Hard Thresholding is Non-Convex, Scaled

Hard Thresholding is Non-Convex, Scaled.carbide.md

Hard Thresholding is Non-Convex, Scaled

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cell0.js

var lam      = 1.75;
var stdDev1  = Math.sqrt(3 + 0.55 * Math.sqrt(3));
var sigma    = 0.55/stdDev1;
var stdDev2  = Math.sqrt(4 + 0.70 * Math.sqrt(4));
var varsigma = 0.70/stdDev2;
var theta    = 1/(1 + sigma**2);
var vartheta = 1/(1 + varsigma**2);


var MSE0   = 1;
var MSE1   = (1/2)*(1-theta**2) + (1/2);
var MSE2   = (1/6) + (2/3)*(1-vartheta**2) + (1/6);
var MSE3   = (1/2) + (1/2)*(1-theta**2);
var MSE12  = (1/6)*(1-theta**2) + (1/3)*([1-theta] - [0.5*(2-theta)*vartheta])**2 + (1/3)*(1-vartheta**2) + (1/6);
var MSE13  = (1/2)*(1-theta**2) + (1/2)*(1-theta**2);
var MSE23  = (1/6) + (1/3)*(1-vartheta**2) + (1/3)*([1-theta] - [0.5*(2-theta)*vartheta])**2 + (1/6)*(1-theta**2);
var MSE123 = (1/6)*(1-theta**2) + (2/3)*([1-theta] - [0.5*(2-theta)*vartheta])**2 + (1/6)*(1-theta**2);



var PEN0   = 0;
var PEN1   = lam;
var PEN2   = lam;
var PEN3   = lam;
var PEN12  = 2*lam;
var PEN13  = 2*lam;
var PEN23  = 2*lam;
var PEN123 = 3*lam;



var VAL13  = MSE13 + PEN13;
var VAL12  = MSE12 + PEN12;
var VAL2   = MSE2 + PEN2;
var VAL1   = MSE1 + PEN1;
var VAL123 = MSE123 + PEN123;

VAL13 < VAL12;
VAL2 < VAL1;
VAL2 < VAL12;
VAL2 < VAL123;
VAL2 < 6;


var CORR12 = Math.sqrt(theta*vartheta/3);