trace of quadratic form

[Bob Carpenter]

Is there a reason to have this function signature:

real trace_quad_form(matrix m, vector v)

=def= trace(v' * m * v)

This looks like it'll define the same function as

real quad_form(matrix m, vector v)

=def= v' * m * v

So we're just going to scratch the signature for trace_quad_form.

(We're leaving trace_quad_form(matrix,matrix):real, of course.)

- Bob

[Marcus Brubaker]

I don't think there's a reason other than for completeness.

- Bob

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[Bob Carpenter]

Marcus --- are those tolerance parameters conjunctive or
disjunctive? That is do they all have to be satisfied, or
just one.

And am I understanding that if the init_alpha isn't set
well, the algorithm will adapt its own value?

- Bob

On 10/9/13 3:35 PM, Marcus Brubaker wrote:
> I don't think there's a reason other than for completeness.
>
>
> On Wed, Oct 9, 2013 at 2:31 PM, Bob Carpenter <ca...@alias-i.com <mailto:ca...@alias-i.com>> wrote:
>
> Is there a reason to have this function signature:
>
> real trace_quad_form(matrix m, vector v)
>
> =def= trace(v' * m * v)
>
> This looks like it'll define the same function as
>
> real quad_form(matrix m, vector v)
>
> =def= v' * m * v
>
> So we're just going to scratch the signature for trace_quad_form.
>

> (We're leaving trace_quad_form(matrix,matrix)__:real, of course.)

>
> - Bob
>
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[Marcus Brubaker]

Just one of those conditions being satisfied will result in the algorithm terminating.

init_alpha has a default value (something like 0.0001) which is reasonable for many problems but might be too large or too small depending on the objective function and initialization.  Being too big or too small just means that the first iteration will take longer (require more gradient evaluations) before the line search finds a good step length.  It's not a critical parameter, but if you're optimizing the same model multiple times (as you tweak things or with different data) being able to change it can save some real time.

Cheers,

Marcus

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[Jiqiang Guo]

What is exactly the default init_alpha now implemented in Stan?  It seems that it is doced as 0.001 (https://github.com/stan-dev/stan/blob/feature/issue-211-stan2-manual/src/docs/stan-reference/introduction.tex#L788).

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Jiqiang 

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[Marcus Brubaker]

Regarding the BFGS parameters, that doc should be accurate.

Cheers,

Marcus

[Jiqiang Guo]

Thanks.  I would change init_alpha from 0.0001 to 0.001 then in rstan. 

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Jiqiang