arXiv subjects

Daniele Tramontano

Publications and source records attributed to Daniele Tramontano.

5 recordsLinked to original sources

arXiv2026

Parameter identification in linear non-Gaussian causal models under general confounding

Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent variables. Our focus is on the commonly studied acyclic setting, where each model corresponds to a directed acyclic graph (DAG). For this case, prior literature has demonstrated that connections to overcomplete independent component analysis yield effective criteria to decide parameter identifiability in latent variable models. However, this connection is based on the assumption that the observed variables linearly depend on the latent variables. Departing from this assumption, we treat models that allow for arbitrary non-linear latent confounding. Our main result is a graphical criterion that is necessary and sufficient for deciding the generic identifiability of direct causal effects. Moreover, we provide an algorithmic implementation of the criterion with a run time that is polynomial in the number of observed variables. Finally, we report on estimation heuristics based on the identification result and explore a generalization to models with feedback loops.

stat.ME↗

arXiv2025

Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants

This paper investigates causal effect identification in latent variable Linear Non-Gaussian Acyclic Models (lvLiNGAM) using higher-order cumulants, addressing two prominent setups that are challenging in the presence of latent confounding: (1) a single proxy variable that may causally influence the treatment and (2) underspecified instrumental variable cases where fewer instruments exist than treatments. We prove that causal effects are identifiable with a single proxy or instrument and provide corresponding estimation methods. Experimental results demonstrate the accuracy and robustness of our approaches compared to existing methods, advancing the theoretical and practical understanding of causal inference in linear systems with latent confounders.

stat.ML↗

arXiv2024

Probability Metrics for Tropical Spaces of Different Dimensions

The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently, a new geometric solution has been proposed to address the more challenging problem of comparing measures in Euclidean spaces of differing dimensions. Here, we study the same problem of comparing probability distributions of different dimensions in the tropical setting, which is becoming increasingly relevant in applications involving complex data structures such as phylogenetic trees. Specifically, we construct a Wasserstein distance between measures on different tropical projective tori -- the focal metric spaces in both theory and applications of tropical geometry -- via tropical mappings between probability measures. We prove equivalence of the directionality of the maps, whether mapping from a low dimensional space to a high dimensional space or vice versa. As an important practical implication, our work provides a framework for comparing probability distributions on the spaces of phylogenetic trees with different leaf sets. We demonstrate the computational feasibility of our approach using existing optimisation techniques on both simulated and real data.

math.MG↗

arXiv2024

Causal Effect Identification in LiNGAM Models with Latent Confounders

We study the generic identifiability of causal effects in linear non-Gaussian acyclic models (LiNGAM) with latent variables. We consider the problem in two main settings: When the causal graph is known a priori, and when it is unknown. In both settings, we provide a complete graphical characterization of the identifiable direct or total causal effects among observed variables. Moreover, we propose efficient algorithms to certify the graphical conditions. Finally, we propose an adaptation of the reconstruction independent component analysis (RICA) algorithm that estimates the causal effects from the observational data given the causal graph. Experimental results show the effectiveness of the proposed method in estimating the causal effects.

stat.ML↗

arXiv2022

Learning Linear Non-Gaussian Polytree Models

In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees. Our approach combines the Chow--Liu algorithm, which first learns the undirected tree structure, with novel schemes to orient the edges. The orientation schemes assess algebraic relations among moments of the data-generating distribution and are computationally inexpensive. We establish high-dimensional consistency results for our approach and compare different algorithmic versions in numerical experiments.

stat.ML↗