static public int [] MultiNomialLogRegressionLowerBoundNewtonRaphson(double [][] input1, int[] labels, string SaveFile)
{
// http://accord-framework.net/docs/html/T_Accord_Statistics_Models_Regression_MultinomialLogisticRegression.htm
// Create a estimation algorithm to estimate the regression
LowerBoundNewtonRaphson lbnr = new LowerBoundNewtonRaphson()
{
MaxIterations = 10,
Tolerance = 1e-6
};
// *******************************************************************************
var cv = CrossValidation.Create(
k: 10, // We will be using 10-fold cross validation
// First we define the learning algorithm:
learner: (p) => new LowerBoundNewtonRaphson(),
// Now we have to specify how the n.b. performance should be measured:
loss: (actual, expected, p) => new ZeroOneLoss(expected).Loss(actual),
// This function can be used to perform any special
// operations before the actual learning is done, but
// here we will just leave it as simple as it can be:
fit: (teach, x, y, w) => teach.Learn(x, y, w),
// Finally, we have to pass the input and output data
// that will be used in cross-validation.
x: input1, y: labels
);
// Genrate a cross validation of the data
var cvresult = cv.Learn(input1, labels);
// iteratively estimate the model
MultinomialLogisticRegression mlr = lbnr.Learn(input1, labels);
// Generate statistics from confusion matrices
ConfusionMatrix cm = ConfusionMatrix.Estimate(mlr, input1, labels);
GeneralConfusionMatrix gcm = cvresult.ToConfusionMatrix(input1, labels);
Funcs.Utility.OutPutStats(cvresult.NumberOfSamples, cvresult.NumberOfInputs,
cvresult.Training.Mean, gcm.Accuracy, cm.FalsePositives, cm.FalseNegatives, cm.FScore);
// We can compute the model answers
int[] answers = mlr.Decide(input1);
string modelsavefile = SaveFile.Replace(".csv", ".MLR.save");
mlr.Save(modelsavefile, compression: SerializerCompression.None);
return(answers);
}
#pragma warning restore 612, 618
/// <summary>
/// Learns a model that can map the given inputs to the given outputs.
/// </summary>
/// <param name="x">The model inputs.</param>
/// <param name="y">The desired outputs associated with each <paramref name="x">inputs</paramref>.</param>
/// <param name="weights">The weight of importance for each input-output pair.</param>
/// <returns>
/// A model that has learned how to produce <paramref name="y" /> given <paramref name="x" />.
/// </returns>
public MultinomialLogisticRegression Learn(double[][] x, double[][] y, double[] weights = null)
{
var learning = new LowerBoundNewtonRaphson(regression)
{
Tolerance = tolerance,
Iterations = iterations
};
learning.Learn(x, y, weights);
computeInformation(x, y);
return(regression);
}
public void doc_learn()
{
#region doc_learn
// Declare a very simple classification/regression
// problem with only 2 input variables (x and y):
double[][] inputs =
{
new[] { 3.0, 1.0 },
new[] { 7.0, 1.0 },
new[] { 3.0, 1.1 },
new[] { 3.0, 2.0 },
new[] { 6.0, 1.0 },
};
// Class labels for each of the inputs
int[] outputs =
{
0, 2, 0, 1, 2
};
// Create a estimation algorithm to estimate the regression
LowerBoundNewtonRaphson lbnr = new LowerBoundNewtonRaphson()
{
MaxIterations = 100,
Tolerance = 1e-6
};
// Now, we will iteratively estimate our model:
MultinomialLogisticRegression mlr = lbnr.Learn(inputs, outputs);
// We can compute the model answers
int[] answers = mlr.Decide(inputs);
// And also the probability of each of the answers
double[][] probabilities = mlr.Probabilities(inputs);
// Now we can check how good our model is at predicting
double error = new ZeroOneLoss(outputs).Loss(answers);
// We can also verify the classes with highest
// probability are the ones being decided for:
int[] argmax = probabilities.ArgMax(dimension: 1); // should be same as 'answers'
#endregion
Assert.AreEqual(0, error);
Assert.AreEqual(answers, argmax);
}
/// <summary>
/// Computes the Multiple Linear Regression Analysis.
