Related papers: The Recovery of Causal Poly-Trees from Statistical…
We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed trough the random branching process.…
Causal Bayesian networks are widely used tools for summarising the dependencies between variables and elucidating their putative causal relationships. By restricting the search to trees, for example, learning the optimum from data is…
Supertree methods are tree reconstruction techniques that combine several smaller gene trees (possibly on different sets of species) to build a larger species tree. The question of interest is whether the reconstructed supertree converges…
We give simply exponential lower bounds on the probabilities of a given strongly Rayleigh distribution, depending only on its expectation. This resolves a weak version of a problem left open by Karlin-Klein-Oveis Gharan in their recent…
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…
In this paper, we provide a polynomial time algorithm to calculate the probability of a {\it ranked} gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The…
To draw scientifically meaningful conclusions and build reliable models of quantitative phenomena, cause and effect must be taken into consideration (either implicitly or explicitly). This is particularly challenging when the measurements…
With the increasing need of personalised decision making, such as personalised medicine and online recommendations, a growing attention has been paid to the discovery of the context and heterogeneity of causal relationships. Most existing…
This paper proposes an approach to analyze an event log of a business process in order to generate case-level recommendations of treatments that maximize the probability of a given outcome. Users classify the attributes in the event log…
Linear structural causal models (SCMs) are used to express and analyse the relationships between random variables. Direct causal effects are represented as directed edges and confounding factors as bidirected edges. Identifying the causal…
In this study, we address causal inference when only observational data and a valid causal ordering from the causal graph are available. We introduce a set of flow models that can recover component-wise, invertible transformation of…
Large deviation principles and related results are given for a class of Markov chains associated to the "leaves" in random recursive trees and preferential attachment random graphs, as well as the "cherries" in Yule trees. In particular,…
In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
Background: Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each interior vertex x of T it is known whether x…
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…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
Causal Structure Learning (CSL), also referred to as causal discovery, amounts to extracting causal relations among variables in data. CSL enables the estimation of causal effects from observational data alone, avoiding the need to perform…
Decision trees are a popular family of models due to their attractive properties such as interpretability and ability to handle heterogeneous data. Concurrently, missing data is a prevalent occurrence that hinders performance of machine…
When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…