How to create function handle using random output

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Jacob Thompson
Jacob Thompson 2023-2-22
评论： Walter Roberson 2023-3-1
Hi all,
I am trying to implement something called a "Tailored Randomized Block-MH" algorithm, which requires me to take a likelihood function, change a subset of parameters while fixing the others through the optimization step.
Suppose I have a function f([p,q,r,x,y,z]) and a randomization step tells me to hold [p,q,r] at [p_bar,q_bar,r_bar] fixed while changing [x,y,z]. I can type manually something like:
maximand = @(x) f([p_bar,q_bar,r_bar,[x_1,x_2,x_3])
how would I do something like this using just the output from the output of, say, randperm(3)?
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Walter Roberson
Walter Roberson 2023-2-23
Which specific optimizer are you using? Some of them make it easier than others.
Jacob Thompson
Jacob Thompson 2023-2-23
I usually use fminunc but anything capable of simulated annealing will work

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回答（3 个）

Jan
Jan 2023-2-23
Maybe:
maximand = @(x) f([p_bar, q_bar, r_bar, x(randperm(3, 3))])
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Walter Roberson
Walter Roberson 2023-2-23
That potentially returns one of six different values, depending on which permutation occurs. It might possibly make sense to me to deliberately try all permutations of x, six calls to f, but I am having difficulty thinking of a context in which randomly selecting would be useful.
Jacob Thompson
Jacob Thompson 2023-2-23
That's not quite what I'm looking for. I don't want the order of variables to be randomized once we've already decided which parameters are fixed and which are allowed to vary to maximize the maximand, but rather I want to randomize the choice of which parameters to fix and which to vary in order to maximize the maximand.

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Walter Roberson
Walter Roberson 2023-2-23
For fmincon and simulannealbnd the easiest way to handle this is to use the same function call in each case, but set the ub and lb the same for the entries that are to be fixed for this run.
For example,
rvars = sort(randperm(numel(UB),NumFixedVars));
fixedvals = LB(rvars) + rand(1,NumFixedVars) .* (UB(rvars) - LB(rvars));
LB(rvars) = fixedvals; UB(rvars) = fixedvals;
x0(rvars) = fixedvals;
[bestx, fvals, exitflag] = fmincon(fun, x0, A, b, Aeq, beq, LB, UB, nonlcon, opts);
This code picks random variable indices. Then it picks random values between the lower and upper bound for those variables, and sets the lower and upper bound to be the same for those variables, and proceeds to run the optimization.
You might, of course, have had completely different logic in mind as to how to choose the fixed values for the variables, so alter the fixedvals assignment as appropriate for your situation.
Jacob Thompson
Jacob Thompson 2023-3-1
I'm quite certain that I figured this out, thanks for the help guys.
function liki = fmin(x,current,block)
% y = zeros(1,16);
noblock = setdiff(1:16,block);
y = zeros(size(current));
y(noblock) = current(noblock);
elements = length(block);
for i = 1:elements
y(block(i)) = x(i);
end
liki = -dsgeliki(y) - prior(y);
end

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