scholarly journals Extended Graphical Lasso for Multiple Interaction Networks for High Dimensional Compositional Data

2021 ◽  
Author(s):  
Yang Xu ◽  
Hongmei Jiang ◽  
Wenxin Jiang
Keyword(s):  
Compositional Data ◽  
Underlying Mechanism ◽  
Interaction Networks ◽  
High Dimensional ◽  
Data Simulation ◽  
Real World Data ◽  
Graphical Lasso ◽  
Alternating Direction ◽  
Multiple Association ◽  
Multiple Interaction

AbstractCompositional data are quantitative descriptions of the parts of some whole, conveying relative information, which are ubiquitous in many fields. There has been a spate of interest in association networks for such data in biological and medical research, for example, microbial interaction networks. In this paper, we propose a novel method, the extended joint hub graphical lasso (EDOHA), to estimate multiple related interaction networks for high dimensional compositional data across multiple distinct classes. To be specific, we construct a convex penalized log likelihood optimization problem using log ratios of compositional data and solve it with an alternating direction method of multipliers (ADMM) algorithm. The performance of the proposed method in the simulated studies shows that EDOHA has remarkable advantages in recognizing class-specific hubs than the existing comparable methods. We also present three applications of real datasets. Biological interpretations of our results confirm those of previous studies and offer a more comprehensive understanding of the underlying mechanism in disease.Author summaryReconstruction of multiple association networks from high dimensional compositional data is an important topic, especially in biology. Previous studies focused on estimating different networks and detecting common hubs among all classes. Integration of information over different classes of data while allowing difference in the hub nodes is also biologically plausible. Therefore, we propose a method, EDOHA, to jointly construct multiple interaction networks with capacity in finding different hub networks for each class of data. Simulation studies show the better performance over conventional methods. The method has been demonstrated in three real world data.

Fast Algorithms for LS and LAD-Collaborative Regression

2021 ◽  
Author(s):  
Jun Sun ◽  
Lingchen Kong ◽  
Mei Li
Keyword(s):  
Numerical Experiments ◽  
Modern Science ◽  
Alternating Direction Method ◽  
Least Square ◽  
High Dimensional ◽  
Statistical Interpretation ◽  
Absolute Deviation ◽  
Linear Rate ◽  
Alternating Direction ◽  
High Dimensional Datasets

With the development of modern science and technology, it is easy to obtain a large number of high-dimensional datasets, which are related but different. Classical unimodel analysis is less likely to capture potential links between the different datasets. Recently, a collaborative regression model based on least square (LS) method for this problem has been proposed. In this paper, we propose a robust collaborative regression based on the least absolute deviation (LAD). We give the statistical interpretation of the LS-collaborative regression and LAD-collaborative regression. Then we design an efficient symmetric Gauss–Seidel-based alternating direction method of multipliers algorithm to solve the two models, which has the global convergence and the Q-linear rate of convergence. Finally we report numerical experiments to illustrate the efficiency of the proposed methods.

scholarly journals Integrating Multiple Interaction Networks for Gene Function Inference

Molecules ◽  
2018 ◽  
Vol 24 (1) ◽  
pp. 30 ◽  
Author(s):  
Jingpu Zhang ◽  
Lei Deng
Keyword(s):  
State Of The Art ◽  
Interaction Networks ◽  
Dimensional Representation ◽  
Functional Interaction ◽  
High Throughput Data ◽  
Multiple Networks ◽  
The Past ◽  
Proteomic Data ◽  
Multiple Interaction ◽  
Low Dimensional

In the past few decades, the number and variety of genomic and proteomic data available have increased dramatically. Molecular or functional interaction networks are usually constructed according to high-throughput data and the topological structure of these interaction networks provide a wealth of information for inferring the function of genes or proteins. It is a widely used way to mine functional information of genes or proteins by analyzing the association networks. However, it remains still an urgent but unresolved challenge how to combine multiple heterogeneous networks to achieve more accurate predictions. In this paper, we present a method named ReprsentConcat to improve function inference by integrating multiple interaction networks. The low-dimensional representation of each node in each network is extracted, then these representations from multiple networks are concatenated and fed to gcForest, which augment feature vectors by cascading and automatically determines the number of cascade levels. We experimentally compare ReprsentConcat with a state-of-the-art method, showing that it achieves competitive results on the datasets of yeast and human. Moreover, it is robust to the hyperparameters including the number of dimensions.

scholarly journals High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis

Biometrika ◽  
2021 ◽  
Author(s):  
Pixu Shi ◽  
Yuchen Zhou ◽  
Anru R Zhang
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
Estimation Error ◽  
Real Data ◽  
Upper And Lower Bounds ◽  
High Dimensional ◽  
Compositional Data Analysis ◽  
Sequencing Data ◽  
Contrast Model ◽  
Critical Issues

Abstract In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the classic log-contrast model is often used where read counts are normalized into compositions. However, zero read counts and the randomness in covariates remain critical issues. In this article, we introduce a surprisingly simple, interpretable, and efficient method for the estimation of compositional data regression through the lens of a novel high-dimensional log-error-in-variable regression model. The proposed method provides both corrections on sequencing data with possible overdispersion and simultaneously avoids any subjective imputation of zero read counts. We provide theoretical justifications with matching upper and lower bounds for the estimation error. The merit of the procedure is illustrated through real data analysis and simulation studies.

