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Aug
12
revised Maximization of a nasty Gaussian likelihood
added 193 characters in body
Aug
12
comment Maximization of a nasty Gaussian likelihood
No, as I said, I'm trying for nonsquare $A$ matrices, the counterexample was with $3\times 2$ matrix. So I'm not saying that the proof is wrong for invertible $A$, what I'm saying our suggestion in comments seems wrong. (Also I found an error in my proof that $\lambda \to \infty$ makes solution the pseudoinverse -- trying to work on it).
Aug
12
revised Maximization of a nasty Gaussian likelihood
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Aug
12
revised Maximization of a nasty Gaussian likelihood
added 212 characters in body
Aug
12
revised Maximization of a nasty Gaussian likelihood
added 77 characters in body
Aug
12
comment Maximization of a nasty Gaussian likelihood
I tried this for 2-dimensional examples, plotted the contour of the likelihood wrt $x$, and also plot the analytical solution we suggest. Unfortunately, it is usually too far from the true maxima. So... I still have a problem :)
Aug
12
comment Maximization of a nasty Gaussian likelihood
Yes that is the applying pseudoinverse, i.e. $x = (A^\top A)^{-1} A^\top y$. I also think that. Thanks a million again!
Aug
12
comment Maximization of a nasty Gaussian likelihood
great! let me check also the details above. thanks a million!
Aug
12
comment Maximization of a nasty Gaussian likelihood
is it possible that solution is $x = (A^\top A)^{-1} A^\top y$, what do you think? I say this completely with a gut feeling, but normally the problem is least squares if we don't have $x$ in the covariance, and the solution is this (and yours). Is it possible that somehow covariance is irrelevant in the maximisation? (I am intentionally being vague)
Aug
12
accepted Sum of two kronecker products as a kronecker product
Aug
12
accepted Maximum likelihood estimate of $N$ (trials) in Binomial
Aug
12
revised Maximization of a nasty Gaussian likelihood
deleted 80 characters in body
Aug
12
comment Maximization of a nasty Gaussian likelihood
Thanks! I will work through the details. May I thank you if I use this solution in the paper? as an anonymous user? :-)
Aug
12
revised Maximization of a nasty Gaussian likelihood
added 67 characters in body
Aug
12
comment Maximization of a nasty Gaussian likelihood
No it is not even square. (I had to state it, my fault). Just saw your solution, thanks! but I guess it is not generalisable to nonsquare case?
Aug
12
comment Maximization of a nasty Gaussian likelihood
Yes. I already plotted some low dimensional examples, its behaviour is changing with $\lambda$ but in general it is nonconvex (have two modes in 1-dim, I'm not sure for 2-dim). Somebody said may be it can be solved by a reparametrization, so I posted this.
Aug
12
revised Maximization of a nasty Gaussian likelihood
added 9 characters in body
Aug
12
comment Maximization of a nasty Gaussian likelihood
Yes exactly. $\mathcal{N}(y;\mu,\Sigma)$ means, density is defined over $y$ with mean $\mu$ and covariance $\Sigma$.
Aug
12
revised Maximization of a nasty Gaussian likelihood
added 5 characters in body
Aug
12
asked Maximization of a nasty Gaussian likelihood