A novel approach based on variational inference to simultaneously infer both the latent clusters and causal structures is presented and an approximate posterior over clusters and graph-structure is learned by considering variational distributions based on categorical and Bernoulli models.
Abstract
Causal discovery aims to understand the relationships between individual random variables. In many applications, such as brain imaging and climate modeling, it is more meaningful to consider interactions among groups of variables. Existing methods assume that knowledge of such groups or clusters is explicitly available when modeling interactions. However, in practice, these clusters as well as the causal relationships among them, are latent. In this paper, we present a novel approach based on variational inference to simultaneously infer both the latent clusters and causal structures. We learn an approximate posterior over clusters and graph-structure by considering variational distributions based on categorical and Bernoulli models respectively. We derive variational lower bounds and estimation techniques to learn variational and model parameters. The effectiveness of our proposed methods for cluster and causal discovery are demonstrated on both synthetic and real data sets.
This work considers the task of conditional causal discovery as a Bayesian inference problem, in which the posterior is targeted over causal graphs and parameters conditional on an event such as a causal-effect constraint, and adapts rare-event estimation techniques to perform inference the joint graph-parameter space.
Cixuan Zhang, Guy Van den Broeck, Benjie Wang· 0 citations
Causal representation learning aims to infer a small set of causally related latent variables and to model their causal relationships in order to explain high-dimensional observed data. Recent studies have made progress in identifying causal representations from time series by hypothesizing temporal structures among latent components. However, these methods are constrained by the observation scale and sampling regularity, as they typically assume that latent components evolve at discrete time steps. Moreover, they do not explicitly identify the causal graph among latent components, which limits the interpretability of the learned representations. To address these limitations, we propose Continuous Causal Component and Structure Discovery (C3SD). We theoretically show that latent causal components and their causal relationships can be identified up to permutation equivalence by modeling synchronous sparsity in the mapping between latent components and observed variables. Building on this result, C3SD employs a dual sparsity-induced autoencoder to infer latent causal components, together with an adaptive group lasso to jointly structure the encoding and decoding matrices. In addition, a neural ordinary differential equation–based joint autoencoder models the continuous-time causal dynamics of the latent components and recovers their underlying dynamical causal structure. Extensive experiments demonstrate that C3SD effectively identifies latent components and the causal mechanisms driving their continuous temporal evolution, particularly in sparsely and irregularly sampled time series.
Dezhi Yang, Jun Wang, C. Domeniconi et al.· Proceedings of the 32nd ACM...· 0 citations
Functional clustering is an important tool for identifying latent heterogeneity in functional data and has been widely applied across various scientific fields. However, many existing methods are not fully adaptive, as they may require the number of clusters to be prespecified and may lack automatic control over the smoothness of the underlying functions. They also commonly assume independent and identically distributed errors, thereby overlooking additional within-curve dependence. We propose a fully adaptive Bayesian procedure for functional clustering that addresses these limitations through Dirichlet process priors, adaptive smoothness control, and flexible covariance modeling. For computational scalability, the proposed method employs variational inference as an efficient alternative to Markov chain Monte Carlo. Together, these features provide a unified Bayesian framework for functional clustering and cluster-specific mean function estimation in the presence of structured within-curve dependence.
LoCaLS is proposed, a local causal structure learning algorithm that is sound and complete under standard assumptions and identifies the same direct causes and effects of a target variable as those identifiable by global causal discovery methods, while allowing for latent variables and selection bias.
Zheng Li, Hao Zhang, Ruxin Wang et al.· arXiv.org· 1 citation
We propose a Bayesian model-based approach for clustering functional data with an unknown number of clusters and temporally correlated observations. Cluster-specific mean functions are represented using B-spline basis expansions, while within-curve dependence is modeled through an Ornstein--Uhlenbeck covariance structure. A truncated Dirichlet process mixture is used to infer the effective number of clusters, and a variational EM algorithm is developed for efficient posterior approximation. Simulation studies show that the proposed method performs well under both correctly specified and misspecified mean-function settings and compares favorably with several existing functional clustering methods. Comparisons with MCMC indicate that the variational approximation yields consistent clustering and parameter estimates but at substantially lower computational cost. An application to Canadian daily temperature curves further demonstrates the practical usefulness of the method in identifying interpretable functional clusters while accounting for temporal dependence.
SVI-DAG is proposed, a structured variational inference approach to Bayesian causal discovery using observational data and prior beliefs that uses normalizing flows to model dependencies between edges, supporting expressive and multimodal posterior learning over DAGs.
Shrenik Zinage· 0 citations
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