Related papers: Causal Dependence Tree Approximations of Joint Dis…
Probability trees are one of the simplest models of causal generative processes. They possess clean semantics and -- unlike causal Bayesian networks -- they can represent context-specific causal dependencies, which are necessary for e.g.…
We provide finite sample guarantees for the classical Chow-Liu algorithm (IEEE Trans.~Inform.~Theory, 1968) to learn a tree-structured graphical model of a distribution. For a distribution $P$ on $\Sigma^n$ and a tree $T$ on $n$ nodes, we…
We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery). The first…
Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering ply-trees from empirically measured probability distributions of pairs of variables. The method…
Causal inference is essential for data-driven decision-making, as it aims to uncover causal relationships from observational data. However, identifying causality remains challenging due to the potential for confounding and the distinction…
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…
The past two decades have seen a growing interest in combining causal information, commonly represented using causal graphs, with machine learning models. Probability trees provide a simple yet powerful alternative representation of causal…
Causal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between…
We consider the problem of learning underlying tree structure from noisy, mixed data obtained from a linear model. To achieve this, we use the expectation maximization algorithm combined with Chow-Liu minimum spanning tree algorithm. This…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
This paper considers the $\varepsilon$-differentially private (DP) release of an approximate cumulative distribution function (CDF) of the samples in a dataset. We assume that the true (approximate) CDF is obtained after lumping the data…
The broad abundance of time series data, which is in sharp contrast to limited knowledge of the underlying network dynamic processes that produce such observations, calls for a rigorous and efficient method of causal network inference. Here…
The connection between the maximum spanning tree in a directed graph and the best dependency tree of a sentence has been exploited by the NLP community. However, for many dependency parsing schemes, an important detail of this approach is…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
We develop Clustered Random Forests, a random forests algorithm for clustered data, arising from independent groups that exhibit within-cluster dependence. The leaf-wise predictions for each decision tree making up clustered random forests…
This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution…
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…
The most fundamental problem in statistical causality is determining causal relationships from limited data. Probability trees, which combine prior causal structures with Bayesian updates, have been suggested as a possible solution. In this…
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,…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…