Example #1
0
 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);
   }
 }
Example #2
0
    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);
      }
    }
Example #3
0
 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);
   }
 }
Example #4
0
    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);
      }
    }
Example #5
0
 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);
   }
 }
Example #6
0
    // 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);
      }
    }