/// </summary>
///
public bool Compute()
{
double delta;
int iteration = 0;
var learning = new LowerBoundNewtonRaphson(regression);
do // learning iterations until convergence
{
delta = learning.Run(inputData, outputData);
iteration++;
} while (delta > tolerance && iteration < iterations);
// Check if the full model has converged
bool converged = iteration < iterations;
computeInformation();
return(converged);
}
private MultinomialLogisticRegression buildModel()
{
if (independent == null)
{
formatData();
}
mlr = new MultinomialLogisticRegression(nvars, ncat);
LowerBoundNewtonRaphson lbn = new LowerBoundNewtonRaphson(mlr);
do
{
delta = lbn.Run(independent, dependent);
iteration++;
} while (iteration < totit && delta > converg);
coefficients = mlr.Coefficients;
standarderror = new double[ncat - 1][];
waldstat = new double[ncat - 1][];
waldpvalue = new double[ncat - 1][];
for (int i = 0; i < coefficients.Length; i++)
{
double[] steArr = new double[nvars + 1];
double[] waldStatArr = new double[nvars + 1];
double[] waldPvalueArr = new double[nvars + 1];
for (int j = 0; j < nvars + 1; j++)
{
Accord.Statistics.Testing.WaldTest wt = mlr.GetWaldTest(i, j);
steArr[j] = wt.StandardError;
waldStatArr[j] = wt.Statistic;
waldPvalueArr[j] = wt.PValue;
}
waldstat[i] = waldStatArr;
waldpvalue[i] = waldPvalueArr;
standarderror[i] = steArr;
}
loglikelihood = mlr.GetLogLikelihood(independent, dependent);
deviance = mlr.GetDeviance(independent, dependent);
x2 = mlr.ChiSquare(independent, dependent).Statistic;
pv = mlr.ChiSquare(independent, dependent).PValue;
return(mlr);
}
private static void multinomial(double[][] inputs, int[] outputs)
{
var lbnr = new LowerBoundNewtonRaphson()
{
MaxIterations = 100,
Tolerance = 1e-6
};
// Learn a multinomial logistic regression using the teacher:
MultinomialLogisticRegression mlr = lbnr.Learn(inputs, outputs);
// We can compute the model answers
int[] answers = mlr.Decide(inputs);
// And also the probability of each of the answers
double[][] probabilities = mlr.Probabilities(inputs);
// Now we can check how good our model is at predicting
double error = new AccuracyLoss(outputs).Loss(answers);
// We can also verify the classes with highest
// probability are the ones being decided for:
int[] argmax = probabilities.ArgMax(dimension: 1); // should be same as 'answers'
}
public void RegressTest2()
{
double[][] inputs;
int[] outputs;
CreateInputOutputsExample1(out inputs, out outputs);
// Create a new Multinomial Logistic Regression for 3 categories
var mlr = new MultinomialLogisticRegression(inputs: 2, categories: 3);
// Create a estimation algorithm to estimate the regression
LowerBoundNewtonRaphson lbnr = new LowerBoundNewtonRaphson(mlr);
// Now, we will iteratively estimate our model. The Run method returns
// the maximum relative change in the model parameters and we will use
// it as the convergence criteria.
