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 int mimpute(double[] u, Loss multi_loss) {
assert multi_loss.isForCategorical()
: "Loss function " + multi_loss + " not applicable to categoricals";
switch (multi_loss) {
case Categorical:
case Ordinal:
double[] cand = new double[u.length];
for (int a = 0; a < cand.length; a++) cand[a] = mloss(u, a, multi_loss);
return ArrayUtils.minIndex(cand);
default:
throw new RuntimeException("Unknown multidimensional loss function " + multi_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);
}
}
public static double[] mlgrad(double[] u, int a, Loss multi_loss) {
assert multi_loss.isForCategorical()
: "Loss function " + multi_loss + " not applicable to categoricals";
if (a < 0 || a > u.length - 1)
throw new IllegalArgumentException(
"Index must be between 0 and " + String.valueOf(u.length - 1));
double[] grad = new double[u.length];
switch (multi_loss) {
case Categorical:
for (int i = 0; i < u.length; i++) grad[i] = (1 + u[i] > 0) ? 1 : 0;
grad[a] = (1 - u[a] > 0) ? -1 : 0;
return grad;
case Ordinal:
for (int i = 0; i < u.length - 1; i++) grad[i] = (a > i && 1 - u[i] > 0) ? -1 : 0;
return grad;
default:
throw new RuntimeException("Unknown multidimensional loss function " + multi_loss);
}
}
public static double mloss(double[] u, int a, Loss multi_loss) {
assert multi_loss.isForCategorical()
: "Loss function " + multi_loss + " not applicable to categoricals";
if (a < 0 || a > u.length - 1)
throw new IllegalArgumentException(
"Index must be between 0 and " + String.valueOf(u.length - 1));
double sum = 0;
switch (multi_loss) {
case Categorical:
for (int i = 0; i < u.length; i++) sum += Math.max(1 + u[i], 0);
sum += Math.max(1 - u[a], 0) - Math.max(1 + u[a], 0);
return sum;
case Ordinal:
for (int i = 0; i < u.length - 1; i++) sum += Math.max(a > i ? 1 - u[i] : 1, 0);
return sum;
default:
throw new RuntimeException("Unknown multidimensional loss function " + multi_loss);
}
}
