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Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
For measuring the strength of visually-observed subpopulation differences, the Population Difference Criterion is proposed to assess the statistical significance of visually observed subpopulation differences. It addresses the following…
We discuss two novel approaches to the classical two-sample problem. Our starting point are properly standardized and combined, very popular in several areas of statistics and data analysis, ordinal dominance and receiver characteristic…
In comparative research on time-to-event data for two groups, when two survival curves cross each other, it may be difficult to use the log-rank test and hazard ratio (HR) to properly assess the treatment benefit. Our aim was to identify a…
Performance measurement is an essential task once a statistical model is created. The Area Under the receiving operating characteristics Curve (AUC) is the most popular measure for evaluating the quality of a binary classifier. In this…
Survival trees are popular alternatives to Cox or Aalen regression models that offer both modelling flexibility and graphical interpretability. This paper introduces a new algorithm for survival trees that relaxes the assumption of…
Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming…
Neurons in higher cortical areas, such as the prefrontal cortex, are known to be tuned to a variety of sensory and motor variables. The resulting diversity of neural tuning often obscures the represented information. Here we introduce a…
A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…
Hypothesis tests based on linear models are widely accepted by organizations that regulate clinical trials. These tests are derived using strong assumptions about the data-generating process so that the resulting inference can be based on…
Modern data analysis across diverse disciplines increasingly relies on time series. Many of these datasets exhibit cyclostationarity, where patterns approximately repeat in a regular manner, often across multiple time scales, such as daily,…
Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities…
For marketing or power grid management purposes, many studies based on the analysis of the total electricity consumption curves of groups of customers are now carried out by electricity companies. Aggregated total or mean load curves are…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
Self-supervised learning aims to learn a embedding space where semantically similar samples are close. Contrastive learning methods pull views of samples together and push different samples away, which utilizes semantic invariance of…
Researchers often have datasets measuring features $x_{ij}$ of samples, such as test scores of students. In factor analysis and PCA, these features are thought to be influenced by unobserved factors, such as skills. Can we determine how…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Distributed Constraint Optimization Problems (DCOPs) are a widely studied class of optimization problems in which interaction between a set of cooperative agents are modeled as a set of constraints. DCOPs are NP-hard and significant effort…
Prior to clinical applications, it is critical that risk prediction models are evaluated in independent studies that did not contribute to model development. While prospective cohort studies provide a natural setting for model validation,…