arXiv subjects

Markus Pauly

Publications and source records attributed to Markus Pauly.

At least 37 records · Page 2Linked to original sources

arXiv2024

Which Imputation Fits Which Feature Selection Method? A Survey-Based Simulation Study

Tree-based learning methods such as Random Forest and XGBoost are still the gold-standard prediction methods for tabular data. Feature importance measures are usually considered for feature selection as well as to assess the effect of features on the outcome variables in the model. This also applies to survey data, which are frequently encountered in the social sciences and official statistics. These types of datasets often present the challenge of missing values. The typical solution is to impute the missing data before applying the learning method. However, given the large number of possible imputation methods available, the question arises as to which should be chosen to achieve the 'best' reflection of feature importance and feature selection in subsequent analyses. In the present paper, we investigate this question in a survey-based simulation study for eight state-of-the art imputation methods and three learners. The imputation methods comprise listwise deletion, three MICE options, four \texttt{missRanger} options as well as the recently proposed mixGBoost imputation approach. As learners, we consider the two most common tree-based methods, Random Forest and XGBoost, and an interpretable linear model with regularization.

stat.AP↗

arXiv2024

Even naive trees are consistent

The last decade has shed some light on theoretical properties such as their consistency for regression tasks. In the current paper, we propose a new class of very simple learners based on so-called naive trees. These naive trees partition the feature space completely at random and independent of the data. Although counter-intuitive, we prove these naive trees and ensembles are consistent under fairly general assumptions. However, naive trees appear to be too simple for actual application. We therefore analyze their finite sample properties in a simulation and small benchmark study. We find a slow convergence speed and a rather poor predictive performance. Based on these results, we finally discuss to what extent consistency proofs help to justify the application of complex learning algorithms.

math.ST↗

arXiv2024

Is GPT-4 Less Politically Biased than GPT-3.5? A Renewed Investigation of ChatGPT's Political Biases

This work investigates the political biases and personality traits of ChatGPT, specifically comparing GPT-3.5 to GPT-4. In addition, the ability of the models to emulate political viewpoints (e.g., liberal or conservative positions) is analyzed. The Political Compass Test and the Big Five Personality Test were employed 100 times for each scenario, providing statistically significant results and an insight into the results correlations. The responses were analyzed by computing averages, standard deviations, and performing significance tests to investigate differences between GPT-3.5 and GPT-4. Correlations were found for traits that have been shown to be interdependent in human studies. Both models showed a progressive and libertarian political bias, with GPT-4's biases being slightly, but negligibly, less pronounced. Specifically, on the Political Compass, GPT-3.5 scored -6.59 on the economic axis and -6.07 on the social axis, whereas GPT-4 scored -5.40 and -4.73. In contrast to GPT-3.5, GPT-4 showed a remarkable capacity to emulate assigned political viewpoints, accurately reflecting the assigned quadrant (libertarian-left, libertarian-right, authoritarian-left, authoritarian-right) in all four tested instances. On the Big Five Personality Test, GPT-3.5 showed highly pronounced Openness and Agreeableness traits (O: 85.9%, A: 84.6%). Such pronounced traits correlate with libertarian views in human studies. While GPT-4 overall exhibited less pronounced Big Five personality traits, it did show a notably higher Neuroticism score. Assigned political orientations influenced Openness, Agreeableness, and Conscientiousness, again reflecting interdependencies observed in human studies. Finally, we observed that test sequencing affected ChatGPT's responses and the observed correlations, indicating a form of contextual memory.

cs.CL↗

arXiv2024

AR-Sieve Bootstrap for the Random Forest and a simulation-based comparison with rangerts time series prediction

The Random Forest (RF) algorithm can be applied to a broad spectrum of problems, including time series prediction. However, neither the classical IID (Independent and Identically distributed) bootstrap nor block bootstrapping strategies (as implemented in rangerts) completely account for the nature of the Data Generating Process (DGP) while resampling the observations. We propose the combination of RF with a residual bootstrapping technique where we replace the IID bootstrap with the AR-Sieve Bootstrap (ARSB), which assumes the DGP to be an autoregressive process. To assess the new model's predictive performance, we conduct a simulation study using synthetic data generated from different types of DGPs. It turns out that ARSB provides more variation amongst the trees in the forest. Moreover, RF with ARSB shows greater accuracy compared to RF with other bootstrap strategies. However, these improvements are achieved at some efficiency costs.

