public final double lgrad(double u, double a, Loss loss) {
assert loss.isForNumeric() : "Loss function " + loss + " not applicable to numerics";
switch (loss) {
case Quadratic:
return 2 * (u - a);
case Absolute:
return Math.signum(u - a);
case Huber:
return Math.abs(u - a) <= 1 ? u - a : Math.signum(u - a);
case Poisson:
assert a >= 0 : "Poisson loss L(u,a) requires variable a >= 0";
return Math.exp(u) - a;
case Hinge:
// return a*u <= 1 ? -a : 0;
return a == 0
? (-u <= 1 ? 1 : 0)
: (u <= 1 ? -1 : 0); // Booleans are coded as {0,1} instead of {-1,1}
case Logistic:
// return -a/(1+Math.exp(a*u));
return a == 0
? 1 / (1 + Math.exp(-u))
: -1 / (1 + Math.exp(u)); // Booleans are coded as {0,1} instead of {-1,1}
case Periodic:
return ((2 * Math.PI) / _period) * Math.sin((a - u) * (2 * Math.PI) / _period);
default:
throw new RuntimeException("Unknown loss function " + loss);
}
}
public final double loss(double u, double a, Loss loss) {
assert loss.isForNumeric() : "Loss function " + loss + " not applicable to numerics";
switch (loss) {
case Quadratic:
return (u - a) * (u - a);
case Absolute:
return Math.abs(u - a);
case Huber:
return Math.abs(u - a) <= 1 ? 0.5 * (u - a) * (u - a) : Math.abs(u - a) - 0.5;
case Poisson:
assert a >= 0 : "Poisson loss L(u,a) requires variable a >= 0";
return Math.exp(u)
+ (a == 0 ? 0 : -a * u + a * Math.log(a) - a); // Since \lim_{a->0} a*log(a) = 0
case Hinge:
// return Math.max(1-a*u,0);
return Math.max(1 - (a == 0 ? -u : u), 0); // Booleans are coded {0,1} instead of {-1,1}
case Logistic:
// return Math.log(1 + Math.exp(-a * u));
return Math.log(
1 + Math.exp(a == 0 ? u : -u)); // Booleans are coded {0,1} instead of {-1,1}
case Periodic:
return 1 - Math.cos((a - u) * (2 * Math.PI) / _period);
default:
throw new RuntimeException("Unknown loss function " + loss);
}
}
public static double impute(double u, Loss loss) {
assert loss.isForNumeric() : "Loss function " + loss + " not applicable to numerics";
switch (loss) {
case Quadratic:
case Absolute:
case Huber:
case Periodic:
return u;
case Poisson:
return Math.exp(u) - 1;
case Hinge:
case Logistic:
return u > 0 ? 1 : 0; // Booleans are coded as {0,1} instead of {-1,1}
default:
throw new RuntimeException("Unknown loss function " + loss);
}
}