scholarly journals Learning Discriminative Correlation Subspace for Heterogeneous Domain Adaptation

2017 ◽  
Author(s):  
Yuguang Yan ◽  
Wen Li ◽  
Michael Ng ◽  
Mingkui Tan ◽  
Hanrui Wu ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Domain Adaptation ◽  
Data Sets ◽  
Target Domain ◽  
Real World Data ◽  
Discriminative Ability ◽  
Convex Optimization Problem ◽  
Alternating Direction ◽  
Feature Spaces ◽  
Target Data

Domain adaptation aims to reduce the effort on collecting and annotating target data by leveraging knowledge from a different source domain. The domain adaptation problem will become extremely challenging when the feature spaces of the source and target domains are different, which is also known as the heterogeneous domain adaptation (HDA) problem. In this paper, we propose a novel HDA method to find the optimal discriminative correlation subspace for the source and target data. The discriminative correlation subspace is inherited from the canonical correlation subspace between the source and target data, and is further optimized to maximize the discriminative ability for the target domain classifier. We formulate a joint objective in order to simultaneously learn the discriminative correlation subspace and the target domain classifier. We then apply an alternating direction method of multiplier (ADMM) algorithm to address the resulting non-convex optimization problem. Comprehensive experiments on two real-world data sets demonstrate the effectiveness of the proposed method compared to the state-of-the-art methods.

scholarly journals Data segmentation based on the local intrinsic dimension

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Michele Allegra ◽  
Elena Facco ◽  
Francesco Denti ◽  
Alessandro Laio ◽  
Antonietta Mira
Keyword(s):  
High Dimensional Data ◽  
Large Data ◽  
Large Data Sets ◽  
High Dimensional ◽  
Data Sets ◽  
Imaging Data ◽  
Unsupervised Segmentation ◽  
Real World Data ◽  
Data Set ◽  
Intrinsic Dimension

Abstract One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data. Contrary to common intuition, there are cases where the ID varies within the same data set. This fact has been highlighted in technical discussions, but seldom exploited to analyze large data sets and obtain insight into their structure. Here we develop a robust approach to discriminate regions with different local IDs and segment the points accordingly. Our approach is computationally efficient and can be proficiently used even on large data sets. We find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded versus unfolded configurations in a protein molecular dynamics trajectory, active versus non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. A simple topological feature, the local ID, is thus sufficient to achieve an unsupervised segmentation of high-dimensional data, complementary to the one given by clustering algorithms.

scholarly journals Two-sample tests of high-dimensional means for compositional data

Biometrika ◽  
2017 ◽  
Vol 105 (1) ◽  
pp. 115-132 ◽  
Author(s):  
Yuanpei Cao ◽  
Wei Lin ◽  
Hongzhe Li
Keyword(s):  
Compositional Data ◽  
High Dimensional

scholarly journals Efficient Proximal Gradient Algorithms for Joint Graphical Lasso

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1623
Author(s):  
Jie Chen ◽  
Ryosuke Shimmura ◽  
Joe Suzuki
Keyword(s):  
Graphical Model ◽  
State Of The Art ◽  
High Accuracy ◽  
Alternating Direction Method ◽  
Main Approach ◽  
First Order ◽  
Gradient Algorithms ◽  
Graphical Lasso ◽  
Alternating Direction ◽  
Accuracy And Precision

We consider learning as an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order methods and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterates in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.

scholarly journals Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation

2021 ◽  
Vol 12 ◽  
Author(s):  
Michael Greenacre ◽  
Marina Martínez-Álvaro ◽  
Agustín Blasco
Keyword(s):  
Data Analysis ◽  
Compositional Data ◽  
High Dimensional ◽  
Compositional Data Analysis ◽  
Rna Transcripts ◽  
Operational Taxonomic Units ◽  
Logratio Transformation ◽  
Large Numbers ◽  
Fixed Reference ◽  
Reference Component

Microbiome and omics datasets are, by their intrinsic biological nature, of high dimensionality, characterized by counts of large numbers of components (microbial genes, operational taxonomic units, RNA transcripts, etc.). These data are generally regarded as compositional since the total number of counts identified within a sample is irrelevant. The central concept in compositional data analysis is the logratio transformation, the simplest being the additive logratios with respect to a fixed reference component. A full set of additive logratios is not isometric, that is they do not reproduce the geometry of all pairwise logratios exactly, but their lack of isometry can be measured by the Procrustes correlation. The reference component can be chosen to maximize the Procrustes correlation between the additive logratio geometry and the exact logratio geometry, and for high-dimensional data there are many potential references. As a secondary criterion, minimizing the variance of the reference component's log-transformed relative abundance values makes the subsequent interpretation of the logratios even easier. On each of three high-dimensional omics datasets the additive logratio transformation was performed, using references that were identified according to the abovementioned criteria. For each dataset the compositional data structure was successfully reproduced, that is the additive logratios were very close to being isometric. The Procrustes correlations achieved for these datasets were 0.9991, 0.9974, and 0.9902, respectively. We thus demonstrate, for high-dimensional compositional data, that additive logratios can provide a valid choice as transformed variables, which (a) are subcompositionally coherent, (b) explain 100% of the total logratio variance and (c) come measurably very close to being isometric. The interpretation of additive logratios is much simpler than the complex isometric alternatives and, when the variance of the log-transformed reference is very low, it is even simpler since each additive logratio can be identified with a corresponding compositional component.

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