stat.ML↗

arXiv2024

TREE: Tree Regularization for Efficient Execution

The rise of machine learning methods on heavily resource constrained devices requires not only the choice of a suitable model architecture for the target platform, but also the optimization of the chosen model with regard to execution time consumption for inference in order to optimally utilize the available resources. Random forests and decision trees are shown to be a suitable model for such a scenario, since they are not only heavily tunable towards the total model size, but also offer a high potential for optimizing their executions according to the underlying memory architecture. In addition to the straightforward strategy of enforcing shorter paths through decision trees and hence reducing the execution time for inference, hardware-aware implementations can optimize the execution time in an orthogonal manner. One particular hardware-aware optimization is to layout the memory of decision trees in such a way, that higher probably paths are less likely to be evicted from system caches. This works particularly well when splits within tree nodes are uneven and have a high probability to visit one of the child nodes. In this paper, we present a method to reduce path lengths by rewarding uneven probability distributions during the training of decision trees at the cost of a minimal accuracy degradation. Specifically, we regularize the impurity computation of the CART algorithm in order to favor not only low impurity, but also highly asymmetric distributions for the evaluation of split criteria and hence offer a high optimization potential for a memory architecture-aware implementation. We show that especially for binary classification data sets and data sets with many samples, this form of regularization can lead to an reduction of up to approximately four times in the execution time with a minimal accuracy degradation.

cs.LG↗

arXiv2024

Comparing statistical and machine learning methods for time series forecasting in data-driven logistics -- A simulation study

Many planning and decision activities in logistics and supply chain management are based on forecasts of multiple time dependent factors. Therefore, the quality of planning depends on the quality of the forecasts. We compare various forecasting methods in terms of out of the box forecasting performance on a broad set of simulated time series. We simulate various linear and non-linear time series and look at the one step forecast performance of statistical learning methods.

stat.ML↗

arXiv2024

Multiple Comparison Procedures for Simultaneous Inference in Functional MANOVA

Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to compare different groups or to infer factor effects. We propose a new class of testing procedures for arbitrary linear hypotheses in general factorial designs with functional data. Our methods allow global as well as multiple inference of both, univariate and multivariate mean functions without assuming particular error distributions nor homoscedasticity. That is, we allow for different structures of the covariance functions between groups. To this end, we use point-wise quadratic-form-type test functions that take potential heteroscedasticity into account. Taking the supremum over each test function, we define a class of local test statistics. We analyse their (joint) asymptotic behaviour and propose a resampling approach to approximate the limit distributions. The resulting global and multiple testing procedures are asymptotic valid under weak conditions and applicable in general functional MANOVA settings. We evaluate their small-sample performance in extensive simulations and finally illustrate their applicability by analysing a multivariate functional air pollution data set.

stat.ME↗

arXiv2024

How to Simulate Realistic Survival Data? A Simulation Study to Compare Realistic Simulation Models

In statistics, it is important to have realistic data sets available for a particular context to allow an appropriate and objective method comparison. For many use cases, benchmark data sets for method comparison are already available online. However, in most medical applications and especially for clinical trials in oncology, there is a lack of adequate benchmark data sets, as patient data can be sensitive and therefore cannot be published. A potential solution for this are simulation studies. However, it is sometimes not clear, which simulation models are suitable for generating realistic data. A challenge is that potentially unrealistic assumptions have to be made about the distributions. Our approach is to use reconstructed benchmark data sets %can be used as a basis for the simulations, which has the following advantages: the actual properties are known and more realistic data can be simulated. There are several possibilities to simulate realistic data from benchmark data sets. We investigate simulation models based upon kernel density estimation, fitted distributions, case resampling and conditional bootstrapping. In order to make recommendations on which models are best suited for a specific survival setting, we conducted a comparative simulation study. Since it is not possible to provide recommendations for all possible survival settings in a single paper, we focus on providing realistic simulation models for two-armed phase III lung cancer studies. To this end we reconstructed benchmark data sets from recent studies. We used the runtime and different accuracy measures (effect sizes and p-values) as criteria for comparison.

stat.AP↗

arXiv2024

Human Vs. Machines: Who Wins In Semiconductor Market Forecasting?

"If you ask ten experts, you will get ten different opinions." This common proverb illustrates the common association of expert forecasts with personal bias and lack of consistency. On the other hand, digitization promises consistency and explainability through data-driven forecasts employing machine learning (ML) and statistical models. In the following, we compare such forecasts to expert forecasts from the World Semiconductor Trade Statistics (WSTS), a leading semiconductor market data provider.

stat.AP↗

arXiv2024

Behind the Screen: Investigating ChatGPT's Dark Personality Traits and Conspiracy Beliefs

