Interfacing Statistics, Machine Learning and Data Science from a Probabilistic Modelling Viewpoint

Topic Information

Dear Colleagues,

Modern statistics is the science of learning from data. As a discipline, it is concerned with the collection, analysis, and interpretation of data, as well as the effective communication and presentation of results relying on data. Statistics is a highly interdisciplinary field; in developing methods and studying the theory that underlies the methods, statisticians draw on a great variety of mathematical and computational tools.

Today, vast amounts of data are transforming the world and the way we live in it. Statistical methods and theories are used everywhere, from health, science and business to managing traffic and studying sustainability and climate change. This, in turn, will create the need for a much closer collaboration between statisticians, mathematicians, computer scientists and domain scientists. The call for a new generation of data scientists working at this interface is becoming louder and louder; there is a strong need to develop data-science university curricula.

Undoubtedly, fundamental statistical research has laid important foundations upon which Data Science approaches have been established. Conversely, modern (applied) statistics is continuing to pave a broad road to its data-science future.

Machine Learning has substantially advanced through statistical learning. Two fundamental ideas in the field of statistical learning are uncertainty and variation. The common basis for dealing with these complex issues is probabilistic modelling of the problems at hand.

The aim of this Topic is to encourage interested researchers in applied mathematics and statistics, engineering science disciplines, and bio-, geo- and environmental sciences to present original and recent developments on interfacing statistical inference with advanced machine learning and data science concepts and approaches for model selection, data analysis, estimation and prediction, uncertainty quantification and risk analysis in their research work. We particularly welcome novel applications of these concepts for the following:

• Statistical process control in industrial manufacturing;
• Predicting natural hazards and climate change processes;
• Graph modelling for energy, telecommunication and environmental monitoring;
• Development of efficient numerical algorithms for big data analysis;
• Model estimation (including variable selection) and validation;
• Regularisation methods;
• Causal inference and targeted learning;
• Ensemble learning methods.

Note that submission is still possible until 31 December 2024, despite of missed abstract submission deadline.

Prof. Dr. Jürgen Pilz
Dr. Noelle I. Samia
Prof. Dr. Dirk Husmeier
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Entropy entropy	2.1	4.9	1999	22.3 Days	CHF 2600
Mathematics mathematics	2.3	4.0	2013	18.3 Days	CHF 2600
Modelling modelling	1.3	2.7	2020	18.9 Days	CHF 1000
Stats stats	0.9	0.6	2018	19.7 Days	CHF 1600

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Published Papers (5 papers)

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All Entropy Mathematics Modelling Stats

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20 pages, 3076 KiB  

Open AccessArticle

Is Anonymization Through Discretization Reliable? Modeling Latent Probability Distributions for Ordinal Data as a Solution to the Small Sample Size Problem

by Stefan Michael Stroka and Christian Heumann

Stats 2024, 7(4), 1189-1208; https://doi.org/10.3390/stats7040070 - 17 Oct 2024

Viewed by 1034

Abstract

The growing interest in data privacy and anonymization presents challenges, as traditional methods such as ordinal discretization often result in information loss by coarsening metric data. Current research suggests that modeling the latent distributions of ordinal classes can reduce the effectiveness of anonymization [...] Read more.

The growing interest in data privacy and anonymization presents challenges, as traditional methods such as ordinal discretization often result in information loss by coarsening metric data. Current research suggests that modeling the latent distributions of ordinal classes can reduce the effectiveness of anonymization and increase traceability. In fact, combining probability distributions with a small training sample can effectively infer true metric values from discrete information, depending on the model and data complexity. Our method uses metric values and ordinal classes to model latent normal distributions for each discrete class. This approach, applied with both linear and Bayesian linear regression, aims to enhance supervised learning models. Evaluated with synthetic datasets and real-world datasets from UCI and Kaggle, our method shows improved mean point estimation and narrower prediction intervals compared to the baseline. With 5–10% training data randomly split from each dataset population, it achieves an average 10% reduction in MSE and a ~5–10% increase in R² on out-of-sample test data overall. Full article

(This article belongs to the Topic Interfacing Statistics, Machine Learning and Data Science from a Probabilistic Modelling Viewpoint)

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34 pages, 23631 KiB  

Open AccessArticle

FFT-Based Probability Density Imaging of Euler Solutions

by Shujin Cao, Peng Chen, Guangyin Lu, Zhiyuan Ma, Bo Yang and Xinyue Chen

Entropy 2024, 26(6), 517; https://doi.org/10.3390/e26060517 - 15 Jun 2024

Viewed by 1663

Abstract

When using traditional Euler deconvolution optimization strategies, it is difficult to distinguish between anomalies and their corresponding Euler tails (those solutions are often distributed outside the anomaly source, forming “tail”-shaped spurious solutions, i.e., misplaced Euler solutions, which must be removed or marked) with [...] Read more.

