Data availabilitySummary statistics generated by COVID-19 Host Genetics Initiative are available online (https://www.covid19hg.org/results/r6/). The analyses described here use the freeze 6 data. The COVID-19 Host Genetics Initiative continues to regularly release new data freezes. Summary statistics for samples from individuals of non-European ancestry are not currently available owing to the small individual sample sizes of these groups, but the results for 23 loci lead variants are reported in Supplementary Table 3. Individual-level data can be requested directly from the authors of the contributing studies, listed in Supplementary Table 1.

Scalability is a key requirement for any KDD and data mining algorithm, and one of the biggest research challenges is to develop methods that allow to use large amounts of data. One possible approach for dealing with huge amounts of data is to take a random sample and do data mining on it, since for many data mining applications approximate answers are acceptable. However, as argued by several researchers, random sampling is difficult to use due to the difficulty of determining an appropriate sample size. In this paper, we take a sequential sampling approach for solving this difficulty, and propose an adaptive sampling algorithm that solves a general problem covering many problems arising in applications of discovery science. The algorithm obtains examples sequentially in an on-line fashion, and it determines from the obtained examples whether it has already seen a large enough number of examples. Thus, sample size is not fixed a priori; instead, it adaptively depends on the situation. Due to this adaptiveness, if we are not in a worst case situation as fortunately happens in many practical applications, then we can solve the problem with a number of examples much smaller than the required in the worst case. For illustrating the generality of our approach, we also describe how different instantiations of it can be applied to scale up knowledge discovery problems that appear in several areas.

In this paper, we show how to extend the argument due to Bonet, Pitassi and Raz to show that bounded-depth Frege proofs do not have feasible interpolation, assuming that factoring of Blum integers or computing the Diffie-Hellman function is sufficiently hard. It follows as a corollary that bounded-depth Frege is not automatizable; in other words, there is no deterministic polynomial-time algorithm that will output a short proof if one exists. A notable feature of our argument is its simplicity.

Abstract. In this paper we present a experimental evaluation of a boosting based learning system and show that can be run efficiently over a large dataset. The system uses as base learner decision stumps, single atribute decision trees with only two terminal nodes. To select the best decision stump at each iteration we use an adaptive sampling method. As a boosting algorithm, we use a modification of AdaBoost that is suitable to be combined with a base learner that does not use all the dataset. We provide experimental evidence that our method is as accurate as the equivalent algorithm that uses all the dataset but much faster.

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