c# – 计算函数/蒙特卡罗方法合理性的算法

http://www-stat.stanford.edu/~cgates/PERSI/papers/MCMCRev.pdf

F是从char到char的函数.假设P1(f)是该函数的“合理性”度量.算法是：

从对函数的初步猜测开始,比如f,然后是新的函数f * –

>计算Pl(f).
>通过对值f进行随机转置来更改为f *,将其分配给两个符号.
>计算Pl(f *);如果这大于Pl(f),则接受f *.
>如果没有,翻转一个Pl(f)/ Pl(f *)硬币;如果它出现在头上,接受f *.
>如果硬币抛出尾巴,请留在f.

我正在使用以下代码实现此功能.我正在使用c#,但试图让每个人都更加简化.如果有更好的论坛,请告诉我.

var current_f = Initial();    // current accepted function f
 var current_Pl_f = InitialPl();  // current plausibility of accepted function f

 for (int i = 0; i < 10000; i++)
        {
            var candidate_f = Transpose(current_f); // create a candidate function

            var candidate_Pl_f = ComputePl(candidate_f);  // compute its plausibility

            if (candidate_Pl_f > current_Pl_f)            // candidate Pl has improved
            {
                current_f = candidate_f;            // accept the candidate
                current_Pl_f = candidate_Pl_f; 
            }
            else                                    // otherwise flip a coin
            {
                int flip = Flip(); 

                if (flip == 1)                      // heads
                {
                    current_f = candidate_f;        // accept it anyway
                    current_Pl_f = candidate_Pl_f; 
                }
                else if (flip == 0)                 // tails
                {
                    // what to do here ?
                }
            }
        }

我的问题基本上是否看起来像是实现该算法的最佳方法.尽管实施了这种方法,我似乎可能会陷入一些局部最大值/局部最小值.

编辑 – 这是Transpose()方法背后的本质问题.我使用类型<<的字典/哈希表char,char>>候选函数用于查看任何给定的char – > char变换.因此,转置方法只是在字典中交换两个指示函数行为的值.

private Dictionary<char,char> Transpose(Dictionary<char,char> map,params int[] indices)
    {
        foreach (var index in indices)
        {
            char target_val = map.ElementAt(index).Value;   // get the value at the index

            char target_key = map.ElementAt(index).Key;     // get the key at the index

            int _rand = _random.Next(map.Count);   // get a random key (char) to swap with

            char rand_key = map.ElementAt(_rand).Key;

            char source_val = map[rand_key]; // the value that currently is used by the source of the swap

            map[target_key] = source_val; // make the swap

            map[rand_key] = target_val;
        }

        return map; 
    }

请记住,使用基础字典的候选函数基本上只是：

public char GetChar(char in,Dictionary<char,char> theMap)
{
     return theMap[char]; 
}

这是计算Pl(f)的函数：

public decimal ComputePl(Func<char,char> candidate,string encrypted,decimal[][] _matrix)
    {
        decimal product = default(decimal);

        for (int i = 0; i < encrypted.Length; i++)
        {
            int j = i + 1;

            if (j >= encrypted.Length)
            {
                break;
            }

            char a = candidate(encrypted[i]);
            char b = candidate(encrypted[j]);

            int _a = GetIndex(_alphabet,a); // _alphabet is just a string/char[] of all avl chars 
            int _b = GetIndex(_alphabet,b);

            decimal _freq = _matrix[_a][_b]; 

            if (product == default(decimal))
            {
                product = _freq;
            }
            else
            {
                product = product * _freq;
            }
        }

        return product;
    }