对 One vs. All Regression 中函数句柄的混淆

Question

我正在 coursera 上学习 Andrew Ng 的机器学习课程，我很困惑为什么一个特定的例子在 One vs. All 分类中有效：

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
%   logisitc 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 use 
%       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);
%

initial_theta = zeros(n + 1, 1);

options = optimset('GradObj', 'on', 'MaxIter', 50);

for i = 1:num_labels

    c = i * ones(size(y));
    fprintf('valores')
    [theta] = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), initial_theta, options);
    all_theta(i,:) = theta;

end


% =========================================================================


end

我对以下行感到特别困惑：[theta] = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), initial_theta, options);。 lrCostFunction 被定义为具有参数 theta, X, y, lambda，所以我不知道 t 在那里做什么。

此外，将 theta 括在方括号中的目的是什么：[theta]？

任何有关单步执行此代码的帮助都将非常有用。谢谢。

Answer 1

您正在查看定义匿名函数的行。匿名函数就像函数的简写定义，以 @ 开头，后跟此函数的参数（在您的例子中为 t）。这个参数t作为第一个参数传递给函数lrCostFunction()，实际上是theta参数。即，您要求函数 fmincg() 最小化此匿名函数的输出，它是 lrCostFunction() 的包装器，以便您在使用 X、[=19= 时最小化 theta ] 和 lambda 在匿名函数定义之外定义。

为了更好的理解匿名函数，可以拆分代码：

 func_handle = @(t)(lrCostFunction(t, X, (y == c), lambda)) % anonymous function
 func_handle(initial_theta); % returns the cost at the initial_theta
 [theta] = fmincg(func_handle, initial_theta, options);

查看官方Matlab documentation了解匿名函数的详细信息

theta 两边的括号是多余的。

对 One vs. All Regression 中函数句柄的混淆

Confusion about function handles in One vs. All Regression

matlab

machine-learning

function-handle