hqt*_*hqt 42 algorithm machine-learning octave neural-network
我经常fminunc用于逻辑回归问题.我已经在网上读过Andrew Ng使用的,fmincg而不是fminunc相同的论点.结果不同,往往fmincg更精确,但不是太多.(我将fmincg函数fminunc的结果与同一数据进行比较)
所以,我的问题是:这两个功能有什么区别？每个功能实现了什么算法？(现在,我只是使用这些功能而不确切知道它们是如何工作的).
谢谢 :)
gre*_*egS 23
与其他答案相反,这里建议fmincg和fminunc之间的主要区别在于准确性或速度,对某些应用程序而言,最重要的区别可能是内存效率.在Coursera的Andrew Ng的机器学习课程的编程练习4(即神经网络训练)中,ex4.m关于fmincg的评论是
%% ===================第8部分:训练NN ===================
%你现在已经实施训练神经
网络所需的所有代码.为了训练你的神经网络,我们现在将使用"fmincg",
%是一个与"fminunc"类似的函数.回想一下,这些
%高级优化器能够有效地训练我们的成本函数,
只要我们为它们提供梯度计算.
像原版海报一样,我也很好奇ex4.m的结果可能会因fminunc而不是fmincg而有所不同.所以我试着替换fmincg调用
options = optimset('MaxIter', 50);
[nn_params, cost] = fmincg(costFunction, initial_nn_params, options);
以下调用fminunc
options = optimset('GradObj', 'on', 'MaxIter', 50);
[nn_params, cost, exit_flag] = fminunc(costFunction, initial_nn_params, options);
但从Windows上运行的32位版本的Octave获得以下错误消息:
错误:内存耗尽或请求的大小对于Octave索引类型的范围太大 - 尝试返回提示
在Windows上运行的32位MATLAB版本提供了更详细的错误消息:
使用查找
内存不足时出错.键入HELP MEMORY以获取选项.
spones中的错误(第14行)
[i,j] = find(S);
颜色错误(第26行)
J = spones(J);
sfminbx中的错误(第155行)
group = color(Hstr,p);
fminunc中的错误(第408行)
[x,FVAL,〜,EXITFLAG,OUTPUT,GRAD,HESSIAN] = sfminbx(funfcn,x,l,u,...
ex4中的错误(第205行)
[nn_params,cost,exit_flag] = fminunc(costFunction,initial_nn_params,options);
我的笔记本电脑上的MATLAB内存命令报告:
最大可能阵列:2046 MB(2.146e + 09字节)*
可用于所有阵列的内存:3402 MB(3.568e + 09字节)**
MATLAB使用的内存:373 MB(3.910e + 08字节)
物理内存(RAM) :3561 MB(3.734e + 09字节)
*受可用的连续虚拟地址空间限制.
**受虚拟地址空间限制.
我以前认为Ng教授选择使用fmincg训练ex4.m神经网络(有400个输入功能,401包括偏置输入)以提高训练速度.但是,现在我相信他使用fmincg的原因是为了提高内存效率,以便在32位版本的Octave/MATLAB上进行训练.关于获得在Windows操作系统上运行的64位Octave版本的必要工作的简短讨论就在这里.
Edw*_*xon 13
根据Andrew Ng本人的说法,fmincg用来不是为了获得更准确的结果(记住,你的成本函数在任何一种情况下都是相同的,你的假设不是更简单或更复杂)但是因为它更有效地做了特别复杂的梯度下降假设.他自己似乎使用fminunc假设几乎没有特征的地方,但fmincg它有数百个.
为什么fmincg有效？
这是源代码的副本,其中包含解释所使用的各种算法的注释.这是一种愚蠢的行为,因为在学习区分狗和椅子时,孩子的大脑会做同样的事情.
这是fmincg.m的Octave源.
function [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');