There is no maximum likelihood solution to a GP with a single training point, but you can certainly draw samples from the posterior; in fact, you can draw samples from the prior (without conditioning on data). That may help you determine if your covariance function is reasonable: samples from the prior should look like data that you might expect to see.
I'm unfamiliar with the sklearn implementation of GP, but I put some MATLAB code demonstrating unconditioned and conditioned draws (using the ordinary squared exponential covariance function) at https://gist.github.com/1406331. See chapter 2 of the Rasmussen and Williams book (iirc) for details. -Ken On Tue, Nov 29, 2011 at 3:07 PM, Vlad Niculae <[email protected]> wrote: > On Tue, Nov 29, 2011 at 10:02 PM, Alexandre Gramfort > <[email protected]> wrote: >> Hi Alex, >> >> I would say: >> >> if it makes sense to fit a GP with only one point: >> it should be fixed > > Note that even though it might not make any sense in practice, unless > there's a mathematical reason that I'm missing, it shouldn't be > prohibited, if only for didactical purposes, in my opinion. > > Vlad > >> else: >> raise a nicer error message >> >> Alex >> >> On Tue, Nov 29, 2011 at 7:10 PM, Alexandre Passos >> <[email protected]> wrote: >>> Hi, >>> >>> Currently the fit function in GaussianProcess throws a weird exception >>> when only one training example is passed to fit(): >>> >>>>>> from sklearn.gaussian_process import GaussianProcess >>> from sklearn.gaussian_process import GaussianProcess >>>>>> gp.fit([[1., 2.]], [-1.0]) >>> gp.fit([[1., 2.]], [-1.0]) >>> Traceback (most recent call last): >>> File "<stdin>", line 1, in <module> >>> File >>> "/Users/apassos/Library/Python/2.7/lib/python/site-packages/sklearn/gaussian_process/gaussian_process.py", >>> line 281, in fit >>> if np.min(np.sum(D, axis=1)) == 0. \ >>> File >>> "/System/Library/Frameworks/Python.framework/Versions/2.7/Extras/lib/python/numpy/core/fromnumeric.py", >>> line 1862, in amin >>> return amin(axis, out) >>> ValueError: zero-size array to ufunc.reduce without identity >>>>>> >>> >>> Should this be fixed or should a better error message be passed? >>> -- >>> - Alexandre >>> >>> ------------------------------------------------------------------------------ >>> All the data continuously generated in your IT infrastructure >>> contains a definitive record of customers, application performance, >>> security threats, fraudulent activity, and more. Splunk takes this >>> data and makes sense of it. IT sense. And common sense. >>> http://p.sf.net/sfu/splunk-novd2d >>> _______________________________________________ >>> Scikit-learn-general mailing list >>> [email protected] >>> https://lists.sourceforge.net/lists/listinfo/scikit-learn-general >>> >> >> ------------------------------------------------------------------------------ >> All the data continuously generated in your IT infrastructure >> contains a definitive record of customers, application performance, >> security threats, fraudulent activity, and more. Splunk takes this >> data and makes sense of it. IT sense. And common sense. >> http://p.sf.net/sfu/splunk-novd2d >> _______________________________________________ >> Scikit-learn-general mailing list >> [email protected] >> https://lists.sourceforge.net/lists/listinfo/scikit-learn-general > > ------------------------------------------------------------------------------ > All the data continuously generated in your IT infrastructure > contains a definitive record of customers, application performance, > security threats, fraudulent activity, and more. Splunk takes this > data and makes sense of it. IT sense. And common sense. > http://p.sf.net/sfu/splunk-novd2d > _______________________________________________ > Scikit-learn-general mailing list > [email protected] > https://lists.sourceforge.net/lists/listinfo/scikit-learn-general ------------------------------------------------------------------------------ All the data continuously generated in your IT infrastructure contains a definitive record of customers, application performance, security threats, fraudulent activity, and more. Splunk takes this data and makes sense of it. IT sense. And common sense. http://p.sf.net/sfu/splunk-novd2d _______________________________________________ Scikit-learn-general mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/scikit-learn-general
