4 research outputs found
Combining predictions from linear models when training and test inputs differ
Methods for combining predictions from different models in a supervised
learning setting must somehow estimate/predict the quality of a model's
predictions at unknown future inputs. Many of these methods (often implicitly)
make the assumption that the test inputs are identical to the training inputs,
which is seldom reasonable. By failing to take into account that prediction
will generally be harder for test inputs that did not occur in the training
set, this leads to the selection of too complex models. Based on a novel,
unbiased expression for KL divergence, we propose XAIC and its special case
FAIC as versions of AIC intended for prediction that use different degrees of
knowledge of the test inputs. Both methods substantially differ from and may
outperform all the known versions of AIC even when the training and test inputs
are iid, and are especially useful for deterministic inputs and under covariate
shift. Our experiments on linear models suggest that if the test and training
inputs differ substantially, then XAIC and FAIC predictively outperform AIC,
BIC and several other methods including Bayesian model averaging.Comment: 12 pages, 2 figures. To appear in Proceedings of the 30th Conference
on Uncertainty in Artificial Intelligence (UAI2014). This version includes
the supplementary material (regularity assumptions, proofs
Combining predictions from linear models when training and test inputs differ
Methods for combining predictions from different models in a
supervised learning setting must somehow estimate/predict the
quality of a model's predictions at unknown future inputs.
Many of these methods (often implicitly) make the assumption that the
test inputs are identical to the training inputs, which is seldom
reasonable. By failing to take into account that prediction will
generally be harder for test inputs that did not occur in the
training set, this leads to the selection of too complex models.
Based on a novel, unbiased expression for KL divergence, we propose
XAIC and its special case FAIC as versions of AIC intended for
prediction that use different degrees of knowledge of the test
inputs. Both methods substantially differ from and may
outperform all the known
versions of AIC \emph{even when the training and test inputs are iid}, and
are especially useful for deterministic inputs and under covariate
shift. Our experiments on linear models suggest that if the test
and training inputs differ substantially, then XAIC and FAIC
predictively outperform AIC, BIC and several other methods including
Bayesian model averaging
Better predictions when models are wrong or underspecified
Many statistical methods rely on models of reality in order to learn from data and to make predictions about future data. By necessity, these models usually do not match reality exactly, but are either wrong (none of the hypotheses in the model provides an accurate description of reality) or underspecified (the hypotheses in the model describe only part of the data). In this thesis, we discuss three scenarios involving models that are wrong or underspecified. In each case, we find that standard statistical methods may fail, sometimes dramatically, and present different methods that continue to perform well even if the models are wrong or underspecified. The first two of these scenarios involve regression problems and investigate AIC (Akaike's Information Criterion) and Bayesian statistics. The third scenario has the famous Monty Hall problem as a special case, and considers the question how we can update our belief about an unknown outcome given new evidence when the precise relation between outcome and evidence is unknown.UBL - phd migration 201
Better predictions when models are wrong or underspecified
Many statistical methods rely on models of reality in order to learn from data and to make predictions about future data. By necessity, these models usually do not match reality exactly, but are either wrong (none of the hypotheses in the model provides an accurate description of reality) or underspecified (the hypotheses in the model describe only part of the data). In this thesis, we discuss three scenarios involving models that are wrong or underspecified. In each case, we find that standard statistical methods may fail, sometimes dramatically, and present different methods that continue to perform well even if the models are wrong or underspecified. The first two of these scenarios involve regression problems and investigate AIC (Akaike's Information Criterion) and Bayesian statistics. The third scenario has the famous Monty Hall problem as a special case, and considers the question how we can update our belief about an unknown outcome given new evidence when the precise relation between outcome and evidence is unknown.UBL - phd migration 201