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package hex.genmodel.algos.glrm;
import hex.genmodel.utils.ArrayUtils;
/**
* Loss function for the GLRM algorithm.
*/
public enum GlrmLoss {
//--------------------------------------------------------------------------------------------------------------------
// Loss functions for numeric features
//--------------------------------------------------------------------------------------------------------------------
Quadratic {
@Override public boolean isForNumeric() { return true; }
@Override public boolean isForCategorical() { return false; }
@Override public boolean isForBinary() { return false; }
@Override public double loss(double u, double a) {
return (u - a)*(u - a);
}
@Override public double lgrad(double u, double a) {
return 2*(u - a);
}
@Override public double impute(double u) {
return u;
}
},
Absolute {
@Override public boolean isForNumeric() { return true; }
@Override public boolean isForCategorical() { return false; }
@Override public boolean isForBinary() { return false; }
@Override public double loss(double u, double a) {
return Math.abs(u - a);
}
@Override public double lgrad(double u, double a) {
return Math.signum(u - a);
}
@Override public double impute(double u) {
return u;
}
},
Huber {
@Override public boolean isForNumeric() { return true; }
@Override public boolean isForCategorical() { return false; }
@Override public boolean isForBinary() { return false; }
@Override public double loss(double u, double a) {
double x = u - a;
return x > 1? x - 0.5 : x < -1 ? -x - 0.5 : 0.5*x*x;
}
@Override public double lgrad(double u, double a) {
double x = u - a;
return x > 1? 1 : x < -1 ? -1 : x;
}
@Override public double impute(double u) {
return u;
}
},
Poisson {
@Override public boolean isForNumeric() { return true; }
@Override public boolean isForCategorical() { return false; }
@Override public boolean isForBinary() { return false; }
@Override public double loss(double u, double a) {
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
}
@Override public double lgrad(double u, double a) {
assert a >= 0 : "Poisson loss L(u,a) requires variable a >= 0";
return Math.exp(u) - a;
}
@Override public double impute(double u) {
return Math.exp(u);
}
},
Periodic {
@Override public boolean isForNumeric() { return true; }
@Override public boolean isForCategorical() { return false; }
@Override public boolean isForBinary() { return false; }
private double f;
private int period;
@Override public double loss(double u, double a) {
return 1 - Math.cos((u - a)*f);
}
@Override public double lgrad(double u, double a) {
return f * Math.sin((u - a)*f);
}
@Override public double impute(double u) {
return u;
}
@Override public void setParameters(int period) {
this.period = period;
f = 2 * Math.PI / period;
}
@Override public String toString() { return "Periodic(" + period + ")"; }
},
//--------------------------------------------------------------------------------------------------------------------
// Loss functions for binary features
//--------------------------------------------------------------------------------------------------------------------
Logistic {
@Override public boolean isForNumeric() { return false; }
@Override public boolean isForCategorical() { return false; }
@Override public boolean isForBinary() { return true; }
@Override public double loss(double u, double a) {
assert a == 0 || a == 1 : "Logistic loss should be applied to binary features only";
return Math.log(1 + Math.exp((1 - 2*a)*u));
}
@Override public double lgrad(double u, double a) {
double s = 1 - 2*a;
return s/(1 + Math.exp(-s*u));
}
@Override public double impute(double u) {
return u > 0? 1 : 0;
}
},
Hinge {
@Override public boolean isForNumeric() { return false; }
@Override public boolean isForCategorical() { return false; }
@Override public boolean isForBinary() { return true; }
@Override public double loss(double u, double a) {
assert a == 0 || a == 1 : "Hinge loss should be applied to binary variables only";
return Math.max(1 + (1 - 2*a)*u, 0);
}
@Override public double lgrad(double u, double a) {
double s = 1 - 2*a;
return 1 + s*u > 0? s : 0;
}
@Override public double impute(double u) {
return u > 0? 1 : 0;
}
},
//--------------------------------------------------------------------------------------------------------------------
// Loss functions for multinomial features
//--------------------------------------------------------------------------------------------------------------------
Categorical {
@Override public boolean isForNumeric() { return false; }
@Override public boolean isForCategorical() { return true; }
