arXiv subjects

Andreas Alfons

Publications and source records attributed to Andreas Alfons.

10 recordsLinked to original sources

arXiv2024

Towards Reliable Recommender Systems for Rating Data

Recommender systems are widely used in the digital landscape to match users with content fitting their preferences. However, growing concerns about fake accounts, strategic manipulation, and other deceptive online behavior place increasing pressure on the reliability of these systems. A common statistical approach behind recommender systems is so-called matrix completion, which predicts how users would rate items they have not yet consumed based on patterns in observed ratings. Realistically applying matrix completion methods requires jointly addressing several overlooked challenges: (i) ratings on discrete scales (such as 1--5 stars); (ii) the presence of malicious users who deliberately manipulate the system to their advantage through fake profiles; (iii) ratings missing not at random since users are more likely to consume items they expect to like; and (iv) fostering transparency, reproducibility, and stability. We jointly address these challenges by proposing a novel method, Robust Discrete Matrix Completion (RDMC), designed to capture the key characteristics of sparse rating data while remaining reliable in the presence of manipulation. We evaluate RDMC through two case studies and carefully designed simulation experiments. Our work thereby offers a statistically-sound blueprint for future studies on how to evaluate recommender systems under realistic scenarios.

stat.ML↗

arXiv2024

Robust Estimation of Polychoric Correlation

Polychoric correlation is often an important building block in the analysis of rating data, particularly for structural equation models. However, the commonly employed maximum likelihood (ML) estimator is highly susceptible to misspecification of the polychoric correlation model, for instance through violations of latent normality assumptions. We propose a novel estimator that is designed to be robust against partial misspecification of the polychoric model, that is, when the model is misspecified for an unknown fraction of observations, such as careless respondents. To this end, the estimator minimizes a robust loss function based on the divergence between observed frequencies and theoretical frequencies implied by the polychoric model. In contrast to existing literature, our estimator makes no assumption on the type or degree of model misspecification. It furthermore generalizes ML estimation, is consistent as well as asymptotically normally distributed, and comes at no additional computational cost. We demonstrate the robustness and practical usefulness of our estimator in simulation studies and an empirical application on a Big Five administration. In the latter, the polychoric correlation estimates of our estimator and ML differ substantially, which, after further inspection, is likely due to the presence of careless respondents that the estimator helps identify.

stat.ME↗

arXiv2024

Tandem clustering with invariant coordinate selection

For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized for focusing solely on inertia so that the first components do not necessarily retain the structure of interest for clustering. To address this limitation, a new tandem clustering approach based on invariant coordinate selection (ICS) is proposed. By jointly diagonalizing two scatter matrices, ICS is designed to find structure in the data while providing affine invariant components. Certain theoretical results have been previously derived and guarantee that under some elliptical mixture models, the group structure can be highlighted on a subset of the first and/or last components. However, ICS has garnered minimal attention within the context of clustering. Two challenges associated with ICS include choosing the pair of scatter matrices and selecting the components to retain. For effective clustering purposes, it is demonstrated that the best scatter pairs consist of one scatter matrix capturing the within-cluster structure and another capturing the global structure. For the former, local shape or pairwise scatters are of great interest, as is the minimum covariance determinant (MCD) estimator based on a carefully chosen subset size that is smaller than usual. The performance of ICS as a dimension reduction method is evaluated in terms of preserving the cluster structure in the data. In an extensive simulation study and empirical applications with benchmark data sets, various combinations of scatter matrices as well as component selection criteria are compared in situations with and without outliers. Overall, the new approach of tandem clustering with ICS shows promising results and clearly outperforms the PCA-based approach.

stat.ME↗

arXiv2023

Efficient Computation of Sparse and Robust Maximum Association Estimators

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association estimators without imposing constraints on the covariance structure. The approach splits the problem into a robust estimation phase, followed by optimization of a decoupled, biconvex problem to derive the sparse canonical vectors. An augmented Lagrangian algorithm, combined with a modified adaptive gradient descent method, induces sparsity through simultaneous updates of both canonical vectors. Results demonstrate improved precision over existing methods, with high-dimensional empirical examples illustrating the effectiveness of this approach. The methodology can also be extended to other robust sparse estimators.

stat.CO↗

arXiv2023

When Respondents Don't Care Anymore: Identifying the Onset of Careless Responding

Questionnaires in the behavioral sciences tend to be lengthy. However, literature suggests that survey length is a contributing factor to careless responding, with longer questionnaires yielding higher probability that participants start responding carelessly. Consequently, in long surveys a large number of participants may engage in careless responding, posing a major threat to internal validity. We propose a novel method for identifying the onset of careless responding (or an absence thereof) that searches for a changepoint in combined measurements of multiple dimensions in which carelessness may manifest, such as inconsistency and invariability. It is highly flexible, based on machine learning, and provides statistical guarantees for controlling the false positive rate. In simulation experiments, the proposed method achieves high accuracy in identifying carelessness onset and discriminates well between attentive and various types of careless responding, even when a large number of careless respondents are present. An empirical application highlights how identifying partial carelessness uncovers novel insights on careless responding behavior. Furthermore, we provide the freely available open source software package "carelessonset" to facilitate adoption by empirical researchers.

stat.ME↗

arXiv2022

Robust Mediation Analysis: The R Package robmed

Mediation analysis is one of the most widely used statistical techniques in the social, behavioral, and medical sciences. Mediation models allow to study how an independent variable affects a dependent variable indirectly through one or more intervening variables, which are called mediators. The analysis is often carried out via a series of linear regressions, in which case the indirect effects can be computed as products of coefficients from those regressions. Statistical significance of the indirect effects is typically assessed via a bootstrap test based on ordinary least-squares estimates. However, this test is sensitive to outliers or other deviations from normality assumptions, which poses a serious threat to empirical testing of theory about mediation mechanisms. The R package robmed implements a robust procedure for mediation analysis based on the fast-and-robust bootstrap methodology for robust regression estimators, which yields reliable results even when the data deviate from the usual normality assumptions. Various other procedures for mediation analysis are included in package robmed as well. Moreover, robmed introduces a new formula interface that allows to specify mediation models with a single formula, and provides various plots for diagnostics or visual representation of the results.

stat.CO↗

arXiv2017

SparseStep: Approximating the Counting Norm for Sparse Regularization

The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and iteratively strengthening this approximation to arrive at a sparse solution. Theoretical analysis of the penalty function shows that the estimator yields unbiased estimates of the parameter vector. An iterative majorization algorithm is derived which has a straightforward implementation reminiscent of ridge regression. In addition, the SparseStep algorithm is compared with similar methods through a rigorous simulation study which shows it often outperforms existing methods in both model fit and prediction accuracy.

stat.ME↗

arXiv2015

The shooting S-estimator for robust regression

To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as S-estimation have been proposed. These estimators flag any observation with a large residual as an outlier and downweight it in the further procedure. However, a large residual may be caused by an outlier in only one single predictor variable, and downweighting the complete observation results in a loss of information. Therefore, we propose the shooting S-estimator, a regression estimator that is especially designed for situations where a large number of observations suffer from contamination in a small number of predictor variables. The shooting S-estimator combines the ideas of the coordinate descent algorithm with simple S-regression, which makes it robust against componentwise contamination, at the cost of failing the regression equivariance property.

stat.ME↗

arXiv2015

The Influence Function of Penalized Regression Estimators

To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse least trimmed squares (LTS) estimator have been proposed. The robustness of these regression methods can be measured with the influence function. It quantifies the effect of infinitesimal perturbations in the data. Furthermore it can be used to compute the asymptotic variance and the mean squared error. In this paper we compute the influence function, the asymptotic variance and the mean squared error for penalized M-estimators and the sparse LTS estimator. The asymptotic biasedness of the estimators make the calculations nonstandard. We show that only M-estimators with a loss function with a bounded derivative are robust against regression outliers. In particular, the lasso has an unbounded influence function.

math.ST↗

arXiv2013

Sparse least trimmed squares regression for analyzing high-dimensional large data sets

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the data. This paper combines robust regression and sparse model estimation. A robust and sparse estimator is introduced by adding an $L_1$ penalty on the coefficient estimates to the well-known least trimmed squares (LTS) estimator. The breakdown point of this sparse LTS estimator is derived, and a fast algorithm for its computation is proposed. In addition, the sparse LTS is applied to protein and gene expression data of the NCI-60 cancer cell panel. Both a simulation study and the real data application show that the sparse LTS has better prediction performance than its competitors in the presence of leverage points.

stat.AP↗