R中逻辑回归公式的实现

Question

我想R中使用随机梯度下降,以建立自己的回归函数,但我现在所拥有的使权重成长过程中没有约束,因此从来没有停止:

# Logistic regression
# Takes training example vector, output vector, learn rate scalar, and convergence delta limit scalar
my_logr <- function(training_examples,training_outputs,learn_rate,conv_lim) {
  # Initialize gradient vector
  gradient <- as.vector(rep(0,NCOL(training_examples)))
  # Difference between weights
  del_weights <- as.matrix(1)
  # Weights
  weights <- as.matrix(runif(NCOL(training_examples)))
  weights_old <- as.matrix(rep(0,NCOL(training_examples)))

  # Compute gradient
  while(norm(del_weights) > conv_lim) {

    for (k in 1:NROW(training_examples)) {
      gradient <- gradient + 1/NROW(training_examples)*
        ((t(training_outputs[k]*training_examples[k,]
            /(1+exp(training_outputs[k]*t(weights)%*%as.numeric(training_examples[k,]))))))
    }

    # Update weights
    weights <- weights_old - learn_rate*gradient
    del_weights <- as.matrix(weights_old - weights)
    weights_old <- weights

    print(weights)
  }
    return(weights)
}

可以使用以下代码测试该函数:

data(iris) # Iris data already present in R    
# Dataset for part a (first 50 vs. last 100)
iris_a <- iris
iris_a$Species <- as.integer(iris_a$Species)
# Convert list to binary class
for (i in 1:NROW(iris_a$Species)) {if (iris_a$Species[i] != "1") {iris_a$Species[i] <- -1}}    
random_sample <- sample(1:NROW(iris),50)

weights_a <- my_logr(iris_a[random_sample,1:4],iris_a$Species[random_sample],1,.1)

我仔细检查了我对阿布 - 莫斯塔法的算法,如下:

1. 初始化权重向量
2. 对于每个时间步计算梯度:
   gradient <- -1/N * sum_{1 to N} (training_answer_n * training_Vector_n / (1 + exp(training_answer_n * dot(weight,training_vector_n))))
3. weight_new <- weight - learn_rate*gradient
4. 重复直到体重增量足够小

我在这里错过了什么吗？

Answer 1

从数学角度来看，权重向量上不受约束的大小不会产生唯一的解决方案。当我将这两行添加到分类器函数时，它分两步收敛：

# Normalize
weights <- weights/norm(weights)

...

# Update weights
weights <- weights_old - learn_rate*gradient
weights <- weights / norm(weights)

我无法使 @SimonO101 工作，并且我没有使用此代码进行实际工作（有像 之类的内置函数glm），因此足以执行我理解的循环。整个函数如下：

# Logistic regression
# Takes training example vector, output vector, learn rate scalar, and convergence delta limit scalar
my_logr <- function(training_examples,training_outputs,learn_rate,conv_lim) {
  # Initialize gradient vector
  gradient <- as.vector(rep(0,NCOL(training_examples)))
  # Difference between weights
  del_weights <- as.matrix(1)
  # Weights
  weights <- as.matrix(runif(NCOL(training_examples)))
  weights_old <- as.matrix(rep(0,NCOL(training_examples)))

  # Normalize
  weights <- weights/norm(weights)

  # Compute gradient
  while(norm(del_weights) > conv_lim) {

    for (k in 1:NCOL(training_examples)) {
      gradient <- gradient - 1/NROW(training_examples)*
        ((t(training_outputs[k]*training_examples[k,]
            /(1+exp(training_outputs[k]*t(weights)%*%as.numeric(training_examples[k,]))))))
    }
#     gradient <- -1/NROW(training_examples) * sum(training_outputs * training_examples / (1 + exp(training_outputs * weights%*%training_outputs) ) )

    # Update weights
    weights <- weights_old - learn_rate*gradient
    weights <- weights / norm(weights)
    del_weights <- as.matrix(weights_old - weights)
    weights_old <- weights

    print(weights)
  }
    return(weights)
}