[SciPy-user] curve_fit step-size and optimal parameters

josef.pktd@gmai... josef.pktd@gmai...
Wed Jun 10 11:27:42 CDT 2009


On Wed, Jun 10, 2009 at 12:12 PM, <josef.pktd@gmail.com> wrote:
> On Wed, Jun 10, 2009 at 3:58 AM, Sebastian
> Walter<sebastian.walter@gmail.com> wrote:
>> If you try to fit the frequency with the least-squares distance  the
>> problem is not only nonlinearity
>> but rather the fact that the objective functions has many local minimizers.
>> At least that's what I have observed in a toy example once.
>>
>> Has anyone experience what to do in that case? (Maybe use L1 norm instead?)
>
> I would look at estimation in frequency domain, which I know next to
> nothing about.
>
> But for your example, I manged to get the estimate either by adding a
> bit of noise to your y, or by estimating the constant separately. When
> I remove the constant, the indeterminacy (?) in the parameter estimate
> went away. Also if there is a small trend then the estimation worked.
>
> The other way, I would try in cases like this would be to use a
> penalization term (as in Tychonov or Ridge) in the objective function,
> but I didn't try out how well this would work in your case.
>

Your example also estimates correctly with a starting value V0 = 0 or
small negative V0.
In scipy stats, I also found a distribution, where the estimation
converges to the correct estimate only from one side of the true
parameter (but no idea why)

Josef


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