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);
}
}
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);
}
}
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 final double[] rproxgrad_x(double[] u, double alpha) { return rproxgrad(u, alpha,
// _gamma_x, _regularization_x, RandomUtils.getRNG(_seed)); }
// public final double[] rproxgrad_y(double[] u, double alpha) { return rproxgrad(u, alpha,
// _gamma_y, _regularization_y, RandomUtils.getRNG(_seed)); }
static double[] rproxgrad(
double[] u, double alpha, double gamma, Regularizer regularization, Random rand) {
if (u == null || alpha == 0 || gamma == 0) return u;
double[] v = new double[u.length];
switch (regularization) {
case None:
return u;
case Quadratic:
for (int i = 0; i < u.length; i++) v[i] = u[i] / (1 + 2 * alpha * gamma);
return v;
case L2:
// Proof uses Moreau decomposition; see section 6.5.1 of Parikh and Boyd
// https://web.stanford.edu/~boyd/papers/pdf/prox_algs.pdf
double weight = 1 - alpha * gamma / ArrayUtils.l2norm(u);
if (weight < 0) return v; // Zero vector
for (int i = 0; i < u.length; i++) v[i] = weight * u[i];
return v;
case L1:
for (int i = 0; i < u.length; i++)
v[i] = Math.max(u[i] - alpha * gamma, 0) + Math.min(u[i] + alpha * gamma, 0);
return v;
case NonNegative:
for (int i = 0; i < u.length; i++) v[i] = Math.max(u[i], 0);
return v;
case OneSparse:
int idx = ArrayUtils.maxIndex(u, rand);
v[idx] = u[idx] > 0 ? u[idx] : 1e-6;
return v;
case UnitOneSparse:
idx = ArrayUtils.maxIndex(u, rand);
v[idx] = 1;
return v;
case Simplex:
// Proximal gradient algorithm by Chen and Ye in http://arxiv.org/pdf/1101.6081v2.pdf
// 1) Sort input vector u in ascending order: u[1] <= ... <= u[n]
int n = u.length;
int[] idxs = new int[n];
for (int i = 0; i < n; i++) idxs[i] = i;
ArrayUtils.sort(idxs, u);
// 2) Calculate cumulative sum of u in descending order
// cumsum(u) = (..., u[n-2]+u[n-1]+u[n], u[n-1]+u[n], u[n])
double[] ucsum = new double[n];
ucsum[n - 1] = u[idxs[n - 1]];
for (int i = n - 2; i >= 0; i--) ucsum[i] = ucsum[i + 1] + u[idxs[i]];
// 3) Let t_i = (\sum_{j=i+1}^n u[j] - 1)/(n - i)
// For i = n-1,...,1, set optimal t* to first t_i >= u[i]
double t = (ucsum[0] - 1) / n; // Default t* = (\sum_{j=1}^n u[j] - 1)/n
for (int i = n - 1; i >= 1; i--) {
double tmp = (ucsum[i] - 1) / (n - i);
if (tmp >= u[idxs[i - 1]]) {
t = tmp;
break;
}
}
// 4) Return max(u - t*, 0) as projection of u onto simplex
double[] x = new double[u.length];
for (int i = 0; i < u.length; i++) x[i] = Math.max(u[i] - t, 0);
return x;
default:
throw new RuntimeException("Unknown regularization function " + regularization);
}
}