@Override public boolean isForBinary() { return false; }
@Override public double mloss(double[] u, int a) {
return mloss(u, a, u.length);
}
// this function performs the same function as the one above but it is memory optimized for the original
// GLRM.java code. See GLRM.java for details
@Override public double mloss(double[] u, int a, int u_len) {
if (!(a >= 0 && a < u_len))
throw new IndexOutOfBoundsException("a must be between 0 and " + (u_len - 1));
double sum = 0;
for (int ind=0; ind < u_len; ind++)
sum += Math.max(1 + u[ind], 0);
sum += Math.max(1 - u[a], 0) - Math.max(1 + u[a], 0);
return sum;
}
@Override public double[] mlgrad(double[] u, int a) {
double[] grad = new double[u.length];
return mlgrad(u, a, grad, u.length);
}
@Override public double[] mlgrad(double[] u, int a, double[] grad, int u_len) {
if (!(a >= 0 && a < u_len)) throw new IndexOutOfBoundsException("a must be between 0 and " + (u_len - 1));
for (int i = 0; i < u_len; i++)
grad[i] = (1 + u[i] > 0) ? 1 : 0;
grad[a] = (1 - u[a] > 0) ? -1 : 0;
return grad;
}
@Override public int mimpute(double[] u) {
return ArrayUtils.maxIndex(u);
}
},
Ordinal {
@Override public boolean isForNumeric() { return false; }
@Override public boolean isForCategorical() { return true; }
@Override public boolean isForBinary() { return false; }
@Override public double mloss(double[] u, int a) { return mloss(u, a, u.length); }
@Override public double mloss(double[] u, int a, int u_len) {
if (!(a >= 0 && a < u_len)) throw new IndexOutOfBoundsException("a must be between 0 and " + (u_len - 1));
double sum = 0;
for (int i = 0; i < u_len - 1; i++)
sum += a > i ? Math.max(1 - u[i], 0) : 1;
return sum;
}
@Override public double[] mlgrad(double[] u, int a) {
double[] grad = new double[u.length];
return mlgrad(u, a, grad, u.length);
}
@Override public double[] mlgrad(double[] u, int a, double[] grad, int u_len) {
if (!(a >= 0 && a < u_len)) throw new IndexOutOfBoundsException("a must be between 0 and " + (u_len - 1));
for (int i = 0; i < u_len - 1; i++)
grad[i] = (a > i && 1 - u[i] > 0) ? -1 : 0;
return grad;
}
@Override public int mimpute(double[] u) {
double sum = u.length - 1;
double best_loss = sum;
int best_a = 0;
for (int a = 1; a < u.length; a++) {
sum -= Math.min(1, u[a - 1]);
if (sum < best_loss) {
best_loss = sum;
best_a = a;
}
}
return best_a;
}
};
//--------------------------------------------------------------------------------------------------------------------
// Public interface
//--------------------------------------------------------------------------------------------------------------------
public abstract boolean isForNumeric();
public abstract boolean isForCategorical();
public abstract boolean isForBinary();
/** Loss function for numeric variables */
public double loss(double u, double a) { throw new UnsupportedOperationException(); }
/** \grad_u L(u,a): Derivative of the numeric loss function with respect to u */
public double lgrad(double u, double a) { throw new UnsupportedOperationException(); }
/** \argmin_a L(u, a): Data imputation for real numeric values */
public double impute(double u) { throw new UnsupportedOperationException(); }
/** Loss function for categorical variables where the size of u represents the true column length. */
public double mloss(double[] u, int a) { throw new UnsupportedOperationException(); }
/** Loss function for categorical variables performing same function as mloss above. However, in this case,
* the size of u can be much bigger than what is needed. The actual length of u is now specified in u_len. */
public double mloss(double[] u, int a, int u_len) { throw new UnsupportedOperationException(); }
/** \grad_u L(u,a): Gradient of multidimensional loss function with respect to u */
public double[] mlgrad(double[] u, int a) { throw new UnsupportedOperationException(); }
/** \grad_u L(u,a): Gradient of multidimensional loss function with respect to u. This method avoids the
* memory allocation compared to the method above by passing in a array prod which can be longer
* than the actual column length. The actual column length for prod is now specified by u_len. */
public double[] mlgrad(double[] u, int a, double[] prod, int u_len) { throw new UnsupportedOperationException(); }
/** \argmin_a L(u, a): Data imputation for categorical values {0, 1, 2, ...} */
public int mimpute(double[] u) { throw new UnsupportedOperationException(); }
/** Initialize additional parameters on the loss function. Currently used by Periodic class only. */
public void setParameters(int p) { throw new UnsupportedOperationException(); }
}