ChatGPT is notorious for its intransparent behavior. This paper tries to shed light on this, providing an in-depth analysis of the dark personality traits and conspiracy beliefs of GPT-3.5 and GPT-4. Different psychological tests and questionnaires were employed, including the Dark Factor Test, the Mach-IV Scale, the Generic Conspiracy Belief Scale, and the Conspiracy Mentality Scale. The responses were analyzed computing average scores, standard deviations, and significance tests to investigate differences between GPT-3.5 and GPT-4. For traits that have shown to be interdependent in human studies, correlations were considered. Additionally, system roles corresponding to groups that have shown distinct answering behavior in the corresponding questionnaires were applied to examine the models' ability to reflect characteristics associated with these roles in their responses. Dark personality traits and conspiracy beliefs were not particularly pronounced in either model with little differences between GPT-3.5 and GPT-4. However, GPT-4 showed a pronounced tendency to believe in information withholding. This is particularly intriguing given that GPT-4 is trained on a significantly larger dataset than GPT-3.5. Apparently, in this case an increased data exposure correlates with a greater belief in the control of information. An assignment of extreme political affiliations increased the belief in conspiracy theories. Test sequencing affected the models' responses and the observed correlations, indicating a form of contextual memory.

cs.CL↗

arXiv2024

Evaluating tree-based imputation methods as an alternative to MICE PMM for drawing inference in empirical studies

Dealing with missing data is an important problem in statistical analysis that is often addressed with imputation procedures. The performance and validity of such methods are of great importance for their application in empirical studies. While the prevailing method of Multiple Imputation by Chained Equations (MICE) with Predictive Mean Matching (PMM) is considered standard in the social science literature, the increase in complex datasets may require more advanced approaches based on machine learning. In particular, tree-based imputation methods have emerged as very competitive approaches. However, the performance and validity are not completely understood, particularly compared to the standard MICE PMM. This is especially true for inference in linear models. In this study, we investigate the impact of various imputation methods on coefficient estimation, Type I error, and power, to gain insights that can help empirical researchers deal with missingness more effectively. We explore MICE PMM alongside different tree-based methods, such as MICE with Random Forest (RF), Chained Random Forests with and without PMM (missRanger), and Extreme Gradient Boosting (MIXGBoost), conducting a realistic simulation study using the German National Educational Panel Study (NEPS) as the original data source. Our results reveal that Random Forest-based imputations, especially MICE RF and missRanger with PMM, consistently perform better in most scenarios. Standard MICE PMM shows partially increased bias and overly conservative test decisions, particularly with non-true zero coefficients. Our results thus underscore the potential advantages of tree-based imputation methods, albeit with a caveat that all methods perform worse with an increased missingness, particularly missRanger.

stat.AP↗

arXiv2023

Testing Hypotheses about Correlation Matrices in General MANOVA Designs

Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation matrix. Examples cover MANOVA-type hypothesis of equal correlation matrices as well as testing for special correlation structures such as, e.g., sphericity. Apart from existing fourth moments, our approach requires no other assumptions, allowing applications in various settings. To improve the small sample performance, a bootstrap technique is proposed and theoretically justified. Based on this, we also present a procedure to simultaneously test the hypotheses of equal correlation and equal covariance matrices. The performance of all new test statistics is compared with existing procedures through extensive simulations.

math.ST↗

arXiv2023

General multiple tests for functional data

While there exists several inferential methods for analyzing functional data in factorial designs, there is a lack of statistical tests that are valid (i) in general designs, (ii) under non-restrictive assumptions on the data generating process and (iii) allow for coherent post-hoc analyses. In particular, most existing methods assume Gaussianity or equal covariance functions across groups (homoscedasticity) and are only applicable for specific study designs that do not allow for evaluation of interactions. Moreover, all available strategies are only designed for testing global hypotheses and do not directly allow a more in-depth analysis of multiple local hypotheses. To address the first two problems (i)-(ii), we propose flexible integral-type test statistics that are applicable in general factorial designs under minimal assumptions on the data generating process. In particular, we neither postulate homoscedasticity nor Gaussianity. To approximate the statistics' null distribution, we adopt a resampling approach and validate it methodologically. Finally, we use our flexible testing framework to (iii) infer several local null hypotheses simultaneously. To allow for powerful data analysis, we thereby take the complex dependencies of the different local test statistics into account. In extensive simulations we confirm that the new methods are flexibly applicable. Two illustrate data analyses complete our study. The new testing procedures are implemented in the R package multiFANOVA, which will be available on CRAN soon.

stat.ME↗

arXiv2023

Incompletely observed nonparametric factorial designs with repeated measurements: A wild bootstrap approach

In many life science experiments or medical studies, subjects are repeatedly observed and measurements are collected in factorial designs with multivariate data. The analysis of such multivariate data is typically based on multivariate analysis of variance (MANOVA) or mixed models, requiring complete data, and certain assumption on the underlying parametric distribution such as continuity or a specific covariance structure, e.g., compound symmetry. However, these methods are usually not applicable when discrete data or even ordered categorical data are present. In such cases, nonparametric rank-based methods that do not require stringent distributional assumptions are the preferred choice. However, in the multivariate case, most rank-based approaches have only been developed for complete observations. It is the aim of this work is to develop asymptotic correct procedures that are capable of handling missing values, allowing for singular covariance matrices and are applicable for ordinal or ordered categorical data. This is achieved by applying a wild bootstrap procedure in combination with quadratic form-type test statistics. Beyond proving their asymptotic correctness, extensive simulation studies validate their applicability for small samples. Finally, two real data examples are analyzed.

