scala语言，用 Newton-Raphson算法实现逻辑回归

以下是使用Scala语言实现逻辑回归的Newton-Raphson算法的示例代码：

import breeze.linalg.{DenseMatrix, DenseVector}
import breeze.numerics.{exp, log}
import scala.annotation.tailrec

object LogisticRegression {

  /**
   * Compute the sigmoid function
   *
   * @param z input value
   * @return sigmoid value
   */
  def sigmoid(z: Double): Double = {
    1.0 / (1.0 + exp(-z))
  }

  /**
   * Compute the gradient of the log-likelihood function
   *
   * @param X design matrix
   * @param y target variable
   * @param weights current weights
   * @return gradient vector
   */
  def gradient(X: DenseMatrix[Double], y: DenseVector[Double], weights: DenseVector[Double]): DenseVector[Double] = {
    val activation = sigmoid(X * weights)
    X.t * (activation - y)
  }

  /**
   * Compute the Hessian matrix of the log-likelihood function
   *
   * @param X design matrix
   * @param weights current weights
   * @return Hessian matrix
   */
  def hessian(X: DenseMatrix[Double], weights: DenseVector[Double]): DenseMatrix[Double] = {
    val activation = sigmoid(X * weights)
    val diagonal = activation *:* (1.0 - activation)
    X.t * (X(::, *) * diagonal)
  }

  /**
   * Compute the log-likelihood function
   *
   * @param X design matrix
   * @param y target variable
   * @param weights current weights
   * @return log-likelihood value
   */
  def logLikelihood(X: DenseMatrix[Double], y: DenseVector[Double], weights: DenseVector[Double]): Double = {
    val activation = sigmoid(X * weights)
    val epsilon = 1e-16
    val clippedActivation = activation.map(a => math.max(a, epsilon)).map(a => math.min(a, 1.0 - epsilon))
    val logActivation = log(clippedActivation)
    val logOneMinusActivation = log(1.0 - clippedActivation)
    val logLikelihood = y.t * logActivation + (1.0 - y).t * logOneMinusActivation
    -logLikelihood
  }

  /**
   * Train a logistic regression model using Newton-Raphson algorithm
   *
   * @param X design matrix
   * @param y target variable
   * @param maxIterations maximum number of iterations
   * @param tolerance convergence tolerance
   * @return weights vector
   */
  def train(X: DenseMatrix[Double], y: DenseVector[Double], maxIterations: Int = 100, tolerance: Double = 1e-6): DenseVector[Double] = {

    val numFeatures = X.cols
    val weights = DenseVector.zeros[Double](numFeatures)

    @tailrec
    def loop(iteration: Int): DenseVector[Double] = {
      val grad = gradient(X, y, weights)
      val hess = hessian(X, weights)
      val delta = hess \ grad
      weights -= delta
      val llh = logLikelihood(X, y, weights)
      val improvement = llh - logLikelihood(X, y, weights + delta)
      if (iteration >= maxIterations || improvement < tolerance) {
        weights
      } else {
        loop(iteration + 1)
      }
    }

    loop(0)
  }
}

该示例代码定义了sigmoid函数、梯度函数、Hessian矩阵函数、对数似然函数和训练函数。在训练函数中，使用了尾递归进行迭代，直到满足最大迭代次数或收敛容差的条件为止。最终，训练函数返回权重向量作为模型的输出。