func (p *Predictor) SetDatasetPercentage(training int, testing int) error {
if training+testing == 100 {
p.trainingDatasetPercentage = training
p.testingDatasetPercentage = testing
} else {
return errors.New("Error: Sum of training and testing dataset must equal 100")
}
return nil
}
func (r *Regression) AddDataPoint(data DataPoint) error {
numVariables := len(r.variableNames)
if len(data.Variables) != numVariables {
return errors.New("Error: Number of variables in the data != in the model")
}
r.dataPoints = append(r.dataPoints, data)
r.initialized = true
return nil
}
//Odds ratio is e^coefficient
func (r *Regression) computeOddsRatio() error {
length := len(r.model.Coefficients)
if length == 0 {
return errors.New("Error: Coefficients in models are not generated yet")
}
r.model.OddsRatio = make([]float64, length)
for i := 0; i < length; i++ {
odds := math.Exp(r.model.Coefficients[i])
r.model.OddsRatio[i] = odds
}
return nil
}
//-16325072
//1.08577462845905
//p-Value for wald statistics is coefficient / standard error
func (r *Regression) computeWaldStatistic() error {
length := len(r.model.Coefficients)
if length == 0 {
return errors.New("Error: Coefficients in models are not generated yet")
}
//Assume standard error exists when coefficient is already computed
r.model.WaldStatistics = make([]float64, length)
for i := 0; i < length; i++ {
pvalue := r.model.Coefficients[i] / r.model.StandardErrors[i]
r.model.WaldStatistics[i] = pvalue
}
return nil
}
//lower = coefficient - 1.96 * standard error, upper = coefficient + 1.96 * standard error
func (r *Regression) computeConfidenceInterval() error {
length := len(r.model.Coefficients)
if length == 0 {
return errors.New("Error: Coefficients in models are not generated yet")
}
//Assume standard error exists when coefficient is already computed
r.model.LowerConfidenceIntervals = make([]float64, length)
r.model.UpperConfidenceIntervals = make([]float64, length)
for i := 0; i < length; i++ {
offset := 1.96 * r.model.StandardErrors[i]
r.model.LowerConfidenceIntervals[i] = r.model.Coefficients[i] - offset
r.model.UpperConfidenceIntervals[i] = r.model.Coefficients[i] + offset
}
return nil
}
//Note: W[t-1] is nxn which could be huge so instead of computing b[t] = b[t-1] + inv(X'W[t-1]X)X'(y - p[t-1]) directly
//we compute the W[t-1]X part, without the use of W.
//
//Since W is derived from the prob vector and W has non-0.0 elements only on the diagonal we can avoid a ton of work
//by using the prob vector directly and not computing W at all.
//
//Some of the research papers refer to the product W[t-1]X as X~ hence the name of this method.
//Ex: if xMatrix is 10x4 then W would be 10x10 so WX would be 10x4 -- the same size as X
func (r *Regression) computeXtilde(pVector matrix.Matrix, xMatrix matrix.Matrix) (matrix.Matrix, error) {
pRows := pVector.Rows()
xRows := xMatrix.Rows()
xCols := xMatrix.Cols()
if pRows != xRows {
return nil, errors.New("The pVector and xMatrix are not compatible in computeXtilde")
}
//We are not doing matrix multiplication. the p column vector sort of lays on top of each matrix column.
result := matrix.Zeros(pRows, xCols)
for i := 0; i < pRows; i++ {
for j := 0; j < xCols; j++ {
pVal := pVector.Get(i, 0)
xVal := xMatrix.Get(i, j)
result.Set(i, j, pVal*(1.0-pVal)*xVal) //Note the p(1-p)
}
}
return result, nil
}
//How good are the predictions? (using an already-calculated prob vector)
//Note: it is possible that a model with better (lower) MSE than a second model could give worse predictive accuracy.
