Related papers: Real birational implicitization for statistical mo…

The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of…

Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two…

In this paper, we derive a general asymptotic implied volatility at the first-order for any stochastic volatility model using the heat kernel expansion on a Riemann manifold endowed with an Abelian connection. This formula is particularly…

Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…

We investigate Stochastic Mirror Descent (SMD) with matrix parameters and vector-valued predictions, a framework relevant to multi-class classification and matrix completion problems. Focusing on the overparameterized regime, where the…

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…

We introduce the marked Brauer algebra and the marked Brauer category. These generalize the analogous constructions for the ordinary Brauer algebra to the setting of a homogeneous bilinear form on a $\mathbb{Z}_2$-graded vector space. We…

State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…

Combining the properties of monovariate internal functions as proposed in Kolmogorov superimposition theorem, in tandem with the bounds wielded by the multivariate formulation of Chebyshev inequality, a hybrid model is presented, that…

This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…

Since the end of the XIXth century, we know that each birational map of the complex projective plane is the product of a finite number of quadratic birational maps of the projective plane; this motivates our work which essentially deals…

We address the description of the tropicalization of families of rational varieties under parametrizations with prescribed support, via curve valuations. We recover and extend results by Sturmfels, Tevelev and Yu for generic coefficients,…

In this paper, we extend the classical arithmetic defined over the set of natural numbers N, to the set of all finite directed connected multigraphs having a pair of distinct distinguished vertices. Specifically, we introduce a model F on…

Effective data imputation demands rich latent ``structure" discovery capabilities from ``plain" tabular data. Recent advances in graph neural networks-based data imputation solutions show their strong structure learning potential by…

In a real-world setting, visual recognition systems can be brought to make predictions for images belonging to previously unknown class labels. In order to make semantically meaningful predictions for such inputs, we propose a two-step…

Recent work on graph generative models has made remarkable progress towards generating increasingly realistic graphs, as measured by global graph features such as degree distribution, density, and clustering coefficients. Deep generative…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…

Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically…