Robust logistic zero-sum regression for microbiome compositional data

Monti, Gianna Serafina; Filzmoser, Peter

doi:10.1007/s11634-021-00465-4

Cited by 8 publications

(8 citation statements)

References 30 publications

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“…It has already been used in several benchmark studies in the statistical literature, e.g. (Insolia et al, 2021(Insolia et al, , 2022Monti & Filzmoser, 2021), as well as in empirical research, e.g. (Jensch et al, 2022;Segaert et al, 2018).…”

Section: Statement Of Needmentioning

confidence: 99%

enetLTS: Robust and Sparse Methods for High Dimensional Linear, Binary, and Multinomial Regression

Kurnaz¹,

Filzmoser²

2023

JOSS

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enetLTS is an R package (R-Development-Core-Team, 2021) that provides a fully robust version of the elastic net estimator for high dimensional linear, binary, and multinomial regression. The elastic net penalization provides intrinsic variable selection and coefficient estimates for highly correlated variables, in particular for high dimensional low sample size data sets, and it has been extended to generalized linear regression models (Friedman et al., 2010). Combining these advantages with trimming outliers yields the robust solutions. The main idea of the algorithm is to search for outlier-free subsets on which the classical elastic net estimator can be applied. Outlier-free subsets are determined by trimming the penalized log-likelihood function for the considered regression model. The algorithm starts with 500 elemental subsets only for one combination of the elastic net parameters 𝛼 and 𝜆, and takes the warm start strategy for subsequent combinations in order to save the computation time. The final reweighting step is added to improve the statistical efficiency of the proposed estimators. From this point of view, the enet-LTS estimator can be seen as a trimmed version of the elastic net regression estimator for linear, binary, and multinomial regression (Friedman et al., 2010). Selecting model with the optimal tuning parameters is done via cross-validation, and various plots are available to illustrate model selection and to evaluate the final model estimates.

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Section: Statement Of Needmentioning

confidence: 99%

enetLTS: Robust and Sparse Methods for High Dimensional Linear, Binary, and Multinomial Regression

Kurnaz¹,

Filzmoser²

2023

JOSS

Self Cite

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“…22,23 Log-contrast models have been recently used for regression or classification analysis with high-dimensional compositional covariates. 3,8,10 The general form of these models is given by…”

Section: Compositional Data and Pls Principal Balancesmentioning

confidence: 99%

“…Note that, by taking Equation (3) into account, the regression model in Equation (1) could have been developed directly in clr coefficients (this will be done separately later). The reason is methodological: while in Equation (1) the zero-sum constraint must be imposed, 3 by using clr coefficients in the first instance, it is automatically incorporated before proceeding with standard estimation. In fact, clr coefficients always add up to zero by definition, given the geometric mean placed in the denominator, and any LS-based estimator of a linear model (including PLS regression) preserves this constraint.…”

Section: Log-ratio Representations Of Compositional Datamentioning

confidence: 99%

“…Log‐contrast models have been recently used for regression or classification analysis with high‐dimensional compositional covariates 3,8,10 . The general form of these models is given by

boldy = \ln false(boldX false) \cdot bold-italicβ + bold-italicε,

where

boldy = {false(y_{1}, \dots, y_{n} false)}^{⊤}

is a univariate response variable,

boldX = {false(x_{i j} false)}_{1 \leq i \leq n, 1 \leq j \leq D}

is the matrix of observed compositional predictors (with

\ln false(boldX false)

denoting the elementwise logarithm of

boldX

bold-italicβ

represents the regression coefficients with

\sum_{j = 1}^{D} β_{j} = 0

, and

bold-italicε

stands for the ordinary random error term.…”

Section: Compositional Data and Pls Principal Balancesmentioning

confidence: 99%

“…Compositional data (CoDa) occur in plenty of research fields, such as geochemistry, 1 metabolomics, 2 microbiome data, 3 time use data, 4 or ecology 5 . Let us consider a regression (or classification) task where

boldy = {false(y_{1}, \dots, y_{n} false)}^{⊤}

is a vector of

n

observations of a continuous (or binary) response variable and

boldX = {false(x_{i j} false)}_{1 \leq i \leq n, 1 \leq j \leq D}

is an associated matrix of a

D

‐part compositional predictor.…”

Section: Introductionmentioning

confidence: 99%

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Principal balances of compositional data for regression and classification using partial least squares

Nesrstová,

Wilms,

Palarea‐Albaladejo

et al. 2023

Journal of Chemometrics

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High‐dimensional compositional data are commonplace in the modern omics sciences, among others. Analysis of compositional data requires the proper choice of a log‐ratio coordinate representation, since their relative nature is not compatible with the direct use of standard statistical methods. Principal balances, a particular class of orthonormal log‐ratio coordinates, are well suited to this context as they are constructed so that the first few coordinates capture most of the compositional variability of data set. Focusing on regression and classification problems in high dimensions, we propose a novel partial least squares (PLS) procedure to construct principal balances that maximize the explained variability of the response variable and notably ease interpretability when compared to the ordinary PLS formulation. The proposed PLS principal balance approach can be understood as a generalized version of common log‐contrast models since, instead of just one, multiple orthonormal log‐contrasts are estimated simultaneously. We demonstrate the performance of the proposed method using both simulated and empirical data sets.

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Robust instance-dependent cost-sensitive classification

Vos

Vanderschueren

Verdonck

et al. 2023

Adv Data Anal Classif

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Instance-dependent cost-sensitive (IDCS) learning methods have proven useful for binary classification tasks where individual instances are associated with variable misclassification costs. However, we demonstrate in this paper by means of a series of experiments that IDCS methods are sensitive to noise and outliers in relation to instance-dependent misclassification costs, and their performance strongly depends on the cost distribution of the data sample. Therefore, we propose a generic three-step framework to make IDCS methods more robust: (i) detect outliers automatically, (ii) correct outlying cost information in a data-driven way, and (iii) construct an IDCS learning method using the adjusted cost information. We apply this framework to cslogit, a logistic regression-based IDCS method, to obtain its robust version, which we name r-cslogit. The robustness of this approach is introduced in steps (i) and (ii), where we make use of robust estimators to detect and impute outlying costs of individual instances. The newly proposed r-cslogit method is tested on synthetic and semi-synthetic data and proven to be superior in terms of savings compared to its nonrobust counterpart for variable levels of noise and outliers. All our code is made available online at https://github.com/SimonDeVos/Robust-IDCS.

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Robust logistic zero-sum regression for microbiome compositional data

Cited by 8 publications

References 30 publications

enetLTS: Robust and Sparse Methods for High Dimensional Linear, Binary, and Multinomial Regression

enetLTS: Robust and Sparse Methods for High Dimensional Linear, Binary, and Multinomial Regression

Principal balances of compositional data for regression and classification using partial least squares

Robust instance-dependent cost-sensitive classification

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