When using traditional Euler deconvolution optimization strategies, it is difficult to distinguish between anomalies and their corresponding Euler tails (those solutions are often distributed outside the anomaly source, forming “tail”-shaped spurious solutions, i.e., misplaced Euler solutions, which must be removed or marked) with only the structural index. The nonparametric estimation method based on the normalized B-spline probability density (BSS) is used to separate the Euler solution clusters and mark different anomaly sources according to the similarity and density characteristics of the Euler solutions. For display purposes, the BSS needs to map the samples onto the estimation grid at the points where density will be estimated in order to obtain the probability density distribution. However, if the size of the samples or the estimation grid is too large, this process can lead to high levels of memory consumption and excessive computation times. To address this issue, a fast linear binning approximation algorithm is introduced in the BSS to speed up the computation process and save time. Subsequently, the sample data are quickly projected onto the estimation grid to facilitate the discrete convolution between the grid and the density function using a fast Fourier transform. A method involving multivariate B-spline probability density estimation based on the FFT (BSSFFT), in conjunction with fast linear binning appropriation, is proposed in this paper. The results of two random normal distributions show the correctness of the BSS and BSSFFT algorithms, which is verified via a comparison with the true probability density function (pdf) and Gaussian kernel smoothing estimation algorithms. Then, the Euler solutions of the two synthetic models are analyzed using the BSS and BSSFFT algorithms. The results are consistent with their theoretical values, which verify their correctness regarding Euler solutions. Finally, the BSSFFT is applied to Bishop 5X data, and the numerical results show that the comprehensive analysis of the 3D probability density distributions using the BSSFFT algorithm, derived from the Euler solution subset of $\left\{x_0,y_0,z_0\right\}$, can effectively separate and locate adjacent anomaly sources, demonstrating strong adaptability. Full article

(This article belongs to the Topic Interfacing Statistics, Machine Learning and Data Science from a Probabilistic Modelling Viewpoint)

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15 pages, 324 KiB  

Open AccessArticle

Estimation Approach for a Linear Quantile-Regression Model with Long-Memory Stationary GARMA Errors

by Oumaima Essefiani, Rachid El Halimi and Said Hamdoune

Modelling 2024, 5(2), 585-599; https://doi.org/10.3390/modelling5020031 - 4 Jun 2024

Viewed by 1333

Abstract

The aim of this paper is to assess the significant impact of using quantile analysis in multiple fields of scientific research . Here, we focus on estimating conditional quantile functions when the errors follow a GARMA (Generalized Auto-Regressive Moving Average) model. Our key [...] Read more.

The aim of this paper is to assess the significant impact of using quantile analysis in multiple fields of scientific research . Here, we focus on estimating conditional quantile functions when the errors follow a GARMA (Generalized Auto-Regressive Moving Average) model. Our key theoretical contribution involves identifying the Quantile-Regression (QR) coefficients within the context of GARMA errors. We propose a modified maximum-likelihood estimation method using an EM algorithm to estimate the target coefficients and derive their statistical properties. The proposed procedure yields estimators that are strongly consistent and asymptotically normal under mild conditions. In order to evaluate the performance of the proposed estimators, a simulation study is conducted employing the minimum bias and Root Mean Square Error (RMSE) criterion. Furthermore, an empirical application is given to demonstrate the effectiveness of the proposed methodology in practice. Full article

(This article belongs to the Topic Interfacing Statistics, Machine Learning and Data Science from a Probabilistic Modelling Viewpoint)

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18 pages, 1520 KiB  

Open AccessArticle

Utility in Time Description in Priority Best–Worst Discrete Choice Models: An Empirical Evaluation Using Flynn’s Data

by Sasanka Adikari and Norou Diawara

Stats 2024, 7(1), 185-202; https://doi.org/10.3390/stats7010012 - 19 Feb 2024

Cited by 1 | Viewed by 2029

Abstract

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best–worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer [...] Read more.

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best–worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer over time. The analysis was conducted by using simulated data (choice pairs) based on data from Flynn’s (2007) ‘Quality of Life Experiment’. Most of the traditional approaches assume the choice alternatives are mutually exclusive over time, which is a questionable assumption. We introduced a new copula-based model (CO-CUB) for the transition probability, which can handle the dependent structure of best–worst choices while applying a very practical constraint. We used a conditional logit model to calculate the utility at consecutive time points and spread it to future time points under dynamic programming. We suggest that the CO-CUB transition probability algorithm is a novel way to analyze and predict choices in future time points by expressing human choice behavior. The numerical results inform decision making, help formulate strategy and learning algorithms under dynamic utility in time for best–worst DCEs. Full article

(This article belongs to the Topic Interfacing Statistics, Machine Learning and Data Science from a Probabilistic Modelling Viewpoint)

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22 pages, 1145 KiB  

Open AccessArticle

Transfer Learning in Multiple Hypothesis Testing

by Stefano Cabras and María Eugenia Castellanos Nueda

Entropy 2024, 26(1), 49; https://doi.org/10.3390/e26010049 - 4 Jan 2024

Cited by 1 | Viewed by 2047

Abstract

In this investigation, a synthesis of Convolutional Neural Networks (CNNs) and Bayesian inference is presented, leading to a novel approach to the problem of Multiple Hypothesis Testing (MHT). Diverging from traditional paradigms, this study introduces a sequence-based uncalibrated Bayes factor approach to test [...] Read more.

In this investigation, a synthesis of Convolutional Neural Networks (CNNs) and Bayesian inference is presented, leading to a novel approach to the problem of Multiple Hypothesis Testing (MHT). Diverging from traditional paradigms, this study introduces a sequence-based uncalibrated Bayes factor approach to test many hypotheses using the same family of sampling parametric models. A two-step methodology is employed: initially, a learning phase is conducted utilizing simulated datasets encompassing a wide spectrum of null and alternative hypotheses, followed by a transfer phase applying this fitted model to real-world experimental sequences. The outcome is a CNN model capable of navigating the complex domain of MHT with improved precision over traditional methods, also demonstrating robustness under varying conditions, including the number of true nulls and dependencies between tests. Although indications of empirical evaluations are presented and show that the methodology will prove useful, more work is required to provide a full evaluation from a theoretical perspective. The potential of this innovative approach is further illustrated within the critical domain of genomics. Although formal proof of the consistency of the model remains elusive due to the inherent complexity of the algorithms, this paper also provides some theoretical insights and advocates for continued exploration of this methodology. Full article

(This article belongs to the Topic Interfacing Statistics, Machine Learning and Data Science from a Probabilistic Modelling Viewpoint)

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