The effect of latent confounding processes on the estimation of the strength of causal influences in chain-type networks

The authors acknowledge GTD TauRx Therapeutics centres for generous funding of this research.Peer reviewedPublisher PD

Causal Effect Inference with Deep Latent-Variable Models

Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We build on recent advances in latent variable modeling to simultaneously estimate the unknown latent space summarizing the confounders and the causal effect. Our method is based on Variational Autoencoders (VAE) which follow the causal structure of inference with proxies. We show our method is significantly more robust than existing methods, and matches the state-of-the-art on previous benchmarks focused on individual treatment effects.Comment: Published as a conference paper at NIPS 201

Learning Vector Autoregressive Models with Latent Processes

We study the problem of learning the support of transition matrix between random processes in a Vector Autoregressive (VAR) model from samples when a subset of the processes are latent. It is well known that ignoring the effect of the latent processes may lead to very different estimates of the influences among observed processes, and we are concerned with identifying the influences among the observed processes, those between the latent ones, and those from the latent to the observed ones. We show that the support of transition matrix among the observed processes and lengths of all latent paths between any two observed processes can be identified successfully under some conditions on the VAR model. From the lengths of latent paths, we reconstruct the latent subgraph (representing the influences among the latent processes) with a minimum number of variables uniquely if its topology is a directed tree. Furthermore, we propose an algorithm that finds all possible minimal latent graphs under some conditions on the lengths of latent paths. Our results apply to both non-Gaussian and Gaussian cases, and experimental results on various synthetic and real-world datasets validate our theoretical results

A problem-structuring model for analyzing transportation–environment relationships

This is the post-print version of the final paper published in European Journal of Operational Research. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2009 Elsevier B.V.This study discusses a decision support framework that guides policy makers in their strategic transportation related decisions by using multi-methodology. For this purpose, a methodology for analyzing the effects of transportation policies on environment, society, economy, and energy is proposed. In the proposed methodology, a three-stage problem structuring model is developed. Initially, experts’ opinions are structured by using a cognitive map to determine the relationships between transportation and environmental concepts. Then a structural equation model (SEM) is constructed, based on the cognitive map, to quantify the relations among external transportation and environmental factors. Finally the results of the SEM model are used to evaluate the consequences of possible policies via scenario analysis. In this paper a pilot study that covers only one module of the whole framework, namely transportation–environment interaction module, is conducted to present the applicability and usefulness of the methodology. This pilot study also reveals the impacts of transportation policies on the environment. To achieve a sustainable transportation system, the extent of the relationships between transportation and the environment must be considered. The World Development Indicators developed by the World Bank are used for this purpose

Algorithms of causal inference for the analysis of effective connectivity among brain regions

In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity

Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables

We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations

Multilevel (ML-ICLV) & Single Level Integrated Discrete Choice and Latent Variable (ICLV) Models Using Alternative Latent Structures' Conceptualizations

The aim of the present endeavor is to experiment on integrating discrete choice with latent variable (ICVL) models using alternative factorial structures’ conceptualizations and do so at both Single Level (Level 0) and Multilevel (ML-ICVL). In doing, specific independent variables amenable to alternative latent variables’ conceptualization were selected. These included: a) 1st-order latent variables (1st-order factors) (FM; FW), b) 1st-order latent variables (1st-order factors) (FM; FW) forming a 2nd-order factor (F), c) Multi-level (two-level) factorial structures (FML0; FML1 and FWL0; FWL1), and d) Bi-Factor factorial structures (FM; FW; FG). The results may be of use to researchers interested in using valid, reliable, and accurate structures of latent variables in ICLV models. We confirm that alternative latent structures of divergent factorial nature exist for the same observed variables, and may have different impact upon the dependent observed choice variable in the ICLV models. Second, DCE utility is conceptualized and estimated at both Level 0 and Level 1 and the differences are evident