Causality without Estimands: from Causal Estimation to Black-Box Introspection

Abstract

[eng] The notion of cause and effect is fundamental to our understanding of the real world; ice cream sales correlate with jellyfish stings (both increase during summer), but a ban on ice cream could hardly stop jellyfishes. This discrepancy between the patterns that we observe and the results of our actions is essential: without causal knowledge we are mere spectators of the world, unable to understand its inner workings, enact effective change, explain which factors were responsible for a specific outcome or imagine potential scenarios resulting from alternative decisions.

The field of statistics has traditionally stayed in the realm of observations, powerless in the measurement of causal effects unless by performing randomized experiments. These consist of dividing a set of individuals in two groups at random and assigning a certain action/treatment to each subgroup, to then compare the outcomes of both. This could be applied, for instance, to measure the impact of large-scale advertisement campaigns on sales, test the effects of smoking on the development of lung cancer, or determine the influence of new pedagogical strategies on eventual career success. However, randomized experiments are not always feasible, as is the case in these examples, due to economic, ethical or timing concerns.

Causal Inference is the field that studies how to circumvent this problem: only using observational data, not subject to randomization, it allows us to measure causal effects. Even so, the standard approach for Causal Estimation (CE), estimand-based methods, results in ad hoc models that cannot extrapolate to other datasets with different causal relationships, and often require training a new model every time we want to answer a different query on the same dataset. Contrary to this perspective, estimand-agnostic approaches train a model of the observational distribution that acts as a proxy of the underlying mechanism that generated the data; this model needs to be trained only once and can answer any identifiable queries reliably. However, this latter approach has seldom been studied, primarily because of the difficulty of defining a good model of the target distribution satisfying every causal requirement while still flexible enough to answer the desired causal queries.

This dissertation is focused on the definition of a general estimand-agnostic CE framework, Deep Causal Graphs, that can leverage the expressive modelling capabilities of Neural Networks and Normalizing Flows while still providing a flexible and comprehensive estimation toolkit for all kinds of causal queries. We will contrast its capabilities against other estimand-agnostic approaches and measure its performance in comparison with the state of the art in Causal Query Estimation.

Finally, we will also illustrate the connection between CE and Machine Learning Interpretability, Explainability and Fairness: since the examination of black-boxes often requires to answer many causal queries (e.g., what is the effect of each input variable on the outcome, or how would the outcome have changed had we intervened on a certain input), estimand-based techniques would force us to train as many different models; in contrast, estimand-agnostic frameworks allow us to ask as many questions as needed with just a single trained model, and therefore are essential for this kind of application.