R中的fminsearch比Matlab差

Question

有我的数据(x和y列是相关的):https: //www.dropbox.com/s/b61a7enhoa0p57p/Simple1.csv

我需要的是使用折线拟合数据.执行此操作的Matlab代码是:

spline_fit.m:
function [score, params] = spline_fit (points, x, y)

min_f = min(x)-1;
max_f = max(x);

points = [min_f points max_f];
params = zeros(length(points)-1, 2);

score = 0;
for i = 1:length(points)-1
    in = (x > points(i)) & (x <= points(i+1));
    if sum(in) > 2
        p = polyfit(x(in), y(in), 1);
        pred = p(1)*x(in) + p(2);
        score = score + norm(pred - y(in));
        params(i, :) = p;
    else
       params(i, :) = nan;
    end
end


test.m:
%Find the parameters
r = [100,250,400];
p = fminsearch('spline_fit', r, [], x, y)
[score, param] = spline_fit(p, x, y)

%Plot the result
y1 = zeros(size(x));
p1 = [-inf, p, inf];
for i = 1:size(param, 1)
    in = (x > p1(i)) & (x <= p1(i+1));
    y1(in) = x(in)*param(i,1) + param(i,2);
end

[x1, I] = sort(x);
y1 = y1(I);

plot(x,y,'x',x1,y1,'k','LineWidth', 2)

这确实很好,产生了以下优化:[102.9842,191.0006,41.9912]

我在R中实现了同样的想法:

library(pracma);
spline_fit <- function(x, xx, yy) {

  min_f = min(xx)-1;
  max_f = max(xx);

  points = c(min_f, x, max_f)
  params = array(0, c(length(points)-1, 2));

  score = 0;
  for( i in 1:length(points)-1)
  {
    inn <- (xx > points[i]) & (xx <= points[i+1]);
    if (sum(inn) > 2)
    {
      p <- polyfit(xx[inn], yy[inn], 1);
      pred <- p[1]*xx[inn] + p[2];
      score <- score + norm(as.matrix(pred - yy[inn]),"F");
      params[i,] <- p;
    }
    else
      params[i,] <- NA;
  }  
  score
}

但是我得到了非常糟糕的结果:

> fminsearch(spline_fit,c(100,250,400), xx = Simple1$x, yy = Simple1$y)
$xval
[1] 100.1667 250.0000 400.0000

$fval
[1] 4452.761

$niter
[1] 2

正如您所看到的,它在2次迭代后停止并且不会产生好点.

我很乐意为解决这个问题提供帮助.

此外,如果有人知道如何使用任何免费库在C#中实现它,它会更好.我知道哪里可以获得polyfit,但不知道fminsearch.

Answer 1

这里的问题是可能性表面非常糟糕 - 有多个最小值和不连续跳跃 - 这将使得不同优化器得到的结果几乎是任意的.我承认MATLAB的优化器非常强大,但我想说,除非你使用某种形式的随机全局优化,否则优化器在这种情况下是否会达到全局最小值几乎是偶然(以及你从哪里开始)例如模拟退火.

我选择使用的r内置的优化器(使用内尔德-米德默认情况下),而不是fminsearch从pracma包.

spline_fit <- function(x, xx = Simple1$x, yy=Simple1$y) {

    min_f = min(xx)-1
    max_f = max(xx)

    points = c(min_f, x, max_f)
    params = array(0, c(length(points)-1, 2))

    score = 0
    for( i in 1:(length(points)-1))
    {
        inn <- (xx > points[i]) & (xx <= points[i+1]);
        if (sum(inn) > 2)
        {
            p <- polyfit(xx[inn], yy[inn], 1);
            pred <- p[1]*xx[inn] + p[2];
            score <- score + norm(as.matrix(pred - yy[inn]),"F");
            params[i,] <- p;
        }
        else
            params[i,] <- NA;
    }  
    score
}

library(pracma) ## for polyfit
Simple1 <- read.csv("Simple1.csv")
opt1 <- optim(fn=spline_fit,c(100,250,400), xx = Simple1$x, yy = Simple1$y)
## [1] 102.4365 201.5835 422.2503

这比fminsearch结果更好,但仍然不同于MATLAB结果,并且比它们更糟糕:

## Matlab results:
matlab_fit <- c(102.9842, 191.0006, 421.9912)
spline_fit(matlab_fit, xx = Simple1$x, yy = Simple1$y)
## 3724.3
opt1$val
## 3755.5  (worse)

该bbmle软件包提供了一组用于探索优化表面的实验性/非常好记录的工具集:

library(bbmle)
ss <- slice2D(fun=spline_fit,opt1$par,nt=51)
library(lattice)

围绕optim-estimated参数的2D"切片" .圆圈显示每个切片(打开)中的最佳拟合(实线)和最小值.

png("splom1.png")
print(splom(ss))
dev.off()

matlab和optim fit之间的"切片"表明表面非常坚固:

ss2 <- bbmle:::slicetrans(matlab_fit,opt1$par,spline_fit)
png("slice1.png")
print(plot(ss2))
dev.off()