Algorithm 八度：逻辑回归：fmincg和fminunc之间的差异
对于逻辑回归问题，我经常使用Algorithm 八度：逻辑回归：fmincg和fminunc之间的差异,algorithm,machine-learning,neural-network,octave,Algorithm,Machine Learning,Neural Network,Octave,对于逻辑回归问题，我经常使用fminunc。我在网上读到过使用fmincg而不是fminunc，参数相同的文章。结果是不同的，通常fmincg更精确，但不太多。（我正在将fmincg函数fminunc的结果与相同的数据进行比较） 所以，我的问题是：这两个函数之间有什么区别？每个函数都实现了什么算法？（现在，我只是使用这些函数，而不知道它们是如何工作的） 谢谢：）您必须查看fmincg的代码，因为它不是倍频程的一部分。经过搜索，我发现这是Coursera机器学习课程作为家庭作业的一部分提供的函数文
fminuncfmincgfminuncfmincg谢谢：）您必须查看
fmincgfunction [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
% Minimize a continuous differentialble multivariate function. Starting point
% is given by "X" (D by 1), and the function named in the string "f", must
% return a function value and a vector of partial derivatives. The Polack-
% Ribiere flavour of conjugate gradients is used to compute search directions,
% and a line search using quadratic and cubic polynomial approximations and the
% Wolfe-Powell stopping criteria is used together with the slope ratio method
% for guessing initial step sizes. Additionally a bunch of checks are made to
% make sure that exploration is taking place and that extrapolation will not
% be unboundedly large. The "length" gives the length of the run: if it is
% positive, it gives the maximum number of line searches, if negative its
% absolute gives the maximum allowed number of function evaluations. You can
% (optionally) give "length" a second component, which will indicate the
% reduction in function value to be expected in the first line-search (defaults
% to 1.0). The function returns when either its length is up, or if no further
% progress can be made (ie, we are at a minimum, or so close that due to
% numerical problems, we cannot get any closer). If the function terminates
% within a few iterations, it could be an indication that the function value
% and derivatives are not consistent (ie, there may be a bug in the
% implementation of your "f" function). The function returns the found
% solution "X", a vector of function values "fX" indicating the progress made
% and "i" the number of iterations (line searches or function evaluations,
% depending on the sign of "length") used.
%
% Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
%
% See also: checkgrad
%
% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
%
%
% (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen
%
% Permission is granted for anyone to copy, use, or modify these
% programs and accompanying documents for purposes of research or
% education, provided this copyright notice is retained, and note is
% made of any changes that have been made.
%
% These programs and documents are distributed without any warranty,
% express or implied. As the programs were written for research
% purposes only, they have not been tested to the degree that would be
% advisable in any important application. All use of these programs is
% entirely at the user's own risk.
%
% [ml-class] Changes Made:
% 1) Function name and argument specifications
% 2) Output display
%
% Read options
if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter')
length = options.MaxIter;
else
length = 100;
end
RHO = 0.01; % a bunch of constants for line searches
SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions
INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket
EXT = 3.0; % extrapolate maximum 3 times the current bracket
MAX = 20; % max 20 function evaluations per line search
RATIO = 100; % maximum allowed slope ratio
argstr = ['feval(f, X']; % compose string used to call function
for i = 1:(nargin - 3)
argstr = [argstr, ',P', int2str(i)];
end
argstr = [argstr, ')'];
if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
S=['Iteration '];
i = 0; % zero the run length counter
ls_failed = 0; % no previous line search has failed
fX = [];
[f1 df1] = eval(argstr); % get function value and gradient
i = i + (length<0); % count epochs?!
s = -df1; % search direction is steepest
d1 = -s'*s; % this is the slope
z1 = red/(1-d1); % initial step is red/(|s|+1)
while i < abs(length) % while not finished
i = i + (length>0); % count iterations?!
