A self-consistent probabilistic formulation for inference of interactions

Large molecular interaction networks are nowadays assembled in biomedical researches along with important technological advances. Diverse interaction measures, for which input solely consisting of the incidence of causal-factors, with the corresponding outcome of an inquired effect, are formulated without an obvious mathematical unity. Consequently, conceptual and practical ambivalences arise. We identify here a probabilistic requirement consistent with that input, and find, by the rules of probability theory, that it leads to a model multiplicative in the complement of the effect. Important practical properties are revealed along these theoretical derivations, that has not been noticed before.

HAS-QA: Hierarchical Answer Spans Model for Open-Domain Question Answering

This paper is concerned with open-domain question answering (i.e., OpenQA). Recently, some works have viewed this problem as a reading comprehension (RC) task, and directly applied successful RC models to it. However, the performances of such models are not so good as that in the RC task. In our opinion, the perspective of RC ignores three characteristics in OpenQA task: 1) many paragraphs without the answer span are included in the data collection; 2) multiple answer spans may exist within one given paragraph; 3) the end position of an answer span is dependent with the start position. In this paper, we first propose a new probabilistic formulation of OpenQA, based on a three-level hierarchical structure, i.e., the question level, the paragraph level and the answer span level. Then a Hierarchical Answer Spans Model (HASQA) is designed to capture each probability. HAS-QA has the ability to tackle the above three problems, and experiments on public OpenQA datasets show that it significantly outperforms traditional RC baselines and recent OpenQA baselines.

Variance estimates and almost Euclidean structure

We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on ℝn, which provide sharp distributional inequalities. In the Gaussian context this investigation sheds light to the importance of the statistical measures of dispersion of the norm in connection with the local structure of the ambient space. As a byproduct of our study, we provide a short proof of Dvoretzky’s theorem which not only supports the aforementioned significance but also complements the classical probabilistic formulation.