First WIP for examples

Author: theogf

examples/deepkernellearning.jl

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+using KernelFunctions
+using MLDataUtils
+using Zygote
+using Flux
+using Distributions, LinearAlgebra
+using Plots
+
+Flux.@functor SqExponentialKernel
+Flux.@functor KernelSum
+Flux.@functor Matern32Kernel
+Flux.@functor FunctionTransform
+
+neuralnet = Chain(Dense(1,3),Dense(3,2))
+k = SqExponentialKernel(FunctionTransform(neuralnet))
+xmin = -3; xmax = 3
+x = range(xmin,xmax,length=100)
+x_test = rand(Uniform(xmin,xmax),200)
+x,y = noisy_function(sinc,x;noise=0.1)
+X = reshape(x,:,1)
+λ = [0.1]
+f(x,k,λ) = kernelmatrix(k,X,x,obsdim=1)*inv(kernelmatrix(k,X,obsdim=1)+exp(λ[1])*I)*y
+f(X,k,1.0)
+loss(k,λ) = f(X,k,λ) |> ŷ ->sum(y-ŷ)/length(y)+exp(λ[1])*norm(ŷ)
+loss(k,λ)
+ps = Flux.params(k)
+# push!(ps,λ)
+opt = Flux.Momentum(1.0)
+##
+for i in 1:10
+    grads = Zygote.gradient(()->loss(k,λ),ps)
+    Flux.Optimise.update!(opt,ps,grads)
+    p = Plots.scatter(x,y,lab="data",title="Loss = $(loss(k,λ))")
+    Plots.plot!(x,f(X,k,λ),lab="Prediction",lw=3.0)
+    display(p)
+end

examples/kernelridgeregression.jl

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+using KernelFunctions
+using MLDataUtils
+using Zygote
+using Flux
+using Distributions, LinearAlgebra
+using Plots
+
+Flux.@functor SqExponentialKernel
+Flux.@functor ScaleTransform
+Flux.@functor KernelSum
+Flux.@functor Matern32Kernel
+
+xmin = -3; xmax = 3
+x = range(xmin,xmax,length=100)
+x_test = range(xmin,xmax,length=300)
+x,y = noisy_function(sinc,x;noise=0.1)
+X = reshape(x,:,1)
+X_test = reshape(x_test,:,1)
+k = SqExponentialKernel(1.0)#+Matern32Kernel(2.0)
+λ = [-1.0]
+f(x,k,λ) = kernelmatrix(k,x,X,obsdim=1)*inv(kernelmatrix(k,X,obsdim=1)+exp(λ[1])*I)*y
+f(X,k,1.0)
+loss(k,λ) = f(X,k,λ) |> ŷ ->sum(y-ŷ)/length(y)+exp(λ[1])*norm(ŷ)
+loss(k,λ)
+ps = Flux.params(k)
+push!(ps,λ)
+opt = Flux.Momentum(0.1)
+##
+for i in 1:10
+    grads = Zygote.gradient(()->loss(k,λ),ps)
+    Flux.Optimise.update!(opt,ps,grads)
+    p = Plots.scatter(x,y,lab="data",title="Loss = $(loss(k,λ))")
+    Plots.plot!(x_test,f(X_test,k,λ),lab="Prediction",lw=3.0)
+    display(p)
+end

examples/svm.jl

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+using KernelFunctions
+using MLDataUtils
+using Zygote
+using Flux
+using Distributions, LinearAlgebra
+using Plots
+
+N = 100 #Number of samples
+μ = randn(2,2) # Random Centers
+xgrid = range(-3,3,length=100) # Create a grid
+Xgrid = hcat(collect.(Iterators.product(xgrid,xgrid))...)' #Combine into a 2D grid
+y = rand([-1,1],N) # Select randomly between the two classes
+X = zeros(N,2)
+X[y.==1,:] = rand(MvNormal(μ[:,1],I),count(y.==1))' #Attribute samples from class 1
+X[y.==-1,:] = rand(MvNormal(μ[:,2],I),count(y.==-1))' # Attribute samples from class 2
+
+
+k = SqExponentialKernel(2.0) # Create kernel function
+f(x,k,λ) = kernelmatrix(k,x,X,obsdim=1)*inv(kernelmatrix(k,X,obsdim=1)+exp(λ[1])*I)*y # Optimal prediction f
+svmloss(y,ŷ)= f(X,k,λ) |> ŷ -> sum(maximum.(0.0,1-y*ŷ)) - λ*norm(ŷ) # Total svm loss with regularisation
+pred = f(Xgrid,k,λ) #Compute prediction on a grid
+contourf(xgrid,xgrid,pred)
+scatter!(eachcol(X)...,color=y,lab="data")