相关论文: Ensemble of causal trees
We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two…
Algorithms for causal discovery have recently undergone rapid advances and increasingly draw on flexible nonparametric methods to process complex data. With these advances comes a need for adequate empirical validation of the causal…
We study (plane) tree-valued Markov chains $(T_n,n \geq 1)$ with uniform backward dynamics and show that they can be obtained by sampling from a real tree. As non--plane trees, every such Markov chain is represented by a weighted real tree.…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
In this paper we study asymptotic properties of random forests within the framework of nonlinear time series modeling. While random forests have been successfully applied in various fields, the theoretical justification has not been…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
In this note we study the geometry of the component of the origin in the Uniform Spanning Forest of $\mathbb{Z}^d$, as well as in the Uniform Spanning Tree of wired subgraphs of $\mathbb{Z}^d$, when $d \ge 5$. In particular, we study…
Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks.…
Consider the Erd\H{o}s-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring…
We compare the structures and methods in the theory of causal fermion systems with generalized trace dynamics and non-commutative geometry. Although the three theories differ on many aspects, they agree in that the geometric structure to be…
The set of all possible configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology is a compact metric space. For a typical configuration we show that the wind-tree dynamics has infinite ergodic index in almost…
We establish limit theorems that describe the asymptotic local and global geometric behaviour of random enriched trees considered up to symmetry. We apply these general results to random unlabelled weighted rooted graphs and uniform random…
We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible to distinguish the connected components of the forest from…
Causal inference has gained much popularity in recent years, with interests ranging from academic, to industrial, to educational, and all in between. Concurrently, the study and usage of neural networks has also grown profoundly (albeit at…
In this article we investigate the Uniform Spanning Forest ($\mathsf{USF}$) in the nearest-neighbour integer lattice $\mathbf{Z}^{d+1} = \mathbf{Z}\times \mathbf{Z}^d$ with an assignment of conductances that makes the underlying (Network)…
We prove a number of identities relating the sofic entropy of a certain class of non-expansive algebraic dynamical systems, the sofic entropy of the Wired Spanning Forest and the tree entropy of Cayley graphs of residually finite groups. We…
We present a graph theoretical approach to the configurational statistics of random tree-like objects, such as randomly branching polymers. In particular, for ideal trees we show that Pr\"ufer labelling provides: (i) direct access to the…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on…
We develop a finite-sample, design-based theory for random forests in which each tree is a randomized conditional predictor acting on fixed covariates and the forest is their Monte Carlo average. An exact variance identity separates Monte…