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It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
Frailty models are essential tools in survival analysis for addressing unobserved heterogeneity and random effects in the data. These models incorporate a random effect, the frailty, which is assumed to impact the hazard rate…
Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…
It is usual to rely on the quasi-likelihood methods for deriving statistical methods applied to clustered multinomial data with no underlying distribution. Even though extensive literature can be encountered for these kind of data sets,…
Our goal in this paper is to find a characterization of $n$-dimensional bilinear Hardy inequalities \begin{align*} \bigg\| \,\int_{B(0,\cdot)} f \cdot \int_{B(0,\cdot)} g \,\bigg\|_{q,u,(0,\infty)} & \leq C \, \|f\|_{p_1,v_1,{\mathbb R}^n}…
The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to…
Influence propagation has been the subject of extensive study due to its important role in social networks, epidemiology, and many other areas. Understanding propagation mechanisms is critical to control the spread of fake news or…
This dissertation is based on a project co-founded by the Health Market Quality Program (now Rozetta Institute) and the Australian Institute of Health and Welfare. The overall objective of this work is to provide a framework and a tool for…
Graph Neural Networks (GNNs) have improved unsupervised community detection of clustered nodes due to their ability to encode the dual dimensionality of the connectivity and feature information spaces of graphs. Identifying the latent…
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
In recent years, the concepts of ``diversity'' and ``inclusion'' have attracted considerable attention across a range of fields, encompassing both social and biological disciplines. To fully understand these concepts, it is critical to not…
Public discourse and opinions stem from multiple social groups. Each group has beliefs about a topic (such as vaccination, abortion, gay marriage, etc.), and opinions are exchanged and blended to produce consensus. A particular measure of…
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincar\'e inequalities. Typically two kind of sensitivity indices are linked by a Poincar\'e type inequality, which…
Deep generative models have made much progress in improving training stability and quality of generated data. Recently there has been increased interest in the fairness of deep-generated data. Fairness is important in many applications,…
Prediction of an imminent catastrophic event in a driven disordered system is of paramount importance - from the laboratory scale controlled fracture experiment to the largest scale of mechanical failure i.e., earthquakes. It has been long…
Model fairness (a.k.a., bias) has become one of the most critical problems in a wide range of AI applications. An unfair model in autonomous driving may cause a traffic accident if corner cases (e.g., extreme weather) cannot be fairly…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
Ensuring fairness in AI systems is critical, especially in high-stakes domains such as lending, hiring, and healthcare. This urgency is reflected in emerging global regulations that mandate fairness assessments and independent bias audits.…