double delta;
int iteration = 0;
do
{
// Perform an iteration
delta = lbnr.Run(inputs, outputs);
iteration++;
} while (iteration < 100 && delta > 1e-6);
Assert.AreEqual(52, iteration);
Assert.IsFalse(double.IsNaN(mlr.Coefficients[0][0]));
Assert.IsFalse(double.IsNaN(mlr.Coefficients[0][1]));
Assert.IsFalse(double.IsNaN(mlr.Coefficients[0][2]));
Assert.IsFalse(double.IsNaN(mlr.Coefficients[1][0]));
Assert.IsFalse(double.IsNaN(mlr.Coefficients[1][1]));
Assert.IsFalse(double.IsNaN(mlr.Coefficients[1][2]));
// This is the same example given in R Data Analysis Examples for
// Multinomial Logistic Regression: http://www.ats.ucla.edu/stat/r/dae/mlogit.htm
// brand 2
Assert.AreEqual(-11.774655, mlr.Coefficients[0][0], 1e-4); // intercept
Assert.AreEqual(0.523814, mlr.Coefficients[0][1], 1e-4); // female
Assert.AreEqual(0.368206, mlr.Coefficients[0][2], 1e-4); // age
// brand 3
Assert.AreEqual(-22.721396, mlr.Coefficients[1][0], 1e-4); // intercept
Assert.AreEqual(0.465941, mlr.Coefficients[1][1], 1e-4); // female
Assert.AreEqual(0.685908, mlr.Coefficients[1][2], 1e-4); // age
Assert.IsFalse(double.IsNaN(mlr.StandardErrors[0][0]));
Assert.IsFalse(double.IsNaN(mlr.StandardErrors[0][1]));
Assert.IsFalse(double.IsNaN(mlr.StandardErrors[0][2]));
Assert.IsFalse(double.IsNaN(mlr.StandardErrors[1][0]));
Assert.IsFalse(double.IsNaN(mlr.StandardErrors[1][1]));
Assert.IsFalse(double.IsNaN(mlr.StandardErrors[1][2]));
/*
* // Using the standard Hessian estimation
* Assert.AreEqual(1.774612, mlr.StandardErrors[0][0], 1e-6);
* Assert.AreEqual(0.194247, mlr.StandardErrors[0][1], 1e-6);
* Assert.AreEqual(0.055003, mlr.StandardErrors[0][2], 1e-6);
*
* Assert.AreEqual(2.058028, mlr.StandardErrors[1][0], 1e-6);
* Assert.AreEqual(0.226090, mlr.StandardErrors[1][1], 1e-6);
* Assert.AreEqual(0.062627, mlr.StandardErrors[1][2], 1e-6);
*/
// Using the lower-bound approximation
Assert.AreEqual(1.047378039787443, mlr.StandardErrors[0][0], 1e-6);
Assert.AreEqual(0.153150051082552, mlr.StandardErrors[0][1], 1e-6);
Assert.AreEqual(0.031640507386863, mlr.StandardErrors[0][2], 1e-6);
Assert.AreEqual(1.047378039787443, mlr.StandardErrors[1][0], 1e-6);
Assert.AreEqual(0.153150051082552, mlr.StandardErrors[1][1], 1e-6);
Assert.AreEqual(0.031640507386863, mlr.StandardErrors[1][2], 1e-6);
double ll = mlr.GetLogLikelihood(inputs, outputs);
Assert.AreEqual(-702.97, ll, 1e-2);
Assert.IsFalse(double.IsNaN(ll));
var chi = mlr.ChiSquare(inputs, outputs);
Assert.AreEqual(185.85, chi.Statistic, 1e-2);
Assert.IsFalse(double.IsNaN(chi.Statistic));
var wald00 = mlr.GetWaldTest(0, 0);
var wald01 = mlr.GetWaldTest(0, 1);
var wald02 = mlr.GetWaldTest(0, 2);
var wald10 = mlr.GetWaldTest(1, 0);
var wald11 = mlr.GetWaldTest(1, 1);
var wald12 = mlr.GetWaldTest(1, 2);
Assert.IsFalse(double.IsNaN(wald00.Statistic));
Assert.IsFalse(double.IsNaN(wald01.Statistic));
Assert.IsFalse(double.IsNaN(wald02.Statistic));
Assert.IsFalse(double.IsNaN(wald10.Statistic));
Assert.IsFalse(double.IsNaN(wald11.Statistic));
Assert.IsFalse(double.IsNaN(wald12.Statistic));
/*
* // Using standard Hessian estimation
* Assert.AreEqual(-6.6351, wald00.Statistic, 1e-4);
* Assert.AreEqual( 2.6966, wald01.Statistic, 1e-4);
* Assert.AreEqual( 6.6943, wald02.Statistic, 1e-4);
*
* Assert.AreEqual(-11.0404, wald10.Statistic, 1e-4);
