Related papers: Thoughts on new statistical procedures for age-per…
Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time…
In many situations it could be interesting to ascertain whether nonparametric regression curves can be grouped, especially when confronted with a considerable number of curves. The proposed testing procedure allows to determine groups with…
We present a brief history of the field of interpretable machine learning (IML), give an overview of state-of-the-art interpretation methods, and discuss challenges. Research in IML has boomed in recent years. As young as the field is, it…
The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be…
We use the variety of one-parameter subgroups to define a numerical invariant for a representation of an infinitesimal group scheme. For an indecomposable module M of complexity 1, this number is related to the period of M.
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
Interpretability has arisen as a key desideratum of machine learning models alongside performance. Approaches so far have been primarily concerned with fixed dimensional inputs emphasizing feature relevance or selection. In contrast, we…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
Machine learning solutions for pattern classification problems are nowadays widely deployed in society and industry. However, the lack of transparency and accountability of most accurate models often hinders their safe use. Thus, there is a…
By means of the shift operators we introduce a new periodicity concept on time scales. This new approach will enable researchers to investigate periodicity notion on a large class of time scales whose members may not satisfy the condition:…
A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some…
The paper explores the challenges of regression analysis in evolving data streams, an area that remains relatively underexplored compared to classification. We propose a standardized evaluation process for regression and prediction interval…
Epidemiology characterizes the influence of causes to disease and health conditions of defined populations. Cohort studies are population-based studies involving usually large numbers of randomly selected individuals and comprising numerous…
There exist combable groups in which the conjugacy problem is unsolvable. The isomorphism problem is unsolvable for certain recursive sequences of finite presentations of combable groups.
Chronological age predictors often fail to achieve out-of-distribution (OOD) gen- eralization due to exogenous attributes such as race, gender, or tissue. Learning an invariant representation with respect to those attributes is therefore…
Preprocessing forms an oft-neglected foundation for a wide range of statistical and scientific analyses. However, it is rife with subtleties and pitfalls. Decisions made in preprocessing constrain all later analyses and are typically…
Most of state of the art methods applied on time series consist of deep learning methods that are too complex to be interpreted. This lack of interpretability is a major drawback, as several applications in the real world are critical…
This survey article is the outgrowth of two talks given at the Journ\'ees X-UPS "P\'eriodes et transcendance" at \'Ecole polytechnique. Periods are complex numbers whose real and imaginary parts can be written as integrals of rational…
We consider a compositional data analysis approach to forecasting the age distribution of death counts. Using the age-specific period life-table death counts in Australia obtained from the Human Mortality Database, the compositional data…