Moderated by Stephen Muggleton.

Boris Ryabko

The nonprobabilistic approach to learning the best prediction

The article mentioned above has been submitted to the Electronic Transactions on Artificial Intelligence, and the present page contains the review discussion. Click here for more explanations and for the webpage of theauthor, Boris Ryabko.

Overview of interactions

N:o Question Answer(s) Continued discussion
1 15.10  Anonymous Referee 1
2 15.10  Anonymous Referee 2

Q1. Anonymous Referee 1 (15.10):

Recommendation: The paper can be accepted for ETAI after minor revisions. No further refereeing round is needed.

This paper discusses the problem of predicting the next character in a string using the information of the previous characters. When the source of characters is stationary and ergotic, although an asymptotically optimal prediction method exists, it cannot find "simple" patterns appearing in the string, such as in: 0100100010000100000... This paper introduces a new approach to analyzing such sequences, and shows
1. the existence of large sets of well predictable sequences which cannot be found with the ESS (ergotic and stationary source) model, and
2. the existence of large sets which can be predicted with complex algorithms which do not use only estimations of conditional properties.

It might help if the definitions were more "decorative".

Minor problems:
Introduction: Line 9:

    Each moment $t$ that the gambler divides the capital $V_t$ into
    $|A|$ parts equals $V_tP_I(a | x_1,\ldots, x_t), a \in A$.

    This would read: t equals V_tP_I(...) ? (but probably not)

Q2. Anonymous Referee 2 (15.10):

This paper is apparently of high quality. Unfortunately, the field is outside my area of competence and I cannot give any better judgement than a general appreciation of the quality of the work. My understanding is that it is a very important contribution to the theory of learning and with strong applications to learning e.g. in biological systems that probably are not probabilistic.

The presentation is very expert and it would have been well-written if it had not several (correctable) English mistakes. Regarding some details, I believe it would be useful for many a readers to add a definition of ergodic and stationary processes. I also wonder whether there are any possible connections to Valiant's work that need be explored. Having no access to literature at the moment of writing the review I am only providing one author of an interesting work on what is learnable/not learnable. The authors are Gora et al and I believe one can find a precise reference at the home page of the Logic Section, Department of Mathematics, Warsaw University, or through a search for Andzrej Skowron's page and that Section.


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