* Assert.AreEqual( 2.0609, wald11.Statistic, 1e-4);
* Assert.AreEqual(10.9524, wald12.Statistic, 1e-4);
*/
// Using Lower-Bound approximation
Assert.AreEqual(-11.241995503283842, wald00.Statistic, 1e-4);
Assert.AreEqual(3.4202662152119889, wald01.Statistic, 1e-4);
Assert.AreEqual(11.637150673342207, wald02.Statistic, 1e-4);
Assert.AreEqual(-21.693553825772664, wald10.Statistic, 1e-4);
Assert.AreEqual(3.0423802097069097, wald11.Statistic, 1e-4);
Assert.AreEqual(21.678124991086548, wald12.Statistic, 1e-4);
}
public async Task <MultinomialLogisticRegressionAnalysisItemList> GetLogisticRegressionAnalysisData(
DateTimeOffset?startDate, DateTimeOffset?finishDate,
bool product, bool engineering, bool unanticipated, bool assessmentsTeam, bool enterpriseTeam)
{
var logisticRegressionData = new MultinomialLogisticRegressionAnalysisItemList();
var taskItemRepository = new TaskItemRepository();
var taskItemList = await taskItemRepository.GetTaskItemListAsync(startDate, finishDate);
logisticRegressionData.UserIds = GetUserIds(taskItemList);
var inputs = new List <List <double> >();
var outputList = new List <int>();
var ids = new List <int>();
var titles = new List <string>();
var taskItemHelper = new TaskItemHelper();
foreach (var logisticRegressionTaskItem
in from taskItem in taskItemList
where taskItem.StartTime != null &&
taskItem.FinishTime != null &&
taskItemHelper.TaskItemDevTeamIsSelected(assessmentsTeam, enterpriseTeam, taskItem)
select GetLogisticRegressionTaskItem(taskItem))
{
ids.Add(logisticRegressionTaskItem.Id);
titles.Add(logisticRegressionTaskItem.Title);
inputs.Add(new List <double>
{
logisticRegressionTaskItem.Lifetime.TotalDays,
logisticRegressionTaskItem.LeadTime.TotalDays,
logisticRegressionTaskItem.TimeSpentInBacklog.TotalDays,
(logisticRegressionTaskItem.DevTeamIsAssessments ? 1.0 : 0.0),
(logisticRegressionTaskItem.DevTeamIsEnterprise ? 1.0 : 0.0),
logisticRegressionTaskItem.NumRevisions
});
foreach (var user in logisticRegressionData.UserIds)
{
inputs.Last().Add(logisticRegressionTaskItem.CreatedById == user ? 1.0 : 0.0);
}
foreach (var user in logisticRegressionData.UserIds)
{
inputs.Last().Add(logisticRegressionTaskItem.LastChangedBy.Id == user ? 1.0 : 0.0);
}
outputList.Add((int)logisticRegressionTaskItem.TaskItemType);
}
var inputArray = inputs.Select(inputList => inputList.ToArray()).ToArray();
var actualResults = outputList.ToArray();
var lbnr = new LowerBoundNewtonRaphson()
{
MaxIterations = 100,
Tolerance = 1e-6
};
var mlr = lbnr.Learn(inputArray, actualResults);
var predictions = mlr.Decide(inputArray);
var probabilities = mlr.Probabilities(inputArray);
logisticRegressionData.Error = new ZeroOneLoss(actualResults).Loss(predictions);
for (var i = 0; i < ids.Count; i++)
{
if (taskItemHelper.TaskItemTypeIsSelected(product, engineering, unanticipated, actualResults[i]))
{
var probability = probabilities[i].Max();
var logisticRegressionItem = new MultinomialLogisticRegressionAnalysisItem
{
Id = ids[i],
Inputs = inputs[i],
Title = titles[i],
Actual = actualResults[i],
Prediction = predictions[i],
Probability = probability
};
if (logisticRegressionItem.Actual != logisticRegressionItem.Prediction)
{
logisticRegressionData.Items.Add(logisticRegressionItem);
}
}
}
return(logisticRegressionData);
}