Abstract. To estimate the quality of the induced predictive model we
generally use measures of averaged prediction accuracy, such as the relative
mean squared error on test data. Such evaluation fails to provide
local information about reliability of individual predictions, which can
be important in risk-sensitive fields (medicine, finance, industry etc.).
Related work presented several ways for computing individual prediction
reliability estimates for single-target regression models, but has not
considered their use with multi-target regression models that predict a
vector of independent target variables. In this paper we adapt the existing
single-target reliability estimates to multi-target models. In this way
we try to design reliability estimates, which can estimate the prediction
errors without knowing true prediction errors, for multi-target regression
algorithms, as well. We approach this in two ways: by aggregating reliability
estimates for individual target components, and by generalizing
the existing reliability estimates to higher number of dimensions. The
results revealed favorable performance of the reliability estimates that
are based on bagging variance and local cross-validation approaches. The
results are consistent with the related work in single-target reliability
estimates and provide a support for multi-target decision making.
In the paper we proposed several approaches for estimating the reliabilities of
individual multi-target regression predictions. The aggregated variants (AM, l
and +) produce a single-valued estimate which is preferable for interpretation
and comparison. The last variant (+) is a direct generalization of the singletarget
estimators from the related work.
Our evaluation showed that best results were achieved using the BAGV and
the LCV reliability estimates regardless the estimate variant. This complies with
the related work on the single-target predictions, where these two estimates also
performed well. Although all of the proposed variants achieve comparable results,
our proposed generalization of existing methods (+) is still the preferred variant
due to its lower computational complexity (as estimates are only calculated once
for all of the target attributes) and the solid theoretical background.
In our further work we intend to additionally evaluate other reliability estimates
in combination with several other regression models. We also plan to test
the adaptation of the proposed methods to multi-target classification.
Reliability estimation of individual predictions offers many advantages especially
when making decisions in highly sensitive environment. Our work provides
an effective support for model-independent multi-target regression.