func (r *Regression) meanSquaredError(pVector matrix.Matrix, yVector matrix.Matrix) (mse float64, err error) {
pRows := pVector.Rows()
yRows := yVector.Rows()
if pRows != yRows {
err = errors.New("Error: The prob vector and the y vector are not compatible")
return 0.0, err
}
if pRows == 0 {
return 0.0, nil
}
result := 0.0
for i := 0; i < pRows; i++ {
result += (pVector.Get(i, 0) - yVector.Get(i, 0)) * (pVector.Get(i, 0) - yVector.Get(i, 0))
}
mse = result / float64(pRows)
return mse, nil
}
func (r *Regression) Predict(testData DataPoint) (predicted float64, err error) {
//Create matrix for independent variables
numVariables := len(testData.Variables)
testVariables := matrix.Zeros(1, numVariables+1)
for i := 0; i < numVariables; i++ {
if i == 0 {
testVariables.Set(0, 0, 1)
} else {
testVariables.Set(0, i, testData.Variables[i-i])
}
}
//Create coefficient matrix from already generated model
coeffLen := len(r.model.Coefficients)
bVector := matrix.Zeros(coeffLen, 1)
for i := 0; i < coeffLen; i++ {
bVector.Set(i, 0, r.model.Coefficients[i])
}
//Error checking first
xCols := testVariables.Cols()
bRows := bVector.Rows()
if xCols != bRows {
return 0.0, errors.New("Error:Bad dimensions for xMatrix or bVector in Predict()")
}
//Calculate probability vector
pVector, err := r.constructProbVector(testVariables, bVector)
if err != nil {
return 0.0, err
}
return pVector.Get(0, 0), nil
}
func (r *Regression) GenerateModel(iteration int) error {
if !r.initialized {
return errors.New("Error: Need some data to perform regression")
}
numData := len(r.dataPoints)
numVariables := len(r.variableNames)
if numData <= numVariables {
return errors.New("Error: Datapoints must exceed variables")
}
//Create training data matrix for observed (result) and (independent) variables
trainingObserved := matrix.Zeros(numData, 1)
trainingVariables := matrix.Zeros(numData, numVariables+1)
//Copy data to matrix
for i := 0; i < numData; i++ {
trainingObserved.Set(i, 0, r.dataPoints[i].Result)
for j := 0; j < numVariables+1; j++ {
if j == 0 {
trainingVariables.Set(i, 0, 1)
} else {
trainingVariables.Set(i, j, r.dataPoints[i].Variables[j-1])
}
}
}
if r.debugMode {
r.debugContext.Infof("\n---------- VARIABLES ---------\n%s", trainingVariables.String())
r.debugContext.Infof("\n-------- OBSERVED -------\n%s", trainingObserved.String())
}
//Initialize model arrays
r.model.StandardErrors = make([]float64, numVariables+1)
//Newton-Raphson algorithm stop condition
maxIteration := iteration
epsilon := 0.01 //Stop if all coefficients change less than this | Algorithm has converged
jumpFactor := 1000.0 //Stop if any new coefficients jumps too much | Algorithm spinning out of control
//Use Newton-Raphson to find coefficients that best fit training data
err := r.computeBestCoefficients(trainingVariables, trainingObserved, maxIteration, epsilon, jumpFactor)
if err != nil {
return err
}
//Compute odds ratio of generated coefficients
err = r.computeOddsRatio()
if err != nil {
return err
}
//Compute pValue of wald statistics from the generated coefficients
err = r.computeWaldStatistic()
if err != nil {
return err
}
//Compute confidence interval of generated coefficients
err = r.computeConfidenceInterval()
if err != nil {
return err
}
//Compute log likelihood of the model
err = r.computeLogLikelihood()
if err != nil {
return err
}
//Compute deviance of the model
r.computeDeviance()
//Compute chi-square value
r.computeChiSquare()
return nil
}
func (r *Regression) TestModel(testData []DataPoint) (accuracy float64, err error) {
numData := len(testData)
numVariables := len(testData[0].Variables)
//Create test data matrix for observed (result) and (independent) variables
testObserved := matrix.Zeros(numData, 1)
testVariables := matrix.Zeros(numData, numVariables+1)
//Copy data to matrix
for i := 0; i < numData; i++ {
testObserved.Set(i, 0, testData[i].Result)
for j := 0; j < numVariables+1; j++ {
if j == 0 {
testVariables.Set(i, 0, 1)
} else {
testVariables.Set(i, j, testData[i].Variables[j-1])
}
}
}
//Create coefficient matrix from already generated model
coeffLen := len(r.model.Coefficients)
bVector := matrix.Zeros(coeffLen, 1)
for i := 0; i < coeffLen; i++ {
bVector.Set(i, 0, r.model.Coefficients[i])
}
//Error checking first
xRows := testVariables.Rows()
xCols := testVariables.Cols()
yRows := testObserved.Rows()
bRows := bVector.Rows()
if xCols != bRows || xRows != yRows {
