public void learn_new_mechanism() { #region doc_log_reg_1 // Suppose we have the following data about some patients. // The first variable is continuous and represent patient // age. The second variable is dichotomic and give whether // they smoke or not (This is completely fictional data). // We also know if they have had lung cancer or not, and // we would like to know whether smoking has any connection // with lung cancer (This is completely fictional data). double[][] input = { // age, smokes?, had cancer? new double[] { 55, 0 }, // false - no cancer new double[] { 28, 0 }, // false new double[] { 65, 1 }, // false new double[] { 46, 0 }, // true - had cancer new double[] { 86, 1 }, // true new double[] { 56, 1 }, // true new double[] { 85, 0 }, // false new double[] { 33, 0 }, // false new double[] { 21, 1 }, // false new double[] { 42, 1 }, // true }; bool[] output = // Whether each patient had lung cancer or not { false, false, false, true, true, true, false, false, false, true }; // To verify this hypothesis, we are going to create a logistic // regression model for those two inputs (age and smoking), learned // using a method called "Iteratively Reweighted Least Squares": var learner = new IterativeReweightedLeastSquares <LogisticRegression>() { Tolerance = 1e-4, // Let's set some convergence parameters Iterations = 100, // maximum number of iterations to perform Regularization = 0 }; // Now, we can use the learner to finally estimate our model: LogisticRegression regression = learner.Learn(input, output); // At this point, we can compute the odds ratio of our variables. // In the model, the variable at 0 is always the intercept term, // with the other following in the sequence. Index 1 is the age // and index 2 is whether the patient smokes or not. // For the age variable, we have that individuals with // higher age have 1.021 greater odds of getting lung // cancer controlling for cigarette smoking. double ageOdds = regression.GetOddsRatio(1); // 1.0208597028836701 // For the smoking/non smoking category variable, however, we // have that individuals who smoke have 5.858 greater odds // of developing lung cancer compared to those who do not // smoke, controlling for age (remember, this is completely // fictional and for demonstration purposes only). double smokeOdds = regression.GetOddsRatio(2); // 5.8584748789881331 // If we would like to use the model to predict a probability for // each patient regarding whether they are at risk of cancer or not, // we can use the Probability function: double[] scores = regression.Probability(input); // Finally, if we would like to arrive at a conclusion regarding // each patient, we can use the Decide method, which will transform // the probabilities (from 0 to 1) into actual true/false values: bool[] actual = regression.Decide(input); #endregion double[] expected = { 0.21044171560168326, 0.13242527535212373, 0.65747803433771812, 0.18122484822324372, 0.74755661773156912, 0.61450041841477232, 0.33116705418194975, 0.14474110902457912, 0.43627109657399382, 0.54419383282533118 }; for (int i = 0; i < scores.Length; i++) { Assert.AreEqual(expected[i], scores[i], 1e-8); } double[] transform = regression.Transform(input, scores); for (int i = 0; i < scores.Length; i++) { Assert.AreEqual(expected[i], transform[i], 1e-8); } Assert.AreEqual(1.0208597028836701, ageOdds, 1e-10); Assert.AreEqual(5.8584748789881331, smokeOdds, 1e-6); Assert.AreEqual(-2.4577464307294092, regression.Intercept, 1e-8); Assert.AreEqual(-2.4577464307294092, regression.Coefficients[0], 1e-8); Assert.AreEqual(0.020645118265359252, regression.Coefficients[1], 1e-10); Assert.AreEqual(1.7678893101571855, regression.Coefficients[2], 1e-8); Assert.IsFalse(actual[0]); Assert.IsFalse(actual[1]); Assert.IsTrue(actual[2]); Assert.IsFalse(actual[3]); Assert.IsTrue(actual[4]); Assert.IsTrue(actual[5]); Assert.IsFalse(actual[6]); Assert.IsFalse(actual[7]); Assert.IsFalse(actual[8]); Assert.IsTrue(actual[9]); }