Related papers: Ordinal spaces
How do analysts think about grouping and spatial operations? This overarching question incorporates a number of points for investigation, including understanding how analysts begin to explore a dataset, the types of grouping/spatial…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused…
Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…
Advances in machine learning technologies have led to increasingly powerful models in particular in the context of big data. Yet, many application scenarios demand for robustly interpretable models rather than optimum model accuracy; as an…
The AI revolution is data driven. AI "data wrangling" is the process by which unusable data is transformed to support AI algorithm development (training) and deployment (inference). Significant time is devoted to translating diverse data…
In the field of machine learning there is a growing interest towards more robust and generalizable algorithms. This is for example important to bridge the gap between the environment in which the training data was collected and the…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces,…
In this lecture notes I concentrate on the classic and widely applicable characterization of higher order statistics by joint moments, a.k.a. higher order correlation functions, and directly related statistics. I put special emphasis on…
Decisional systems are based on multidimensional databases improving OLAP analyses. The paper describes a new OLAP operator named "BLEND" to perform multigradual analyses. The operation transforms multidimensional structures during querying…
Object oriented data analysis (OODA) aims at statistically analyzing populations of complicated objects. This paper is motivated by a study of cell images in cell culture biology, which highlights a common critical issue: choice of data…
In ordinal symbolic dynamics, transcripts describe the algebraic relationship between ordinal patterns. Using the concept of transcript, we exploit the mathematical structure of the group of permutations to derive properties and relations…
Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…
Ordinal regression is an important type of learning, which has properties of both classification and regression. Here we describe a simple and effective approach to adapt a traditional neural network to learn ordinal categories. Our…
We examine the role of textual data as study units when conducting causal inference by drawing parallels between human subjects and organized texts. %in human population research. We elaborate on key causal concepts and principles, and…
The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…
Evaluating the reliability of machine learning classifications remains a fundamental challenge in Artificial Intelligence (AI), particularly when the target variable is multidimensional. Classification variables can be expressed by means of…