相关论文: A tree approach to $p$-variation and to integratio…

We study the concept of quadratic variation of a continuous path along a sequence of partitions and its dependence with respect to the choice of the partition sequence. We define the concept of quadratic roughness of a path along a…

In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional It\^o formula…

This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…

Vector autoregression has been widely used for modeling and analysis of multivariate time series data. In high-dimensional settings, model parameter regularization schemes inducing sparsity yield interpretable models and achieved good…

We introduce an operator description for a stochastic sandpile model with a conserved particle density, and develop a path-integral representation for its evolution. The resulting (exact) expression for the effective action highlights…

We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of…

In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…

Shapley Values (SV) are widely used in explainable AI, but their estimation and interpretation can be challenging, leading to inaccurate inferences and explanations. As a starting point, we remind an invariance principle for SV and derive…

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…

In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…

This note is devoted to construct a rough path above a multidimensional fractional Brownian motion $B$ with any Hurst parameter $H\in(0,1)$, by means of its representation as a Volterra Gaussian process. This approach yields some algebraic…

Treewidth is a graph parameter of fundamental importance to algorithmic and structural graph theory. This paper surveys several graph parameters tied to treewidth, including separation number, tangle number, well-linked number and Cartesian…

We discuss a variation of Takagi curves based, however, more on algebraic than geometric principles. Namely, we construct functions of loops in a special binary representation. The graph of these functions usually has chaotic and fractal…

The main tool for stochastic calculus with respect to a multidimensional process $B$ with small H\"older regularity index is rough path theory. Once $B$ has been lifted to a rough path, a stochastic calculus -- as well as solutions to…

We revisit binary decision trees from the perspective of partitions of the data. We introduce the notion of partitioning function, and we relate it to the growth function and to the VC dimension. We consider three types of features:…

We prove an extension to the classical continuity theorem in rough paths. We show that two $p$-rough paths are close in all levels of iterated integrals provided the first $\lfl p \rfl$ terms are close in a uniform sense. Applications…

Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…

In this article we are concerned with the study of the existence and uniqueness of pathwise mild solutions to evolutions equations driven by a H\"older continuous function with H\"older exponent in $(1/3,1/2)$. Our stochastic integral is a…

We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…

This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…