11 research outputs found
Predictive Complexity for Games with Finite Outcome Spaces
Predictive complexity is a generalisation of Kolmogorov complexity motivated by an on-line prediction scenario. It quantifies “unpredictability ” of a sequence in a particular prediction environment. This paper surveys key results on predictive complexity for games with finitely many outcomes. The issues of existence, non-existence, uniqueness, and linear inequalities are covered.
Aggregation Algorithm Vs. Average for Time Series Prediction
Learning with expert advice as a scheme of on-line learning has been very successfully applied to various learning problems due to its strong theoretical basis. In this paper, for the purpose of times se- ries prediction, we investigate the application of Aggregation Algorithm, which a generalisation of the famous weighted majority algorithm. The results of the experiments done, show that the Aggregation Algorithm performs very well in comparison to average
The Fundamental Nature of the Log Loss Function
The standard loss functions used in the literature on probabilistic
prediction are the log loss function, the Brier loss function, and the
spherical loss function; however, any computable proper loss function can be
used for comparison of prediction algorithms. This note shows that the log loss
function is most selective in that any prediction algorithm that is optimal for
a given data sequence (in the sense of the algorithmic theory of randomness)
under the log loss function will be optimal under any computable proper mixable
loss function; on the other hand, there is a data sequence and a prediction
algorithm that is optimal for that sequence under either of the two other
standard loss functions but not under the log loss function.Comment: 12 page
Aggregating Algorithm for Prediction of Packs
This paper formulates a protocol for prediction of packs, which is a special case of on-line prediction under delayed feedback. Under the prediction of packs protocol, the learner must make a few predictions without seeing the respective outcomes and then the outcomes are revealed in one go. The paper develops the theory of prediction with expert advice for packs by generalising the concept of mixability. We propose a number of merging algorithms for prediction of packs with tight worst case loss upper bounds similar to those for Vovk’s Aggregating Algorithm. Unlike existing algorithms for delayed feedback settings, our algorithms do not depend on the order of outcomes in a pack. Empirical experiments on sports and house price datasets are carried out to study the performance of the new algorithms and compare them against an existing method
Aggregating algorithm for prediction of packs
This paper formulates a protocol for prediction of packs, which is a special case of on-line prediction under delayed feedback. Under the prediction of packs protocol, the learner must make a few predictions without seeing the respective outcomes and then the outcomes are revealed in one go. The paper develops the theory of prediction with expert advice for packs by generalising the concept of mixability. We propose a number of merging algorithms for prediction of packs with tight worst case loss upper bounds similar to those for Vovk’s Aggregating Algorithm. Unlike existing algorithms for delayed feedback settings, our algorithms do not depend on the order of outcomes in a pack. Empirical experiments on sports and house price datasets are carried out to study the performance of the new algorithms and compare them against an existing method
Prediction with Expert Advice under Discounted Loss
We study prediction with expert advice in the setting where the losses are
accumulated with some discounting---the impact of old losses may gradually
vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm
for Regression to this case, propose a suitable new variant of exponential
weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte
Competing with stationary prediction strategies
In this paper we introduce the class of stationary prediction strategies and
construct a prediction algorithm that asymptotically performs as well as the
best continuous stationary strategy. We make mild compactness assumptions but
no stochastic assumptions about the environment. In particular, no assumption
of stationarity is made about the environment, and the stationarity of the
considered strategies only means that they do not depend explicitly on time; we
argue that it is natural to consider only stationary strategies even for highly
non-stationary environments.Comment: 20 page