Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms.

Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem in a decision-theoretic framework and demonstrate that a constrained least squares estimator achieves the optimal rate. However, due to its computational complexity, we analyze a popular polynomial-time algorithm, spectral seriation, and show that it is suboptimal. To address this, we propose a novel polynomial-time adaptive sorting algorithm with guaranteed performance improvement. Simulations and analyses of two real single-cell RNA sequencing datasets demonstrate the superiority of our algorithm over existing methods.

Intramedullary nail fixation of fibular fractures in combination with extra-articular distal tibial fractures (AO/OTA 43A): a single-center retrospective study.

Treatment of fibular fractures associated with extra-articular distal tibia fractures is technically challenging and the purpose of this study was to evaluate the use of intramedullary nail fixation of fibular fractures when associated with this fracture. Between January 2018 and December 2021, 33 patients presenting extra-articular distal tibia fractures and fibular fractures (AO/OTA 43A) were treated. Clinical and radiological data were collected during routine postoperative follow-ups. Thirty-one patients were monitored for a period of time ranging from 12 to 23 months, with an average follow-up of 17.5 ± 3.3 months. Fibular bone union took an average of 3.6 ± 0.9 months. At the last follow-up, the average fibular alignment and postoperative ankle talocrural angles were 1.8° and 9.1°, respectively. No detectable radiographic rotational malalignment and serious complications related to the fibular incision was observed. The average AOFAS and OMAS scores at the most recent follow-up were 88.3 ± 6.2 and 87.4 ± 6.0, respectively. Intramedullary nail fixation worked well to keep the fibula in place in fibular fractures connected to extra-articular distal tibia fractures.

Estimation and Inference for High-Dimensional Generalized Linear Models with Knowledge Transfer.

Transfer learning provides a powerful tool for incorporating data from related studies into a target study of interest. In epidemiology and medical studies, the classification of a target disease could borrow information across other related diseases and populations. In this work, we consider transfer learning for high-dimensional generalized linear models (GLMs). A novel algorithm, TransHDGLM, that integrates data from the target study and the source studies is proposed. Minimax rate of convergence for estimation is established and the proposed estimator is shown to be rate-optimal. Statistical inference for the target regression coefficients is also studied. Asymptotic normality for a debiased estimator is established, which can be used for constructing coordinate-wise confidence intervals of the regression coefficients. Numerical studies show significant improvement in estimation and inference accuracy over GLMs that only use the target data. The proposed methods are applied to a real data study concerning the classification of colorectal cancer using gut microbiomes, and are shown to enhance the classification accuracy in comparison to methods that only use the target data.

Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control.

Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied. The target GGM is estimated by incorporating the data from similar and related auxiliary studies, where the similarity between the target graph and each auxiliary graph is characterized by the sparsity of a divergence matrix. An estimation algorithm, Trans-CLIME, is proposed and shown to attain a faster convergence rate than the minimax rate in the single-task setting. Furthermore, we introduce a universal debiasing method that can be coupled with a range of initial graph estimators and can be analytically computed in one step. A debiased Trans-CLIME estimator is then constructed and is shown to be element-wise asymptotically normal. This fact is used to construct a multiple testing procedure for edge detection with false discovery rate control. The proposed estimation and multiple testing procedures demonstrate superior numerical performance in simulations and are applied to infer the gene networks in a target brain tissue by leveraging the gene expressions from multiple other brain tissues. A significant decrease in prediction errors and a significant increase in power for link detection are observed.

Optimal Estimation of Genetic Relatedness in High-dimensional Linear Models.

Estimating the genetic relatedness between two traits based on the genome-wide association data is an important problem in genetics research. In the framework of high-dimensional linear models, we introduce two measures of genetic relatedness and develop optimal estimators for them. One is genetic covariance, which is defined to be the inner product of the two regression vectors, and another is genetic correlation, which is a normalized inner product by their lengths. We propose functional de-biased estimators (FDEs), which consist of an initial estimation step with the plug-in scaled Lasso estimator, and a further bias correction step. We also develop estimators of the quadratic functionals of the regression vectors, which can be used to estimate the heritability of each trait. The estimators are shown to be minimax rate-optimal and can be efficiently implemented. Simulation results show that FDEs provide better estimates of the genetic relatedness than simple plug-in estimates. FDE is also applied to an analysis of a yeast segregant data set with multiple traits to estimate the genetic relatedness among these traits.