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 final double regularize(double[] u, Regularizer regularization) {
if (u == null) return 0;
double ureg = 0;
switch (regularization) {
case None:
return 0;
case Quadratic:
for (int i = 0; i < u.length; i++) ureg += u[i] * u[i];
return ureg;
case L2:
for (int i = 0; i < u.length; i++) ureg += u[i] * u[i];
return Math.sqrt(ureg);
case L1:
for (int i = 0; i < u.length; i++) ureg += Math.abs(u[i]);
return ureg;
case NonNegative:
for (int i = 0; i < u.length; i++) {
if (u[i] < 0) return Double.POSITIVE_INFINITY;
}
return 0;
case OneSparse:
int card = 0;
for (int i = 0; i < u.length; i++) {
if (u[i] < 0) return Double.POSITIVE_INFINITY;
else if (u[i] > 0) card++;
}
return card == 1 ? 0 : Double.POSITIVE_INFINITY;
case UnitOneSparse:
int ones = 0, zeros = 0;
for (int i = 0; i < u.length; i++) {
if (u[i] == 1) ones++;
else if (u[i] == 0) zeros++;
else return Double.POSITIVE_INFINITY;
}
return ones == 1 && zeros == u.length - 1 ? 0 : Double.POSITIVE_INFINITY;
case Simplex:
double sum = 0, absum = 0;
for (int i = 0; i < u.length; i++) {
if (u[i] < 0) return Double.POSITIVE_INFINITY;
else {
sum += u[i];
absum += Math.abs(u[i]);
}
}
return MathUtils.equalsWithinRecSumErr(sum, 1.0, u.length, absum)
? 0
: Double.POSITIVE_INFINITY;
default:
throw new RuntimeException("Unknown regularization function " + regularization);
}
}
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);
}
}