return 0.0, errors.New("Error:Bad dimensions for xMatrix or yVector or bVector in TestModel()")
}
pVector, err := r.constructProbVector(testVariables, bVector)
if err != nil {
return 0.0, err
}
pRows := pVector.Rows()
if pRows != xRows {
return 0.0, errors.New("Error:Unequal rows in prob vector and design matrix in TestModel()")
}
//Initiate cases
numberCasesCorrect := 0
numberCasesWrong := 0
for i := 0; i < yRows; i++ {
pVal := pVector.Get(i, 0)
observedVal := testObserved.Get(i, 0)
if r.debugMode {
r.debugContext.Infof("\nPredicted vs Test Result: %v vs %v\n", pVal, observedVal)
}
if pVal >= 0.50 && observedVal == 1.0 {
numberCasesCorrect += 1
} else if pVal < 0.50 && observedVal == 0.0 {
numberCasesCorrect += 1
} else {
numberCasesWrong += 1
}
}
//Calculate correct prediction percentage
total := numberCasesCorrect + numberCasesWrong
correctPercentage := (100.0 * float64(numberCasesCorrect)) / float64(total)
if r.debugMode {
r.debugContext.Infof("\nCorrect case vs Wrong case: %v vs %v\n", numberCasesCorrect, numberCasesWrong)
r.debugContext.Infof("\nCorrect predicted percentage: %v", correctPercentage)
}
if total == 0 {
return 0.0, nil
} else {
return correctPercentage, nil
}
}
//Log likelihood ln LF = TotalAddition[(Yi * ln Pi) + (1 - Yi) * ln (1 - Pi)]
func (r *Regression) computeLogLikelihood() error {
numData := len(r.dataPoints)
numVariables := len(r.dataPoints[0].Variables)
//Create test data matrix for observed (result) and (independent) variables
testObserved := matrix.Zeros(numData, 1)
testVariables := matrix.Zeros(numData, numVariables+1)
//Copy data to matrix
for i := 0; i < numData; i++ {
testObserved.Set(i, 0, r.dataPoints[i].Result)
for j := 0; j < numVariables+1; j++ {
if j == 0 {
testVariables.Set(i, 0, 1)
} else {
testVariables.Set(i, j, r.dataPoints[i].Variables[j-1])
}
}
}
//Error check the coefficient
coeffLen := len(r.model.Coefficients)
if coeffLen == 0 {
return errors.New("Error: Coefficients in models are not generated yet")
}
//Create coefficient matrix from already generated model
bVector := matrix.Zeros(coeffLen, 1)
for i := 0; i < coeffLen; i++ {
bVector.Set(i, 0, r.model.Coefficients[i])
}
//Error checking again
xRows := testVariables.Rows()
xCols := testVariables.Cols()
yRows := testObserved.Rows()
bRows := bVector.Rows()
if xCols != bRows || xRows != yRows {
return errors.New("Error:Bad dimensions for xMatrix or yVector or bVector in computeLogLikelihood()")
}
pVector, err := r.constructProbVector(testVariables, bVector)
if err != nil {
return err
}
pRows := pVector.Rows()
if pRows != xRows {
return errors.New("Error:Unequal rows in prob vector and design matrix in computeLogLikelihood()")
}
//Initiate cases
logLikelihood := 0.0
for i := 0; i < yRows; i++ {
pVal := pVector.Get(i, 0)
observedVal := testObserved.Get(i, 0)
current := 0.0
if observedVal == 0.0 {
current = math.Log(1 - pVal)
} else if observedVal == 1.0 {
current = math.Log(pVal)
}
if r.debugMode {
r.debugContext.Infof("\nY is %v and P is %v", observedVal, pVal)
r.debugContext.Infof("\n(Yi * ln Pi) + (1 - Yi) * ln (1 - Pi): %v", current)
}
logLikelihood += current
}
if r.debugMode {
r.debugContext.Infof("\nLog likelihood: %v", logLikelihood)
}
//Save the calculated log likelihood result
r.model.LogLikelihood = logLikelihood
return nil
}
//Use the Newton-Raphson technique to estimate logistic regression beta parameters: b[t] = b[t-1] + inv(X'W[t-1]X)X'(Y - p[t-1])
//- xTrainingVector is a design matrix of predictor variables where the first column is augmented with all 1.0 to represent dummy x values for the b0 constant
//- yTrainingVector is a column vector of binary (0.0 or 1.0) dependent variables
//- maxIterations is the maximum number of times to iterate in the algorithm. A value of 1000 is reasonable.
//- epsilon is a closeness parameter: if all new b[i] values after an iteration are within epsilon of
// the old b[i] values, we assume the algorithm has converged and we return. A value like 0.001 is often reasonable.
//- jumpFactor stops the algorithm if any new beta value is jumpFactor times greater than the old value. A value of 1000.0 seems reasonable.
//
//The return is a column vector of the beta estimates: b[0] is the constant, b[1] for x1, etc.
//
//Note: There is a lot that can go wrong here. The algorithm involves finding a matrx inverse (see MatrixInverse) which will throw
//if the inverse cannot be computed. The Newton-Raphson algorithm can generate beta values that tend towards infinity.