X0 = X; f0 = f1; df0 = df1; % make a copy of current values
X = X + z1*s; % begin line search
[f2 df2] = eval(argstr);
i = i + (length<0); % count epochs?!
d2 = df2'*s;
f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1
if length>0, M = MAX; else M = min(MAX, -length-i); end
success = 0; limit = -1; % initialize quanteties
while 1
while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0)
limit = z1; % tighten the bracket
if f2 > f1
z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit
else
A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok!
end
if isnan(z2) | isinf(z2)
z2 = z3/2; % if we had a numerical problem then bisect
end
z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits
z1 = z1 + z2; % update the step
X = X + z2*s;
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
z3 = z3-z2; % z3 is now relative to the location of z2
end
if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1
break; % this is a failure
elseif d2 > SIG*d1
success = 1; break; % success
elseif M == 0
break; % failure
end
A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok!
if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign?
if limit < -0.5 % if we have no upper limit
z2 = z1 * (EXT-1); % the extrapolate the maximum amount
else
z2 = (limit-z1)/2; % otherwise bisect
end
elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max?
z2 = (limit-z1)/2; % bisect
elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit
z2 = z1*(EXT-1.0); % set to extrapolation limit
elseif z2 < -z3*INT
z2 = -z3*INT;
elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit?
z2 = (limit-z1)*(1.0-INT);
end
f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2
z1 = z1 + z2; X = X + z2*s; % update current estimates
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
end % end of line search
if success % if line search succeeded
f1 = f2; fX = [fX' f1]';
fprintf('%s %4i | Cost: %4.6e\r', S, i, f1);
s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
d2 = df1'*s;
if d2 > 0 % new slope must be negative
s = -df1; % otherwise use steepest direction
d2 = -s'*s;
end
z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO
d1 = d2;
ls_failed = 0; % this line search did not fail
else
X = X0; f1 = f0; df1 = df0; % restore point from before failed line search
if ls_failed | i > abs(length) % line search failed twice in a row
break; % or we ran out of time, so we give up
end
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
s = -df1; % try steepest
d1 = -s'*s;
z1 = 1/(1-d1);
ls_failed = 1; % this line search failed
end
if exist('OCTAVE_VERSION')
fflush(stdout);
end
end
fprintf('\n');
function[X，fX，i]=fmincg（f，X，options，P1，P2，P3，P4，P5）
%最小化连续可微分多元函数。起点
%由“X”（D乘以1）给出，且字符串“f”中命名的函数必须
%返回函数值和偏导数向量。波兰人-
