From 06cceabc6e9f8d1c883331955594465d2bc606d2 Mon Sep 17 00:00:00 2001
From: Joakim Skogholt <onlinereg@skogholt.xyz>
Date: Mon, 5 Feb 2024 15:32:24 +0100
Subject: [PATCH] Added fast k-fold update of reg coeffs

---
 src/TR.jl   | 75 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 src/Ting.jl |  1 +
 2 files changed, 76 insertions(+)

diff --git a/src/TR.jl b/src/TR.jl
index 5c3b68e..ca4f5ee 100644
--- a/src/TR.jl
+++ b/src/TR.jl
@@ -1,7 +1,82 @@
 
 
 
+"""
+Fast k-fold cv for updating regression coefficients
+"""
+function TRSegCVUpdate(X, y, lambdas, cv, bold, regType="L2", regParam1=0, regParam2=1e-14)
 
+n, p = size(X);
+mX   = mean(X, dims=1);    
+X    = X .- mX;
+my   = mean(y);    
+y    = y .- my; 
+
+if regType == "bc"
+    regMat  = [I(p); zeros(regParam1,p)]; for i = 1:regParam1 regMat = diff(regMat, dims = 1); end
+elseif regType == "legendre"
+    regMat  = [I(p); zeros(regParam1,p)]; for i = 1:regParam1 regMat = diff(regMat, dims = 1); end
+    P, _    = plegendre(regParam-1, p);   
+    regMat[end-regParam1+1:end,:] = sqrt(regParam2) * P;
+elseif regType == "L2"
+    regMat = I(p);
+elseif regType == "std"
+    regMat = Diagonal(vec(std(X, dims=1)));
+elseif regType == "GL" # Grünwald-Letnikov fractional derivative regulariztion
+    # regParam1 is alpha (order of fractional derivative)
+    C = ones(p)*1.0;
+    for k in 2:p
+        C[k] = (1-(regParam1+1)/(k-1)) * C[k-1];
+    end
+
+    regMat = zeros(p,p);
+
+    for i in 1:p
+        regMat[i:end, i] = C[1:end-i+1];
+    end
+end
+
+
+X       = X / regMat;
+U, s, V = svd(X, full=false);
+
+n_seg     = maximum(cv);
+n_lambdas = length(lambdas);
+my        = mean(y);
+y         = y .- my;
+
+denom  = broadcast(.+, broadcast(./, lambdas, s'), s')'; 
+denom2 = broadcast(.+, ones(n), broadcast(./, lambdas', s.^2))
+resid  = broadcast(.-, y, U * (broadcast(./, s .* (U'*y), denom) + s .* broadcast(.-, 1, broadcast(./, 1, denom2)) .* (V' * bold)))
+rescv  = zeros(n, n_lambdas);
+sdenom = sqrt.(broadcast(./, s, denom))';
+
+for seg in 1:n_seg
+        
+    Useg = U[vec(cv .== seg),:];
+    Id   = 1.0 * I(size(Useg,1)) .- 1/n;
+        
+    for k in 1:n_lambdas
+        Uk                        = Useg .* sdenom[k,:]';
+        rescv[vec(cv .== seg), k] = (Id - Uk * Uk') \ resid[vec(cv .== seg), k];
+    end
+end
+
+press  = sum(rescv.^2, dims=1)';
+rmsecv = sqrt.(1/n .* press);
+bcoeffs = V * broadcast(./, (U' * y), denom);
+bcoeffs = regMat \ bcoeffs;
+
+if my != 0
+    bcoeffs = [my .- mX*bcoeffs; bcoeffs];
+end
+
+lambda_min, lambda_min_ind = findmin(rmsecv)
+lambda_min_ind             = lambda_min_ind[1]
+b_lambda_min               = bcoeffs[:,lambda_min_ind]
+    
+return b_lambda_min, rmsecv, lambda_min, lambda_min_ind
+end
 
 """
 Updates regression coefficient by solving the augmented TR problem [Xs; sqrt(lambda)*I] * beta = [ys; sqrt(lambda)*b_old]
diff --git a/src/Ting.jl b/src/Ting.jl
index d4e6246..561f576 100644
--- a/src/Ting.jl
+++ b/src/Ting.jl
@@ -21,6 +21,7 @@ export TRLooCV
 export TRSegCV
 export regularizationMatrix
 export TRLooCVUpdate
+export TRSegCVUpdate
 
 include("convenience.jl")
 include("TR.jl")