C#: logistic regression for classification

Logistic regression is a classifier. It computes a weighted sum z = w·x + b, passes it through the sigmoid 1 / (1 + e^−z) to get a probability between 0 and 1, and predicts class 1 when the probability is at least 0.5. Unlike a squared-error line fit, it is trained to maximize the likelihood of the labels.

using System;
using System.Globalization;

class Program {
  static double Sigmoid(double z) {
    return 1.0 / (1.0 + Math.Exp(-z));
  }

  static string F(double v) {
    return v.ToString("F2", CultureInfo.InvariantCulture);
  }

  static void Main() {
    double[] hours = { 1, 2, 3, 4, 5, 6 };
    int[] passed = { 0, 0, 1, 0, 1, 1 };
    double w = 0, b = 0, rate = 0.1;

    for (int epoch = 0; epoch < 5000; epoch++) {
      double gw = 0, gb = 0;
      for (int i = 0; i < hours.Length; i++) {
        double error = Sigmoid(w * hours[i] + b) - passed[i];
        gw += error * hours[i] / hours.Length;
        gb += error / hours.Length;
      }
      w -= rate * gw;
      b -= rate * gb;
    }

    Console.WriteLine("w=" + F(w) + " b=" + F(b));
    Console.WriteLine("P(pass | 1h) = " + F(Sigmoid(w * 1 + b)));
    Console.WriteLine("P(pass | 6h) = " + F(Sigmoid(w * 6 + b)));
    int correct = 0;
    for (int i = 0; i < hours.Length; i++) {
      int predicted = Sigmoid(w * hours[i] + b) >= 0.5 ? 1 : 0;
      if (predicted == passed[i]) correct++;
    }
    Console.WriteLine("accuracy: " + correct + "/" + hours.Length);
  }
}

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