  Top-N recommendation aims to recommend each consumer a small set of N items
from a large collection of items, and its accuracy is one of the most common
indexes to evaluate the performance of a recommendation system. While a large
number of algorithms are proposed to push the Top-N accuracy by learning the
user preference from their history purchase data, a predictability question is
naturally raised - whether there is an upper limit of such Top-N accuracy. This
work investigates such predictability by studying the degree of regularity from
a specific set of user behavior data. Quantifying the predictability of Top-N
recommendations requires simultaneously quantifying the limits on the accuracy
of the N behaviors with the highest probability. This greatly increases the
difficulty of the problem. To achieve this, we firstly excavate the
associations among N behaviors with the highest probability and describe the
user behavior distribution based on the information theory. Then, we adopt the
Fano inequality to scale and obtain the Top-N predictability. Extensive
experiments are conducted on the real-world data where significant improvements
are observed compared to the state-of-the-art methods. We have not only
completed the predictability calculation for N targets but also obtained
predictability that is much closer to the true value than existing methods. We
expect our results to assist these research areas where the quantitative
requirement of Top-N predictability is required.
