* y = b dot x + e = b_0 + b_1 * x_1 + ... b_k * x_k + e *
* Note, "protected val" arguments requires by `ResponseSurface`. * @param x the input/data m-by-n matrix * (augment with a first column of ones to include intercept in model) * @param y the response m-vector */ abstract class PredictorMat (protected val x: MatriD, protected val y: VectoD) extends Fit (y, x.dim2, (x.dim2-1, x.dim1-x.dim2)) with Predictor with Error { if (x.dim1 != y.dim) flaw ("constructor", "dimensions of x and y are incompatible") if (x.dim1 < x.dim2) flaw ("constructor", "NEGATIVE df - not enough data rows in matrix to use prediction") private val DEBUG = true // debug flag protected val k = x.dim2 - 1 // number of variables (k = n-1) FIX - assumes intercept protected val m = x.dim1 // number of data points (rows) //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /** Given a set of data vectors 'x's and their corresponding responses 'yy's, * train the prediction function 'yy = f(x)' by fitting its parameters. * The 'x' values must be provided by the implementing class. * @param yy the response vector */ def train (yy: VectoD): PredictorMat //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /** Given a set of data vectors 'x's and their corresponding responses 'y's, * passed into the implementing class, train the prediction function 'y = f(x)' * by fitting its parameters. */ def train (): PredictorMat = train (y) //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /** Compute the error and useful diagnostics for the entire dataset. */ def eval () { e = y - x * b // compute residual/error vector e diagnose (e) // compute diagnostics } // eval //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /** Compute the error and useful diagnostics for the test dataset. * @param xx the test data matrix * @param yy the test response vector */ override def eval (xx: MatriD, yy: VectoD) { e = yy - xx * b // compute residual/error vector e diagnose (e) // compute diagnostics } // eval //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /** Compute diagostics for the regression model. * @param yy the response vector */ def summary () { super.summary (b, { val facCho = new Fac_Cholesky (x.t * x) // create a Cholesky factorization val l_inv = facCho.factor1 ().inverse // take inverse of l from Cholesky factorization val varCov = l_inv.t * l_inv * mse_ // variance-covariance matrix varCov.getDiag ().map (sqrt (_)) }) // standard error of coefficients } // summary //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /** Predict the value of 'y = f(z)' by evaluating the formula 'y = b dot z', * e.g., '(b_0, b_1, b_2) dot (1, z_1, z_2)'. * @param z the new vector to predict */ def predict (z: VectoD): Double = b dot z //:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /** Predict the value of 'y = f(z)' by evaluating the formula 'y = b dot z', * for each row of matrix 'z'. * @param z the new matrix to predict */ def predict (z: MatriD): VectoD = z * b //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /* Use 'k'-fold cross-validation to compute test quality of fit measures by * dividing the dataset into a test dataset and a training dataset. * The test dataset is defined by 'tRange' and the rest of the data is training dataset". * @param x the data matrix * @param y the response vector * @param algor the prediction algorithm being applied (e.g., `RidgeRegression`) * @param k the number of crosses and cross-validations (defaults to 10x). */ def crossValidate (algor: (MatriD, VectoD) => PredictorMat, k: Int = 10): Array [Statistic] = { val stats = Array.fill (fitLabel.length) (new Statistic ()) val tSize = x.dim1 / k for (i <- 0 until k) { val tRange = Range (i * tSize, (i+1) * tSize) // row range for test dataset val x_te = x.slice (tRange) // test data matrix val y_te = y.slice (tRange) // test response vector val x_tr = x.sliceEx (tRange) // training data matrix val y_tr = y.sliceEx (tRange) // training response vector if (DEBUG) { println ("x_te = " + x_te) println ("y_te = " + y_te) println ("x_tr = " + x_tr) println ("y_tr = " + y_tr) } // if val model = algor (x_tr, y_tr) // construct next model using training dataset model.train () // train the model model.eval (x_te, y_te) // evaluate model on test dataset val qm = model.fit // get quality of fit measures for (q <- qm.indices) stats(q).tally (qm(q)) // tally these measures } // for println ("------------------------------------------------------------") println ("stats = " + stats.deep) println ("------------------------------------------------------------") stats } // crossValidate //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: /** The 'crossVal' abstract method must be coded in implementing classes to * call the above 'crossValidate' method. The 'algor' parameter may be * specified as a lambda function to create the prediction algorithm. * @param k the number of crosses and cross-validations (defaults to 10x). */ def crossVal (k: Int = 10) } // PredictorMat abstract class