Observational-Interventional Priors for Dose-Response Learning

Controlled interventions provide the most direct source of information for learning causal effects. In particular, a dose-response curve can be learned by varying the treatment level and observing the corresponding outcomes. However, interventions can be expensive and time-consuming. Observational data, where the treatment is not controlled by a known mechanism, is sometimes available. Under some strong assumptions, observational data allows for the estimation of dose-response curves. Estimating such curves nonparametrically is hard: sample sizes for controlled interventions may be small, while in the observational case a large number of measured confounders may need to be marginalized. In this paper, we introduce a hierarchical Gaussian process prior that constructs a distribution over the dose-response curve by learning from observational data, and reshapes the distribution with a nonparametric affine transform learned from controlled interventions. This function composition from different sources is shown to speed-up learning, which we demonstrate with a thorough sensitivity analysis and an application to modeling the effect of therapy on cognitive skills of premature infants

Causal Inference through a Witness Protection Program

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that exploits observational conditional independencies to suggest "weak" paths in a unknown causal graph. The widely used faithfulness condition of Spirtes et al. is relaxed to allow for varying degrees of "path cancellations" that imply conditional independencies but do not rule out the existence of confounding causal paths. The outcome is a posterior distribution over bounds on the average causal effect via a linear programming approach and Bayesian inference. We claim this approach should be used in regular practice along with other default tools in observational studies.Comment: 41 pages, 7 figure

Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounders

We propose an approach to estimate the effect of multiple simultaneous interventions in the presence of hidden confounders. To overcome the problem of hidden confounding, we consider the setting where we have access to not only the observational data but also sets of single-variable interventions in which each of the treatment variables is intervened on separately. We prove identifiability under the assumption that the data is generated from a nonlinear continuous structural causal model with additive Gaussian noise. In addition, we propose a simple parameter estimation method by pooling all the data from different regimes and jointly maximizing the combined likelihood. We also conduct comprehensive experiments to verify the identifiability result as well as to compare the performance of our approach against a baseline on both synthetic and real-world data.Comment: Accepted to The Conference on Uncertainty in Artificial Intelligence (UAI) 202

Flexible sampling of discrete data correlations without the marginal distributions

Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has gained popularity due to its modular parametrization of joint distributions. Among other properties, copulas provide a recipe for combining flexible models for univariate marginal distributions with parametric families suitable for potentially high dimensional dependence structures. More radically, the extended rank likelihood approach of Hoff (2007) bypasses learning marginal models completely when such information is ancillary to the learning task at hand as in, e.g., standard dimensionality reduction problems or copula parameter estimation. The main idea is to represent data by their observable rank statistics, ignoring any other information from the marginals. Inference is typically done in a Bayesian framework with Gaussian copulas, and it is complicated by the fact this implies sampling within a space where the number of constraints increases quadratically with the number of data points. The result is slow mixing when using off-the-shelf Gibbs sampling. We present an efficient algorithm based on recent advances on constrained Hamiltonian Markov chain Monte Carlo that is simple to implement and does not require paying for a quadratic cost in sample size.Comment: An overhauled version of the experimental section moved to the main paper. Old experimental section moved to supplementary materia

Neural Likelihoods via Cumulative Distribution Functions

We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs). By the application of automatic differentiation with respect to response variables and then to parameters of this CDF representation, we are able to build black box CDF and density estimators. A suite of families is introduced as alternative constructions for the multivariate case. At one extreme, the simplest construction is a competitive density estimator against state-of-the-art deep learning methods, although it does not provide an easily computable representation of multivariate CDFs. At the other extreme, we have a flexible construction from which multivariate CDF evaluations and marginalizations can be obtained by a simple forward pass in a deep neural net, but where the computation of the likelihood scales exponentially with dimensionality. Alternatives in between the extremes are discussed. We evaluate the different representations empirically on a variety of tasks involving tail area probabilities, tail dependence and (partial) density estimation.Comment: 10 page