Related papers: Analysis of variance--why it is more important tha…
Assessing variability according to distinct factors in data is a fundamental technique of statistics. The method commonly regarded to as analysis of variance (ANOVA) is, however, typically confined to the case where all levels of a factor…
The analysis of variance (ANOVA) decomposition offers a systematic method to understand the interaction effects that contribute to a specific decision output. In this paper we introduce Neural-ANOVA, an approach to decompose neural networks…
Classical analysis of variance requires that model terms be labeled as fixed or random and typically culminate by comparing variability from each batch (factor) to variability from errors; without a standard methodology to assess the…
ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and…
Many statistical analyses involve the comparison of multiple data sets collected under different conditions in order to identify the difference in the underlying distributions. A common challenge in multi-sample comparison is the presence…
Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under…
For multivariate nonparametric regression, functional analysis-of-variance (ANOVA) modeling aims to capture the relationship between a response and covariates by decomposing the unknown function into various components, representing main…
In this paper we apply the previously introduced approximation method based on the ANOVA (analysis of variance) decomposition and Grouped Transformations to synthetic and real data. The advantage of this method is the interpretability of…
Traditional analysis of variance (ANOVA) software allows researchers to test for the significance of main effects in the presence of interactions without exposure to the details of how the software encodes main effects and interactions to…
We consider the problem where we have a multi-way table of means, indexed by several factors, where each factor can have a large number of levels. The entry in each cell is the mean of some response, averaged over the observations falling…
Time series classification stands as a pivotal and intricate challenge across various domains, including finance, healthcare, and industrial systems. In contemporary research, there has been a notable upsurge in exploring feature extraction…
Models which estimate main effects of individual variables alongside interaction effects have an identifiability challenge: effects can be freely moved between main effects and interaction effects without changing the model prediction. This…
Factorial designs are frequently used in different fields of science, e.g. psychological, medical or biometric studies. Standard approaches, as the ANOVA $F$-test, make different assumptions on the distribution of the error terms, the…
Hypothesis testing is one of the most common types of data analysis and forms the backbone of scientific research in many disciplines. Analysis of variance (ANOVA) in particular is used to detect dependence between a categorical and a…
We propose two algorithms for boosting random Fourier feature models for approximating high-dimensional functions. These methods utilize the classical and generalized analysis of variance (ANOVA) decomposition to learn low-order functions,…
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…
Analysis of variance (ANOVA) reveals some disadvantages, such as non-robustness against heteroscedastic or non-normal errors and using difference to overall mean as effect sizes only. As an alternative the multiple contrast test comparing…
Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…
Modern machine learning methods are often overparametrized, allowing adaptation to the data at a fine level. This can seem puzzling; in the worst case, such models do not need to generalize. This puzzle inspired a great amount of work,…
Data analysis is a powerful tool in all experimental sciences. Statistical methods, such as sampling theory, computer technologies necessary for handling large amounts of data, skill in analysing information contained in different types of…