': evaluation of F polynomials
• 'C::Matrix{Float64}': evaluation of C polynomials
• 'psi::Float64': vanishing parameter

Returns

• 'Vcoefficientvectors::Matrix{Float64}': Coefficient vectors of polynomials we append to V.
• 'Vevaluationvectors::Matrix{Float64}': Evaluation vectors of polynomials we append to V.
• 'Fcoefficientvectors::Matrix{Float64}': Coefficient vectors of polynomials we append to F.
• 'Fevaluationvectors::Matrix{Float64}': Evaluation vectors of polynomials we append to F.

Evaluates transformation corresponding to the polynomials in V.