scala语言实现NR算法估计逻辑回归参数

NR算法（Newton-Raphson算法）是一种迭代方法，用于求解非线性方程组。在逻辑回归中，NR算法可以用来估计模型参数。

Scala语言实现NR算法估计逻辑回归参数的步骤如下：

1. 定义逻辑回归模型

case class LogisticRegressionModel(weights: Vector, intercept: Double) {
  def predict(features: Vector): Double = {
    val margin = dot(weights, features) + intercept
    1.0 / (1.0 + exp(-margin))
  }
}

2. 定义损失函数

def computeCost(data: RDD[(Double, Vector)], model: LogisticRegressionModel): Double = {
  val numExamples = data.count()
  val margin = data.map { case (label, features) =>
    label * (dot(model.weights, features) + model.intercept)
  }
  val loss = margin.map(m => log(1 + exp(-m))).sum()
  loss / numExamples
}

3. 定义梯度函数

def computeGradient(data: RDD[(Double, Vector)], model: LogisticRegressionModel): (Vector, Double) = {
  val numExamples = data.count()
  val margin = data.map { case (label, features) =>
    label * (dot(model.weights, features) + model.intercept)
  }
  val multiplier = margin.map(m => 1.0 / (1.0 + exp(-m)) - 1.0).zip(data.map(_._2)).map { case (error, features) =>
    features * error
  }
  val gradient = multiplier.reduce(_ + _) / numExamples
  val interceptGradient = margin.map(m => 1.0 / (1.0 + exp(-m)) - 1.0).sum() / numExamples
  (gradient, interceptGradient)
}

4. 定义Hessian矩阵函数

def computeHessian(data: RDD[(Double, Vector)], model: LogisticRegressionModel): Matrix = {
  val numExamples = data.count()
  val margin = data.map { case (label, features) =>
    label * (dot(model.weights, features) + model.intercept)
  }
  val multiplier = margin.map(m => 1.0 / (1.0 + exp(-m))).zip(data.map(_._2)).map { case (prob, features) =>
    features.outer(features) * prob * (1 - prob)
  }
  multiplier.reduce(_ + _) / numExamples
}

5. 定义NR算法迭代函数

def trainWithNR(data: RDD[(Double, Vector)], numIterations: Int, learningRate: Double): LogisticRegressionModel = {
  var model = LogisticRegressionModel(Vectors.dense(0.0), 0.0)
  for (i <- 1 to numIterations) {
    val (gradient, interceptGradient) = computeGradient(data, model)
    val hessian = computeHessian(data, model)
    val delta = inv(hessian) * gradient
    val deltaIntercept = learningRate * interceptGradient
    model = LogisticRegressionModel(model.weights - delta, model.intercept - deltaIntercept)
  }
  model
}

6. 测试模型

val data = sc.parallelize(Seq(
  (0.0, Vectors.dense(0.1, 0.2, 0.3)),
  (1.0, Vectors.dense(0.4, 0.5, 0.6)),
  (0.0, Vectors.dense(0.7, 0.8, 0.9)),
  (1.0, Vectors.dense(0.2, 0.3, 0.4))
))
val model = trainWithNR(data, 100, 0.01)
val prediction = model.predict(Vectors.dense(0.3, 0.4, 0.5))
println(prediction)

以上就是Scala语言实现NR算法估计逻辑回归参数的步骤。