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

We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can…

A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…

Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…

We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…

A learning algorithm is presented which given the structure of a causal tree, will estimate its link probabilities by sequential measurements on the leaves only. Internal nodes of the tree represent conceptual (hidden) variables…

We study combinatorial properties of a rational Dyck path by decomposing it into a tuple of Dyck paths. The combinatorial models such as $b$-Stirling permutations, $(b+1)$-ary trees, parenthesis presentations, and binary trees play central…

With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference…

We consider a stochastic process $Y$ defined by an integral in quadratic mean of a deterministic function $f$ with respect to a Gaussian process $X$, which need not have stationary increments. For a class of Gaussian processes $X$, it is…

Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…

The trace $\tr(q(\ma{L} + q\ma{I})^{-1})$, where $\ma{L}$ is a symmetric diagonally dominant matrix, is the quantity of interest in some machine learning problems. However, its direct computation is impractical if the matrix size is large.…

The paper deals with some properties of set-valued functions having a bounded Riesz p-variation. Set-valued integrals of a Young type for such multifunctions are introduced. Selection results and properties of such setvalued integrals are…

We establish a correspondence between Pavlovian conditioning processes and fractals. The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level. In this way, one can represent a…

We study Thurston equivalence classes of quadratic post-critically finite branched coverings. For these maps, we introduce and study invariant spanning trees. We give a computational procedure for searching for invariant spanning trees.…

Variable trees are a new method for the exploration of discrete multivariate data. They display nested subsets and corresponding frequencies and percentages. Manual calculation of these quantities can be laborious, especially when there are…

We here investigate on the complexity of computing the \emph{tree-length} and the \emph{tree-breadth} of any graph $G$, that are respectively the best possible upper-bounds on the diameter and the radius of the bags in a tree decomposition…

Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…

We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments…

Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes. In recent years, quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the…

We introduce the concept of finite $\gamma$-scaled quadratic variation along a sequence of partitions for paths on a given interval. This concept, with historical roots in the study of Gaussian processes by Gladyshev (1961) and Klein \&…

In this paper, we study rough path properties of stochastic integrals of It\^{o}'s type and Stratonovich's type with respect to $G$-Brownian motion. The roughness of $G$-Brownian Motion is estimated and then the pathwise Norris lemma in…