Related papers: Analyzing the Fine Structure of Distributions
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
We introduce two new tools to assess the validity of statistical distributions. These tools are based on components derived from a new statistical quantity, the $comparison$ $curve$. The first tool is a graphical representation of these…
Subsampling from a large data set is useful in many supervised learning contexts to provide a global view of the data based on only a fraction of the observations. Diverse (or space-filling) subsampling is an appealing subsampling approach…
Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
Turbulence is essential for understanding the structure and dynamics of molecular clouds and star-forming regions. There is a need for adequate tools to describe and characterize the properties of turbulent flows. One-point probability…
The efficiency of modern computer graphics allows us to explore collections of space curves simultaneously with "drag-to-rotate" interfaces. This inspires us to replace "scatterplots of points" with "scatterplots of curves" to…
A novel fusion python application of data mining techniques (DMT) was designed and implemented to locate, identify, and delineate the subsurface structural pattern (SSP) of source rocks for the features of interest underlain the study area.…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…
Assessing equity in treatment of a subpopulation often involves assigning numerical "scores" to all individuals in the full population such that similar individuals get similar scores; matching via propensity scores or appropriate…
Analysis of matrix-variate data is becoming increasingly common in the literature, particularly in the field of clustering and classification. It is well-known that real data, including real matrix-variate data, often exhibit high levels of…
Using the intuition that out-of-distribution data have lower likelihoods, a common approach for out-of-distribution detection involves estimating the underlying data distribution. Normalizing flows are likelihood-based generative models…
The scalability of a particular visualization approach is limited by the ability for people to discern differences between plots made with different datasets. Ideally, when the data changes, the visualization changes in perceptible ways.…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
Parallel coordinates plot (PCP) is an excellent tool for multivariate visualization and analysis, but it may fail to reveal inherent structures for datasets with a large number of items. In this paper, we propose a suite of novel…
Modern data analysis frequently involves variables with highly non-Gaussian marginal distributions. However, commonly used analysis methods are most effective with roughly Gaussian data. This paper introduces an automatic transformation…
The streaming model describes the mapping between real and redshift space for 2-point clustering statistics. Its key element is the probability density function (PDF) of line-of-sight pairwise peculiar velocities. Following a kinetic-theory…
Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks have been shown to be very brittle and are difficult to deploy on…
Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…