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);
}
}
protected double calcLoglik(CoxPHModel model, final CoxPHTask coxMR) {
CoxPHModel.CoxPHParameters p = model._parms;
CoxPHModel.CoxPHOutput o = model._output;
final int n_coef = o.coef.length;
final int n_time = coxMR.sizeEvents.length;
double newLoglik = 0;
for (int j = 0; j < n_coef; ++j) o.gradient[j] = 0;
for (int j = 0; j < n_coef; ++j) for (int k = 0; k < n_coef; ++k) o.hessian[j][k] = 0;
switch (p.ties) {
case efron:
final double[] newLoglik_t = MemoryManager.malloc8d(n_time);
final double[][] gradient_t = malloc2DArray(n_time, n_coef);
final double[][][] hessian_t = malloc3DArray(n_time, n_coef, n_coef);
ForkJoinTask[] fjts = new ForkJoinTask[n_time];
for (int t = n_time - 1; t >= 0; --t) {
final int _t = t;
fjts[t] =
new RecursiveAction() {
@Override
protected void compute() {
final double sizeEvents_t = coxMR.sizeEvents[_t];
if (sizeEvents_t > 0) {
final long countEvents_t = coxMR.countEvents[_t];
final double sumLogRiskEvents_t = coxMR.sumLogRiskEvents[_t];
final double sumRiskEvents_t = coxMR.sumRiskEvents[_t];
final double rcumsumRisk_t = coxMR.rcumsumRisk[_t];
final double avgSize = sizeEvents_t / countEvents_t;
newLoglik_t[_t] = sumLogRiskEvents_t;
System.arraycopy(coxMR.sumXEvents[_t], 0, gradient_t[_t], 0, n_coef);
for (long e = 0; e < countEvents_t; ++e) {
final double frac = ((double) e) / ((double) countEvents_t);
final double term = rcumsumRisk_t - frac * sumRiskEvents_t;
newLoglik_t[_t] -= avgSize * Math.log(term);
for (int j = 0; j < n_coef; ++j) {
final double djTerm =
coxMR.rcumsumXRisk[_t][j] - frac * coxMR.sumXRiskEvents[_t][j];
final double djLogTerm = djTerm / term;
gradient_t[_t][j] -= avgSize * djLogTerm;
for (int k = 0; k < n_coef; ++k) {
final double dkTerm =
coxMR.rcumsumXRisk[_t][k] - frac * coxMR.sumXRiskEvents[_t][k];
final double djkTerm =
coxMR.rcumsumXXRisk[_t][j][k]
- frac * coxMR.sumXXRiskEvents[_t][j][k];
hessian_t[_t][j][k] -=
avgSize * (djkTerm / term - (djLogTerm * (dkTerm / term)));
}
}
}
}
}
};
}
ForkJoinTask.invokeAll(fjts);
for (int t = 0; t < n_time; ++t) newLoglik += newLoglik_t[t];
for (int t = 0; t < n_time; ++t)
for (int j = 0; j < n_coef; ++j) o.gradient[j] += gradient_t[t][j];
for (int t = 0; t < n_time; ++t)
for (int j = 0; j < n_coef; ++j)
for (int k = 0; k < n_coef; ++k) o.hessian[j][k] += hessian_t[t][j][k];
break;
case breslow:
for (int t = n_time - 1; t >= 0; --t) {
final double sizeEvents_t = coxMR.sizeEvents[t];
if (sizeEvents_t > 0) {
final double sumLogRiskEvents_t = coxMR.sumLogRiskEvents[t];
final double rcumsumRisk_t = coxMR.rcumsumRisk[t];
newLoglik += sumLogRiskEvents_t;
newLoglik -= sizeEvents_t * Math.log(rcumsumRisk_t);
for (int j = 0; j < n_coef; ++j) {
final double dlogTerm = coxMR.rcumsumXRisk[t][j] / rcumsumRisk_t;
o.gradient[j] += coxMR.sumXEvents[t][j];
o.gradient[j] -= sizeEvents_t * dlogTerm;
for (int k = 0; k < n_coef; ++k)
o.hessian[j][k] -=
sizeEvents_t
* (((coxMR.rcumsumXXRisk[t][j][k] / rcumsumRisk_t)
- (dlogTerm * (coxMR.rcumsumXRisk[t][k] / rcumsumRisk_t))));
}
}
}
break;
default:
throw new IllegalArgumentException("ties method must be either efron or breslow");
}
return newLoglik;
}