%共轭梯度的Ribiere味用于计算搜索方向，
%以及使用二次和三次多项式近似的线搜索和
%Wolfe-Powell停止准则与斜率法一起使用
%用于猜测初始步长。此外，还对以下各项进行了一系列检查：
%确保正在进行勘探，且不会进行外推
%无限大。“长度”给出了运行的长度：如果是
%如果为正值，则给出最大行搜索数，如果为负值，则给出其最大行搜索数
%绝对值给出了允许的最大函数求值次数。你可以
%（可选）为“长度”指定第二个组件，该组件将指示
%第一行搜索中预期的函数值减少（默认值
%至1.0）。当函数的长度增加或不再增加时，该函数返回
%我们可以取得进展（即，我们至少可以取得进展，或者由于
%数值问题，我们不能再接近了）。如果函数终止
%在几次迭代中，它可能表示函数值
%和衍生工具不一致（即，在
%实现您的“f”功能）。函数返回找到的值
%解决方案“X”，表示所取得进展的函数值“fX”向量
%和“i”迭代次数（行搜索或函数求值，
%取决于使用的“长度”符号。
%
%用法：[X，fX，i]=fmincg（f，X，options，P1，P2，P3，P4，P5）
%
%另见：checkgrad
%
%Carl Edward Rasmussen 2001和2002版权所有。日期2002-02-13
%
%
%（C）版权所有1999年、2000年和2001年，卡尔·爱德华·拉斯穆森
%
%允许任何人复制、使用或修改这些文件
%用于研究或试验目的的计划和随附文件
%教育，前提是保留本版权声明，且注释
%已进行的任何更改。
%
%这些程序和文件的分发没有任何保证，
%明示的或暗示的。因为这些程序是为研究而编写的
%仅出于目的，它们还没有被测试到需要的程度
%适用于任何重要应用。所有这些程序的使用都是免费的
%完全由用户自行承担风险。
%
%[ml类]所做的更改：
%1）函数名和参数规范
%2）输出显示
%
%阅读选项
如果存在（'options'，'var'）&&&~isempty（options）&&isfield（options，'MaxIter'））
长度=options.MaxIter；
其他的
长度=100；
结束
RHO=0.01；%用于行搜索的一组常量
SIG=0.5；%RHO和SIG是Wolfe-Powell条件下的常数
INT=0.1；%不要在当前括号限制的0.1范围内重新评估
EXT=3.0；%外推最大值为当前括号的3倍
最大值=20；%每行搜索最多20次功能评估
比率=100；%最大允许坡率
argstr=['feval（f，X']；%compose用于调用函数的字符串
对于i=1：（纳金-3）
argstr=[argstr'，P'，int2str（i）]；
结束
argstr=[argstr'，）']；
如果最大值（尺寸（长度））=2，则红色=长度（2）；长度=长度（1）；红色=1；结束
S=[‘迭代’]；
i=0；%将游程计数器归零
ls_失败=0；%前一行搜索没有失败
外汇=[]；
[f1 df1]=eval（argstr）；%获取函数值和梯度
i=i+（长度0，M=MAX；否则M=min（MAX，-length-i）；结束
成功=0；限制=-1；%初始化量子
而1
而（（f2>f1+z1*RHO*d1）|（d2>-SIG*d1））和（M>0）
极限=z1；%拧紧支架
如果f2>f1
z2=z3-（0.5*d3*z3*z3）/（d3*z3+f2-f3）；%二次拟合
其他的
A=6*（f2-f3）/z3+3*（d2+d3）；%立方拟合
B=3*（f3-f2）-z3*（d3+2*d2）；
z2=（sqrt（B*B-A*d2*z3*z3）-B）/A；%可能的数字错误-确定！
结束
如果isnan（z2）| isinf（z2）
z2=z3/2；%如果我们有一个数值问题，那么对分
结束
z2=最大值（最小值（z2，INT*z3），（1-INT）*z3）；%不接受太接近极限
z1=z1+z2；%更新步骤
X=X+z2*s；
[f2 df2]=eval（argstr）；
M=M-1；i=i+（长度0%新斜率必须为负
options = optimset('MaxIter', 50);
[nn_params, cost] = fmincg(costFunction, initial_nn_params, options);
options = optimset('GradObj', 'on', 'MaxIter', 50);
[nn_params, cost, exit_flag] = fminunc(costFunction, initial_nn_params, options);
Testing lrCostFunction() with regularization
Cost: 2.534819
Expected cost: 2.534819
Gradients:
0.146561
-0.548558
0.724722
1.398003
Expected gradients:
0.146561
-0.548558
0.724722
1.398003
Program paused. Press enter to continue.
Training One-vs-All Logistic Regression...
id = 1512324857357
Elapsed time is 11.3794 seconds.
Program paused. Press enter to continue.
Training Set Accuracy: 93.100000
Testing lrCostFunction() with regularization
Cost: 2.534819
Expected cost: 2.534819
Gradients:
0.146561
-0.548558
0.724722
1.398003
Expected gradients:
0.146561
-0.548558
0.724722
1.398003
Program paused. Press enter to continue.
Training One-vs-All Logistic Regression...
id = 1512325280047
Elapsed time is 11.7978 seconds.
Training Set Accuracy: 95.120000