吴恩达机器学习III
于2020年11月2日2020年11月2日由Sukuna发布
第一部分:多分类
X:是一个
维的矩阵,里面存的是m组数据集
第一题: 正则化的逻辑回归表达式
代码语言：javascript复制function [J, grad] = lrCostFunction(theta, X, y, lambda)
%LRCOSTFUNCTION Compute cost and gradient for logistic regression with
%regularization
% J = LRCOSTFUNCTION(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
%
% Hint: The computation of the cost function and gradients can be
% efficiently vectorized. For example, consider the computation
%
% sigmoid(X * theta)
%
% Each row of the resulting matrix will contain the value of the
% prediction for that example. You can make use of this to vectorize
% the cost function and gradient computations.
%
% Hint: When computing the gradient of the regularized cost function,
% there're many possible vectorized solutions, but one solution
% looks like:
% grad = (unregularized gradient for logistic regression)
% temp = theta;
% temp(1) = 0; % because we don't add anything for j = 0
% grad = grad YOUR_CODE_HERE (using the temp variable)
%
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);
% ============================================================
grad = grad(:);
end第一题就是求正则化的代价函数,这操作基本上一样的,就提一嘴数据集的格式:X是测试用的数据集,每个行向量都是一组数据,h求出来的就是一组0-1向量
第二题: 一对多的分类
代码语言：javascript复制function [all_theta] = oneVsAll(X, y, num_labels, lambda)
%ONEVSALL trains multiple logistic regression classifiers and returns all
%the classifiers in a matrix all_theta, where the i-th row of all_theta
%corresponds to the classifier for label i
% [all_theta] = ONEVSALL(X, y, num_labels, lambda) trains num_labels
% logistic regression classifiers and returns each of these classifiers
% in a matrix all_theta, where the i-th row of all_theta corresponds
% to the classifier for label i
% Some useful variables
m = size(X, 1);
n = size(X, 2);
% You need to return the following variables correctly
all_theta = zeros(num_labels, n 1);
% Add ones to the X data matrix
X = [ones(m, 1) X];
% ==================== YOUR CODE HERE ======================
% Instructions: You should complete the following code to train num_labels
% logistic regression classifiers with regularization
% parameter lambda.
%
% Hint: theta(:) will return a column vector.
%
% Hint: You can use y == c to obtain a vector of 1's and 0's that tell you
% whether the ground truth is true/false for this class.
%
% Note: For this assignment, we recommend using fmincg to optimize the cost
% function. It is okay to use a for-loop (for c = 1:num_labels) to
% loop over the different classes.
%
% fmincg works similarly to fminunc, but is more efficient when we
% are dealing with large number of parameters.
%
% Example Code for fmincg:
%
% % Set Initial theta
% initial_theta = zeros(n 1, 1);
%
% % Set options for fminunc
% options = optimset('GradObj', 'on', 'MaxIter', 50);
%
% % Run fmincg to obtain the optimal theta
% % This function will return theta and the cost
% [theta] = ...
% fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), ...
% initial_theta, options);
%
options = optimset('GradObj', 'on', 'MaxIter', 50);
initial_theta = zeros(size(X, 2), 1);
for c = 1:num_labels
[all_theta(c, :)] = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), initial_theta, options);
end
% ============================================================
endoptions = optimset(‘param1′,value1,’param2’,value2,…) %设置所有参数及其值，未设置的为默认值
Parameter | Value | Description |
|---|---|---|
Display | ‘off’ | ‘iter’ | ‘final’ | ‘notify’ | ‘off’ 表示不显示输出; ‘iter’ 显示每次迭代的结果; ‘final’ 只显示最终结果; ‘notify’ 只在函数不收敛的时候显示结果. |
MaxFunEvals | positive integer | 函数求值运算（Function Evaluation）的最高次数 |
MaxIter | positive integer | 最大迭代次数. |
TolFun | positive scalar | 函数迭代的终止误差. |
TolX | positive scalar | 结束迭代的X值. |
fmincg这个函数说明的是可以返回
和cost值,具体怎么实现不提,根据这个函数可以求出向量,每次就把行向量的值赋值给X里,迭代即可,返回的是
需要我们
第三题:预测(离散化)迭代函数
这里all_theta是一个
维的矩阵
代码语言：javascript复制function p = predictOneVsAll(all_theta, X)
%PREDICT Predict the label for a trained one-vs-all classifier. The labels
%are in the range 1..K, where K = size(all_theta, 1).
% p = PREDICTONEVSALL(all_theta, X) will return a vector of predictions
% for each example in the matrix X. Note that X contains the examples in
% rows. all_theta is a matrix where the i-th row is a trained logistic
% regression theta vector for the i-th class. You should set p to a vector
% of values from 1..K (e.g., p = [1; 3; 1; 2] predicts classes 1, 3, 1, 2
% for 4 examples)
m = size(X, 1);
num_labels = size(all_theta, 1);
% You need to return the following variables correctly
p = zeros(size(X, 1), 1);
% Add ones to the X data matrix
X = [ones(m, 1) X];
% ==================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
% your learned logistic regression parameters (one-vs-all).
% You should set p to a vector of predictions (from 1 to
% num_labels).
%
% Hint: This code can be done all vectorized using the max function.
% In particular, the max function can also return the index of the
% max element, for more information see 'help max'. If your examples
% are in rows, then, you can use max(A, [], 2) to obtain the max
% for each row.
%
[~, p] = max(X * all_theta.', [], 2);
% ============================================================
endC = max(A,[],dim)
返回A中有dim指定的维数范围中的最大值。比如C=max(A,[],2),在矩阵中，第2维度表示列，第1维度表示行
max这个函数有两个输出，但是调用这个函数的程序只把第二个输出赋值给了p，不需要第一个输出，于是第一个输出就写成~ 第一个输出就是一个索引表,记录着何时会取最大,这个略过,我们不需要 max:求出最可能的特征的值,求每行最大的值即可 X * all_theta.’乘出来就是一个
维的矩阵,保存的是每一个数据集属于哪一个集合的可能性
第二部分 神经网络
第四题:计算神经网络(不要求反向学习)
代码语言：javascript复制function p = predict(Theta1, Theta2, X)
%PREDICT Predict the label of an input given a trained neural network
% p = PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the
% trained weights of a neural network (Theta1, Theta2)
% Useful values
m = size(X, 1);
num_labels = size(Theta2, 1);
% You need to return the following variables correctly
p = zeros(size(X, 1), 1);
% ==================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
% your learned neural network. You should set p to a
% vector containing labels between 1 to num_labels.
%
% Hint: The max function might come in useful. In particular, the max
% function can also return the index of the max element, for more
% information see 'help max'. If your examples are in rows, then, you
% can use max(A, [], 2) to obtain the max for each row.
%
X = [ones(size(X), 1), X]; % Add ones to the X data matrix
X1 = sigmoid(X * Theta1.');
X1 = [ones(size(X1), 1), X1]; % Add ones to the X1 data matrix
[~, p] = max(X1 * Theta2.', [], 2);
% ============================================================
end纯计算,theta是已经计算好的矩阵值,就直接算就行,注意要给计算出来的值一个bias值,就是加一个全是1的行