//If anything bad happens the return is the best beta values known at the time (which could be all 0.0 values but not null).
func (r *Regression) computeBestCoefficients(xTrainingVector matrix.Matrix, yTrainingVector matrix.Matrix, maxIteration int, epsilon float64, jumpFactor float64) error {
//Error checking for the matrix length first
xRows := xTrainingVector.Rows()
xCols := xTrainingVector.Cols()
if xRows != yTrainingVector.Rows() {
return errors.New("Error: Training vectors are not compatible to generate model")
}
//Initial coefficients
coeffVector := matrix.Zeros(xCols, 1)
for i := 0; i < xCols; i++ {
coeffVector.Set(i, 0, 0.0)
}
if r.debugMode {
r.debugContext.Infof("\nInitial coefficients vector:\n%s", coeffVector.String())
}
//Current best coefficients
var bestCoeffVector matrix.Matrix
bestCoeffVector = coeffVector.Copy()
//A column vector of the probabilities of each row using the b[i] values and the x[i] values
pVector, err := r.constructProbVector(xTrainingVector, coeffVector)
if err != nil {
return err
}
if r.debugMode {
r.debugContext.Infof("\nInitial probabilities vector:\n%s", pVector.String())
}
//Check MSE of the prediction
mse, err := r.meanSquaredError(pVector, yTrainingVector)
if err != nil {
return err
}
if r.debugMode {
r.debugContext.Infof("\nInitial MSE:\n%f", mse)
}
//How many times are the new betas worse (i.e., give worse MSE) than the current betas
timesWorse := 0
for i := 0; i < maxIteration; i++ {
//Generate new beta values using Newton-Raphson. Could return null
newCoeffVector := r.constructNewCoefficientsVector(coeffVector, xTrainingVector, yTrainingVector, pVector)
if newCoeffVector == nil {
if r.debugMode {
r.debugContext.Infof("\nNew coefficients vector is null | current product cannot be inverted -- stopping")
}
break
}
if r.debugMode {
r.debugContext.Infof("\nNew calculated coefficients vector:\n%s", newCoeffVector.String())
}
//We are done because of no significant change in beta[]
if r.noChange(coeffVector, newCoeffVector, epsilon) == true {
if r.debugMode {
r.debugContext.Infof("\nNo significant change between old beta values and new beta values -- stopping")
}
break
}
//Any new beta more than jumpFactor times greater than old?
if r.outOfControl(coeffVector, newCoeffVector, jumpFactor) == true {
if r.debugMode {
r.debugContext.Infof("\nThe new coefficients vector has at least one value which changed by a factor of %s -- stopping", jumpFactor)
}
break
}
pVector, err = r.constructProbVector(xTrainingVector, newCoeffVector)
if err != nil {
return err
}
if r.debugMode {
r.debugContext.Infof("\nNew calculated probabilities vector:\n%s", pVector.String())
}
newMSE, err := r.meanSquaredError(pVector, yTrainingVector)
if err != nil {
return err
}
if r.debugMode {
r.debugContext.Infof("\nNew calculated MSE:\n%f", newMSE)
}
if newMSE > mse {
//Update counter if newMSE is worst than the current one
timesWorse += 1
if timesWorse > 4 {
if r.debugMode {
r.debugContext.Infof("\nThe new coefficients vector produced worse predictions even after modification four times in a row -- stopping")
}
break
}
if r.debugMode {
r.debugContext.Infof("\nThe new coefficients vector has produced probabilities which give worse predictions -- modifying new coefficients to halfway between old and new")
}
//Update current: old becomes not the new but halfway between new and old
for k := 0; k < coeffVector.Rows(); k++ {
val := coeffVector.Get(k, 0)
newVal := newCoeffVector.Get(k, 0)
coeffVector.Set(k, 0, (val+newVal)/2.0)
}
//Update current SSD
mse = newMSE
} else {
if r.debugMode {
r.debugContext.Infof("\nThe new coefficients vector has produced probabilities which give better predictions -- updating")
}
coeffVector = newCoeffVector.DenseMatrix() //Update best
bestCoeffVector = coeffVector.Copy() //Update current
mse = newMSE //Update current MSE
timesWorse = 0 //Reset counter
}
if r.debugMode && i == maxIteration-1 {
r.debugContext.Infof("\nExceeded max iterations -- stopping")
}
}
if r.debugMode {
r.debugContext.Infof("\nBest coefficients vector:\n%s", bestCoeffVector.String())
}
//Done, put coefficients data from matrix to arrays
length := bestCoeffVector.Rows()
r.model.Coefficients = make([]float64, length)
for i := 0; i < length; i++ {
r.model.Coefficients[i] = bestCoeffVector.Get(i, 0)
}
return nil
}