用scala实现NR算法,迭代beta和p值,最后比较迭代的p值与真实p值
时间: 2024-01-30 22:01:59 浏览: 28
以下是用Scala实现NR算法的示例代码:
```
import breeze.linalg.{DenseMatrix, DenseVector, inv}
def nr_algorithm(X: DenseMatrix[Double], y: DenseVector[Double], beta: DenseVector[Double], max_iter: Int, tol: Double): (DenseVector[Double], Double) = {
var iter = 0
var p = 0.0
var diff = Double.MaxValue
while (iter < max_iter && diff > tol) {
val eta = X * beta
val mu = 1.0 / (1.0 + math.exp(-eta))
val W = DenseMatrix.eye[Double](X.rows) *:* mu *:* (1.0 - mu)
val z = eta + (y - mu)
val H = X.t * W * X
val grad = X.t * (mu - y)
val delta = inv(H) * grad
beta -= delta
p = 1.0 / (1.0 + math.exp(-X * beta)).toArray.sum
diff = math.abs(p - y.toArray.sum / y.length)
iter += 1
}
(beta, p)
}
val X = DenseMatrix((1.0, 2.0), (1.0, 3.0), (1.0, 4.0), (1.0, 5.0), (1.0, 6.0))
val y = DenseVector(0.0, 0.0, 0.0, 1.0, 1.0)
val beta = DenseVector.zeros[Double](X.cols)
val max_iter = 100
val tol = 1e-6
val (beta_hat, p) = nr_algorithm(X, y, beta, max_iter, tol)
val p_true = y.toArray.sum / y.length
println(s"beta_hat: $beta_hat")
println(s"p: $p")
println(s"p_true: $p_true")
```
在上面的示例代码中,我们首先定义了一个`nr_algorithm`函数,它接受一个$n \times p$的自变量矩阵`X`,一个长度为$n$的因变量向量`y`,一个$p$维的初始系数向量`beta`,最大迭代次数`max_iter`和收敛阈值`tol`作为输入,然后使用Newton-Raphson算法迭代求解最优的系数向量`beta`和预测概率`p`。最后,我们使用一个示例数据集进行测试,并将迭代结果与真实结果进行比较。
值得注意的是,由于Newton-Raphson算法是一种局部优化算法,因此在实际应用中需要进行多次随机初始化和迭代,以避免陷入局部最优解。