Related papers: A category theory approach using preradicals to mo…

This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and…

To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many…

Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…

We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…

Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…

Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories…

After a one-year long effort of research on the field, we developed a machine learning-based classifier, tailored to predict whether a mechanical water meter would fail with passage of time and intensive use as well. A recurrent deep neural…

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while sometimes chaotic,…

Stock and flow diagrams are widely used in epidemiology to model the dynamics of populations. Although tools already exist for building these diagrams and simulating the systems they describe, we have created a new package called StockFlow,…

In category theory, the use of string diagrams is well known to aid in the intuitive understanding of certain concepts, particularly when dealing with adjunctions and monoidal categories. We show that string diagrams are also useful in…

In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Data stream mining aims at extracting meaningful knowledge from continually evolving data streams, addressing the challenges posed by nonstationary environments, particularly, concept drift which refers to a change in the underlying data…

Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of…

In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

We present a light formalism for proofs that encodes their inferential structure, along with a system that transforms these representations into flow-chart diagrams. Such diagrams should improve the comprehensibility of proofs. We discuss…

The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in…

Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…