The risks of mixing dependency lengths from sequences of different length

Mixing dependency lengths from sequences of different length is a common practice in language research. However, the empirical distribution of dependency lengths of sentences of the same length differs from that of sentences of varying length and the distribution of dependency lengths depends on sentence length for real sentences and also under the null hypothesis that dependencies connect vertices located in random positions of the sequence. This suggests that certain results, such as the distribution of syntactic dependency lengths mixing dependencies from sentences of varying length, could be a mere consequence of that mixing. Furthermore, differences in the global averages of dependency length (mixing lengths from sentences of varying length) for two different languages do not simply imply a priori that one language optimizes dependency lengths better than the other because those differences could be due to differences in the distribution of sentence lengths and other factors.Comment: Laguage and referencing has been improved; Eqs. 7, 11, B7 and B8 have been correcte

Large-scale Heteroscedastic Regression via Gaussian Process

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates the latent function and the noise function together in a unified non-parametric Bayesian framework. Though showing remarkable performance, HGP suffers from the cubic time complexity, which strictly limits its application to big data. To improve the scalability, we first develop a variational sparse inference algorithm, named VSHGP, to handle large-scale datasets. Furthermore, two variants are developed to improve the scalability and capability of VSHGP. The first is stochastic VSHGP (SVSHGP) which derives a factorized evidence lower bound, thus enhancing efficient stochastic variational inference. The second is distributed VSHGP (DVSHGP) which (i) follows the Bayesian committee machine formalism to distribute computations over multiple local VSHGP experts with many inducing points; and (ii) adopts hybrid parameters for experts to guard against over-fitting and capture local variety. The superiority of DVSHGP and SVSHGP as compared to existing scalable heteroscedastic/homoscedastic GPs is then extensively verified on various datasets.Comment: 14 pages, 15 figure

There is No Mystery in Social System

There is a gap between the properties of social reality and the natural properties of the material bearer that carries it. Language constructivism uses language representations to bridge this gap, arguing that language constructs social reality. Emergence theory holds that the attributes of social reality cannot be reduced to the physical attributes of the carrier. This process is emergent. Language constructivism regards the process from mental reality to social reality as the product of language's own operation and the secret is hidden in language itself. Emergentism directly led social reality to mysticism. Mental reality is an initial existence, which includes both innate desires and needs and acquired values. Social reality is the external reality created by the subject through action according to his internal needs and desires. Mental reality and social reality are dynamically integrated into each other, which is achieved through rule-based action