2
$\begingroup$

I see a similar problem in How do I fit a constrained regression in R so that coefficients total = 1?

Specifically, my model is $Y_i= \pi_1 X_1+\pi_2 X_2 +...+ \pi_K X_K +\epsilon_i$ with $\pi_k \ge 0$ and $\sum_k \pi_k =1$ . That is $\pi$'s are probabilities. and I need to minimize $\sum_i(Y_i -\pi_1 X_{i1}-\pi_2 X_{i2} -...- \pi_K X_{iK})^2$. However, the number of observations $n$ are few, $n<<K$. The question is how do I minimize so that only a few of $\pi_k$ are $\gt 0$. The answer based on quadratic programming don't take sparseness into account. Do I need to do some sort of regularization?

New contributor
Siddhartha R Dalal is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
$\endgroup$
2
  • 1
    $\begingroup$ How do you define "a few of [the] $\pi_k$"? Could the number of non-zero coefficient estimates be equal to $n$? $\endgroup$
    – jbowman
    May 14 at 1:43
  • $\begingroup$ It should be $n$ or less. $\endgroup$ May 14 at 3:53

0

Your Answer

Siddhartha R Dalal is a new contributor. Be nice, and check out our Code of Conduct.

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.