Robust learning with the Hilbert-Schmidt independence criterion

We investigate the use of a non-parametric independence measure, the Hilbert-Schmidt Independence Criterion (HSIC), as a loss-function for learning robust regression and classification models. This loss-function encourages learning models where the distribution of the residuals between the label and the model-prediction is statistically independent of the distribution of the instances themselves. This loss-function was first proposed by Mooij et al. [2009] in the context of learning causal graphs. We adapt it to the task of robust learning for unsupervised covariate shift: learning on a source domain without access to any instances or labels from the unknown target domain. We prove that the proposed loss is expected to generalize to a class of target domains described in terms of the complexity of their density ratio function with respect to the source domain. Experiments on tasks of unsupervised covariate shift demonstrate that models learned with the proposed loss-function outperform several baseline methods.

Off-Policy Evaluation in Partially Observable Environments

This work studies the problem of batch off-policy evaluation for Reinforcement Learning in partially observable environments. Off-policy evaluation under partial observability is inherently prone to bias, with risk of arbitrarily large errors. We define the problem of off-policy evaluation for Partially Observable Markov Decision Processes (POMDPs) and establish what we believe is the first off-policy evaluation result for POMDPs. In addition, we formulate a model in which observed and unobserved variables are decoupled into two dynamic processes, called a Decoupled POMDP. We show how off-policy evaluation can be performed under this new model, mitigating estimation errors inherent to the procedure we provided for general POMDPs. We demonstrate the pitfalls of off-policy evaluation in POMDPs using a well-known off-policy method, importance sampling, and compare with our result on synthetic medical data.

Explaining Classifiers with Causal Concept Effect (CaCE)

How can we understand classification decisions made by deep neural nets? We propose answering this question by using ideas from causal inference. We define the ``Causal Concept Effect'' (CaCE) as the causal effect that the presence or absence of a concept has on the prediction of a given deep neural net. We then use this measure as a mean to understand what drives the network's prediction and what does not. Yet many existing interpretability methods rely solely on correlations, resulting in potentially misleading explanations. We show how CaCE can avoid such mistakes. In high-risk domains such as medicine, knowing the root cause of the prediction is crucial. If we knew that the network's prediction was caused by arbitrary concepts such as the lighting conditions in an X-ray room instead of medically meaningful concept, this would prevent us from disastrous deployment of such models. Estimating CaCE is difficult in situations where we cannot easily simulate the do-operator. As a simple solution, we propose learning a generative model, specifically a Variational AutoEncoder (VAE) on image pixels or image embeddings extracted from the classifier to measure VAE-CaCE. We show that VAE-CaCE is able to correctly estimate the true causal effect as compared to other baselines in controlled settings with synthetic and semi-natural high dimensional images.

Removing Hidden Confounding by Experimental Grounding

Observational data is increasingly used as a means for making individual-level causal predictions and intervention recommendations. The foremost challenge of causal inference from observational data is hidden confounding, whose presence cannot be tested in data and can invalidate any causal conclusion. Experimental data does not suffer from confounding but is usually limited in both scope and scale. We introduce a novel method of using limited experimental data to correct the hidden confounding in causal effect models trained on larger observational data, even if the observational data does not fully overlap with the experimental data. Our method makes strictly weaker assumptions than existing approaches, and we prove conditions under which it yields a consistent estimator. We demonstrate our method's efficacy using real-world data from a large educational experiment.

Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition

Statisticians have made great progress in creating methods that reduce our reliance on parametric assumptions. However this explosion in research has resulted in a breadth of inferential strategies that both create opportunities for more reliable inference as well as complicate the choices that an applied researcher has to make and defend. Relatedly, researchers advocating for new methods typically compare their method to at best 2 or 3 other causal inference strategies and test using simulations that may or may not be designed to equally tease out flaws in all the competing methods. The causal inference data analysis challenge, "Is Your SATT Where It's At?", launched as part of the 2016 Atlantic Causal Inference Conference, sought to make progress with respect to both of these issues. The researchers creating the data testing grounds were distinct from the researchers submitting methods whose efficacy would be evaluated. Results from 30 competitors across the two versions of the competition (black box algorithms and do-it-yourself analyses) are presented along with post-hoc analyses that reveal information about the characteristics of causal inference strategies and settings that affect performance. The most consistent conclusion was that methods that flexibly model the response surface perform better overall than methods that fail to do so. Finally new methods are proposed that combine features of several of the top-performing submitted methods.

Learning Representations for Counterfactual Inference

Observational studies are rising in importance due to the widespread accumulation of data in fields such as healthcare, education, employment and ecology. We consider the task of answering counterfactual questions such as, "Would this patient have lower blood sugar had she received a different medication?". We propose a new algorithmic framework for counterfactual inference which brings together ideas from domain adaptation and representation learning. In addition to a theoretical justification, we perform an empirical comparison with previous approaches to causal inference from observational data. Our deep learning algorithm significantly outperforms the previous state-of-the-art.

Learning Weighted Representations for Generalization Across Designs

Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from observational data and in unsupervised domain adaptation. We pose both of these problems as prediction under a shift in design. Popular methods for overcoming distributional shift make unrealistic assumptions such as having a well-specified model or knowing the policy that gave rise to the observed data. Other methods are hindered by their need for a pre-specified metric for comparing observations, or by poor asymptotic properties. We devise a bound on the generalization error under design shift, incorporating both representation learning and sample re-weighting. Based on the bound, we propose an algorithmic framework that does not require any of the above assumptions and which is asymptotically consistent. We empirically study the new framework using two synthetic datasets, and demonstrate its effectiveness compared to previous methods.

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.

Estimating individual treatment effect: generalization bounds and algorithms

There is intense interest in applying machine learning to problems of causal inference in fields such as healthcare, economics and education. In particular, individual-level causal inference has important applications such as precision medicine. We give a new theoretical analysis and family of algorithms for predicting individual treatment effect (ITE) from observational data, under the assumption known as strong ignorability. The algorithms learn a "balanced" representation such that the induced treated and control distributions look similar. We give a novel, simple and intuitive generalization-error bound showing that the expected ITE estimation error of a representation is bounded by a sum of the standard generalization-error of that representation and the distance between the treated and control distributions induced by the representation. We use Integral Probability Metrics to measure distances between distributions, deriving explicit bounds for the Wasserstein and Maximum Mean Discrepancy (MMD) distances. Experiments on real and simulated data show the new algorithms match or outperform the state-of-the-art.