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Results tagged with lagrange-multipliers
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user 246889
The method of Lagrange multipliers finds critical points (including maxima and minima) of a differentiable function subject to differentiable constraints.
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Maximum Entropy Discrete Distribution
You have to keep in mind that the index in the summation is a "dummy index", it is only a placeholder for $1,2,3,\cdots$. Therefore, it is not the same $i$ that appears in the derivative! We can clari …
- 2,690
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Finding the MLEs for pi in a contingency table proof
So, we can write the log-likelihood as $\sum_i\sum_jy_{ij}\log(\pi_{i.}\cdot\pi_{.j})$, which means that the Lagrangian is:
$$\mathcal L=\sum_i\sum_jy_{ij}\log(\pi_{i.}\cdot\pi_{.j})-\lambda\sum_i\pi_ …
- 2,690