stat.ME↗

arXiv2023

The Self-Perception and Political Biases of ChatGPT

This contribution analyzes the self-perception and political biases of OpenAI's Large Language Model ChatGPT. Taking into account the first small-scale reports and studies that have emerged, claiming that ChatGPT is politically biased towards progressive and libertarian points of view, this contribution aims to provide further clarity on this subject. For this purpose, ChatGPT was asked to answer the questions posed by the political compass test as well as similar questionnaires that are specific to the respective politics of the G7 member states. These eight tests were repeated ten times each and revealed that ChatGPT seems to hold a bias towards progressive views. The political compass test revealed a bias towards progressive and libertarian views, with the average coordinates on the political compass being (-6.48, -5.99) (with (0, 0) the center of the compass, i.e., centrism and the axes ranging from -10 to 10), supporting the claims of prior research. The political questionnaires for the G7 member states indicated a bias towards progressive views but no significant bias between authoritarian and libertarian views, contradicting the findings of prior reports, with the average coordinates being (-3.27, 0.58). In addition, ChatGPT's Big Five personality traits were tested using the OCEAN test and its personality type was queried using the Myers-Briggs Type Indicator (MBTI) test. Finally, the maliciousness of ChatGPT was evaluated using the Dark Factor test. These three tests were also repeated ten times each, revealing that ChatGPT perceives itself as highly open and agreeable, has the Myers-Briggs personality type ENFJ, and is among the 15% of test-takers with the least pronounced dark traits.

cs.CY↗

arXiv2023

RODD: Robust Outlier Detection in Data Cubes

Data cubes are multidimensional databases, often built from several separate databases, that serve as flexible basis for data analysis. Surprisingly, outlier detection on data cubes has not yet been treated extensively. In this work, we provide the first framework to evaluate robust outlier detection methods in data cubes (RODD). We introduce a novel random forest-based outlier detection approach (RODD-RF) and compare it with more traditional methods based on robust location estimators. We propose a general type of test data and examine all methods in a simulation study. Moreover, we apply ROOD-RF to real world data. The results show that RODD-RF can lead to improved outlier detection.

cs.DB↗

arXiv2023

Robust Confidence Intervals for Meta-Regression with Interaction Effects

Meta-analysis is an important statistical technique for synthesizing the results of multiple studies regarding the same or closely related research question. So-called meta-regression extends meta-analysis models by accounting for studylevel covariates. Mixed-effects meta-regression models provide a powerful tool for evidence synthesis, by appropriately accounting for betweem-study heterogeneity. In fact, modelling the study effect in terms of random effects and moderators not only allows to examine the impact of the moderators, but often leads to more accurate estimates of the involved parameters. Nevertheless, due to the often small number of studies on a specific research topic, interactions are often neglected in meta-regression. In this work, we consider the research questions (i) how moderator interactions influence inference in mixed-effects meta-regression models and (ii) whether some inference methods are more reliable than others. Here, we review robust methods for confidence intervals in meta-regression models including interaction effects. These methods are based on the application of robust sandwich estimators for estimating the variance-covariance matrix of the vector of model coefficients. Furthermore, we compare different versions of these robust estimators in an extensive simulation study. We thereby investigate coverage and length of seven different confidence intervals under varying conditions. We conclude with some practical recommendations.

stat.ME↗

arXiv2023

Dataset Bias in Human Activity Recognition

When creating multi-channel time-series datasets for Human Activity Recognition (HAR), researchers are faced with the issue of subject selection criteria. It is unknown what physical characteristics and/or soft-biometrics, such as age, height, and weight, need to be taken into account to train a classifier to achieve robustness towards heterogeneous populations in the training and testing data. This contribution statistically curates the training data to assess to what degree the physical characteristics of humans influence HAR performance. We evaluate the performance of a state-of-the-art convolutional neural network on two HAR datasets that vary in the sensors, activities, and recording for time-series HAR. The training data is intentionally biased with respect to human characteristics to determine the features that impact motion behaviour. The evaluations brought forth the impact of the subjects' characteristics on HAR. Thus, providing insights regarding the robustness of the classifier with respect to heterogeneous populations. The study is a step forward in the direction of fair and trustworthy artificial intelligence by attempting to quantify representation bias in multi-channel time series HAR data.

eess.SP↗