Is there an Elegant Universal Theory of Prediction?

Could there exist an elegant and universal theory of sequence pre diction? Solomonoff's model of induction rapidly learns to make optimal predict ions for any computable sequence, including probabilistic ones [13, 14]. In deed the problem of sequence prediction could well be considered solved [9, 8], if it were not for the fact that Solomonoff's theoretical model is incomputab le. Among computable theories there exist powerful general predict ors, such as the Lempel-Ziv algorithm [5] and Context Tree Weighting [18], that can learn to predict some complex sequences, but not others. Some prediction methods, such as the Minimum Description Length principle [12] and the Minimum Messa ge Length principle [17], can even be viewed as computable approximation s to Solomonoff induction [10]. However in practice their power and genera lity are limited by the power of compression and coding methods employed, as well as having a significantly reduced data efficiency as compared to Solom onoff induction [11]. This work was supported by SNF grant 200020-107616.