吴恩达机器学习II
于2020年10月26日2020年10月26日由Sukuna发布
注意:X是一个
的矩阵,矩阵的第一列都是1!,
是一个
的向量,保存的是我们要预测的参数值
第一题:sigmoid函数 输入一个矩阵,返回每一个元素做计算的值
代码语言:javascript复制function g = sigmoid(z)
%SIGMOID Compute sigmoid function
% g = SIGMOID(z) computes the sigmoid of z.
% You need to return the following variables correctly
g = zeros(size(z));
% ==================== YOUR CODE HERE ======================
% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
% vector or scalar).
g=1./(ones(size(z)) exp(-z))
% ============================================================
end
第二题:不正则化的梯度迭代: 返回
代码语言:javascript复制function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
% J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
% parameter for logistic regression and the gradient of the cost
% w.r.t. to the parameters.
% Initialize some useful values
m = length(y); % number of training examples
% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));
% ==================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
% You should set J to the cost.
% Compute the partial derivatives and set grad to the partial
% derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%
h = sigmoid(X * theta);
J = (-log(h.')*y - log(ones(1, m) - h.')*(ones(m, 1) - y)) / m;
grad = (X.' * (h - y)) /m;
% ============================================================
end
首先先求出预测值,就用第一题的那个函数,求出预测值(注意:X*theta是第一个实验作业里面的线性回归函数的表达式)注意:h.就是求转置的意思,这样可以带入代价函数算出J grad就是每一次下降的时候递减的值,注意:没算学习效率
第三题:0&1判断 这时候就用一手if对矩阵每个元素进行判定 像exp,log,if这些作用在矩阵里面就是对每个元素求值
代码语言:javascript复制function p = predict(theta, X)
%PREDICT Predict whether the label is 0 or 1 using learned logistic
%regression parameters theta
% p = PREDICT(theta, X) computes the predictions for X using a
% threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
m = size(X, 1); % Number of training examples
% You need to return the following variables correctly
p = zeros(m, 1);
% ===================== YOUR CODE HERE =====================
% Instructions: Complete the following code to make predictions using
% your learned logistic regression parameters.
% You should set p to a vector of 0's and 1's
%
h = sigmoid(X * theta);
p = (h >= 0.5);
% ============================================================
end
第四题:有正则化的代价函数求值:
代码语言:javascript复制function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
% theta as the parameter for regularized logistic regression and the
% gradient of the cost w.r.t. to the parameters.
% Initialize some useful values
m = length(y); % number of training examples
% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));
% ==================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
% You should set J to the cost.
% Compute the partial derivatives and set grad to the partial
% derivatives of the cost w.r.t. each parameter in theta
h = sigmoid(X * theta);
J = (-log(h.')*y - log(ones(1, m) - h.')*(ones(m, 1) - y)) / m (lambda/(2*m)) * sum(theta(2:end).^2);
grad(1) = (X(:, 1).' * (h - y)) /m;
grad(2:end) = (X(:, 2:end).' * (h - y)) /m (lambda/m) * theta(2:end);
% ============================================================
end
这里主要区分了grad中1和2之间的区别,其他的和公式相差无二