Cross-validation of matching correlation analysis by resampling matching weights

Hyperlink regression via Bregman divergence

A collection of U(∈N) data vectors is called a U-tuple, and the association strength among the vectors of a tuple is termed as the hyperlink weight, that is assumed to be symmetric with respect to permutation of the entries in the index. We herein propose Bregman hyperlink regression (BHLR), which learns a user-specified symmetric similarity function such that it predicts the tuple's hyperlink weight from data vectors stored in the U-tuple. BHLR is a simple and general framework for hyper-relational learning, that minimizes Bregman-divergence (BD) between the hyperlink weights and estimated similarities defined for the corresponding tuples; BHLR encompasses various existing methods, such as logistic regression (U=1), Poisson regression (U=1), link prediction (U=2), and those for representation learning, such as graph embedding (U=2), matrix factorization (U=2), tensor factorization (U≥2), and their variants equipped with arbitrary BD. Nonlinear functions (e.g., neural networks), can be employed for the similarity functions. However, there are theoretical challenges such that some of different tuples of BHLR may share data vectors therein, unlike the i.i.d. setting of classical regression. We address these theoretical issues, and proved that BHLR equipped with arbitrary BD and U∈N is (P-1) statistically consistent, that is, it asymptotically recovers the underlying true conditional expectation of hyperlink weights given data vectors, and (P-2) computationally tractable, that is, it is efficiently computed by stochastic optimization algorithms using a novel generalized minibatch sampling procedure for hyper-relational data. Consequently, theoretical guarantees for BHLR including several existing methods, that have been examined experimentally, are provided in a unified manner.

Seasonal Changes of Serum Gonadotropins and Testosterone in Men Revealed by a Large Data Set of Real-World Observations Over Nine Years

Environmental rhythmicity is able to affect the hypothalamic-pituitary-gonadal axis in several animals to achieve reproductive advantages. However, conflicting results were obtained when assessing the environmental-dependent rhythmicity on reproductive hormone secretion in humans. This study was designed to evaluate seasonal fluctuations of the main hormones involved in the hypothalamic-pituitary-gonadal axis in men, using a big data approach. An observational, retrospective, big data trial was carried out, including all testosterone, luteinizing hormone (LH) and follicle-stimulating hormone (FSH) measurements performed in a single laboratory between January 2010 and January 2019 using Chemiluminescent Microparticle Immunoassay. Subjects presenting any factor interfering with the hypothalamic-pituitary-gonadal axis were excluded. The trend and seasonal distributions were analyzed using autoregressive integrated moving average (ARIMA) models. A total of 12,033 data, accounting for 7,491 men (mean age 47.46 ± 13.51 years, range 18-91 years) were included. Testosterone serum levels (mean 5.34 ± 2.06 ng/dL, range 1.70-15.80 ng/dL) showed a seasonal distribution with higher levels in summer and a direct correlation to environmental temperatures and daylight duration. LH levels (mean 4.64 ± 2.54 IU/L, range 1.00-15.00 IU/L) presented 2 peaks of secretion in autumn and spring, independently from environmental parameters. FSH levels (mean 5.51 ± 3.24 IU/L) did not show any seasonal distribution. A clear seasonal fluctuation of both LH and testosterone was demonstrated in a large cohort of adult men, although a circannual seasonality of hypothalamic-pituitary-gonadal hormones in humans could be not strictly evolutionarily required. Testosterone seasonality seems independent from LH fluctuations, which could be regulated by cyclic central genes expression, and more sensible to environmental temperatures and daylight duration.