8,199 research outputs found
Empirical Bernstein stopping
Sampling is a popular way of scaling up machine learning algorithms to large datasets. The question often is how many samples are needed. Adaptive stopping algorithms monitor the performance in an online fashion and they can stop early, saving valuable resources. We consider problems where probabilistic guarantees are desired and demonstrate how recently-introduced empirical Bernstein bounds can be used to design stopping rules that are efficient. We provide upper bounds on the sample complexity of the new rules, as well as empirical results on model selection and boosting in the filtering setting
Most Likely Transformations
We propose and study properties of maximum likelihood estimators in the class
of conditional transformation models. Based on a suitable explicit
parameterisation of the unconditional or conditional transformation function,
we establish a cascade of increasingly complex transformation models that can
be estimated, compared and analysed in the maximum likelihood framework. Models
for the unconditional or conditional distribution function of any univariate
response variable can be set-up and estimated in the same theoretical and
computational framework simply by choosing an appropriate transformation
function and parameterisation thereof. The ability to evaluate the distribution
function directly allows us to estimate models based on the exact likelihood,
especially in the presence of random censoring or truncation. For discrete and
continuous responses, we establish the asymptotic normality of the proposed
estimators. A reference software implementation of maximum likelihood-based
estimation for conditional transformation models allowing the same flexibility
as the theory developed here was employed to illustrate the wide range of
possible applications.Comment: Accepted for publication by the Scandinavian Journal of Statistics
2017-06-1
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