Related papers: Classification from a Computable Viewpoint
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is actually computable. Miller proved that finite-dimensional spheres have computable type, Iljazovi\'c and other authors established the property…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
Category theory provides a powerful tool to organize mathematics. A sample of this descriptive power is given by the categorical analysis of the practice of "classes as shorthands" in ZF set theory. In this case category theory provides a…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
Image processing is an important research area in computer vision. Image segmentation plays the vital rule in image processing research. There exist so many methods for image segmentation. Clustering is an unsupervised study. Clustering can…
Categorization is a fundamental function of minds, with wide ranging implications for the rest of the cognitive system. In humans, categories are shared and communicated between minds, thus requiring explanations at the population level. In…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
We introduce computational causal inference as an interdisciplinary field across causal inference, algorithms design and numerical computing. The field aims to develop software specializing in causal inference that can analyze massive…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
Classification tasks in machine learning involving more than two classes are known by the name of "multi-class classification". Performance indicators are very useful when the aim is to evaluate and compare different classification models…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class…
Conformal predictions make it possible to define reliable and robust learning algorithms. But they are essentially a method for evaluating whether an algorithm is good enough to be used in practice. To define a reliable learning framework…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…
Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the…
One-class classification (OCC) algorithms aim to build classification models when the negative class is either absent, poorly sampled or not well defined. This unique situation constrains the learning of efficient classifiers by defining…