When Causal Inference meets Statistical Analysis

Title: Learning, evaluating and analyzing a recommendation rule for early blood transfer in the ICU

Severely injured patients experiencing hemorrhagic shock often require massive transfusion. Early transfusion of blood products (plasma, platelets and red blood cells) is common and associated with improved outcomes in the hospital. However, determining a right amount of blood products is still a matter of scientific debate. The speaker will present and discuss a methodology to learn, evaluate and analyse a recommendation rule for early blood transfer in the ICU. The study uses data from the French Traumabase, a French observatory for Major Trauma. This is a joint work with Pan Zhao (Inria), Julie Josse (Inria), Nicolas Gatulle (APHP) and the Traumabase Group.

Title: Causal discovery and inference in time series

Time series are present in various forms in many different domains, as healthcare, Industry 4.0, monitoring systems or energy management to name but a few. Despite the presence of temporal information, discovering causal relations and identifying interventions in time series are not easy tasks, in particular when one is dealing with "incomplete" graphs. We will first discuss which causal graphs are relevant to time series and present methods to extract them from observational data and identify interventions in them.

Title: Toward causal inference from high-dimensional observations

Over the last decade, biologists have developed a multitude of tools with which we can generate high-dimensional observations of biological systems. These tools either directly measure causal variables (e.g. the expression levels of genes) or they measure unstructured proxies for the causal variables (e.g. the pixels in an image of a cell). When these high-dimensional causal variables are directly measured, the relationship with outcomes of interest typically remains confounded so we need to rely on experimentation to identify causal effects. The challenge is (1) we often cannot intervene directly on the causal variables, and instead perturb them indirectly, and (2) the number of experiments that we can practically run is typically far fewer than the number of causal variables of interest. I will discuss how we can use instrumental variable methods to estimate causal effects in this regime, and show when we can estimate the causal effect with relatively few experiments despite being underspecified. The second part of my talk will focus on representation learning which is needed when we measure unstructured proxies for the causal variables. These modalities, such as images or sensor data can often be collected cheaply in experiments, but they are challenging to use in a causal inference pipeline without extensive feature engineering or labelling to extract underlying latent factors. I will present results from a series of recent papers that describe when we can disentangle latent variables with identifiability guarantees.

Title: Causal insights from merging data sets and merging data sets via causal insights

While humans often draw causal conclusions from putting observations into the broader context of causal knowledge, AI still needs to develop these techniques. I show how causal insights can be obtained from the synergy of datasets referring to different sets of variables and argue that causal hypotheses then predict joint properties of variables that have never been observed together. This way, causal discovery becomes a prediction task in which additional variable sets play the role of additional data points in traditional iid learning. For instance, a causal DAG can be seen as a binary classifier that tells us which conditional independences are valid, which then enables a statistical learning theory for learning DAGs. I describe "Causal MaxEnt" (a modified version of MaxEnt that is asymmetric with respect to causal directions) as one potential approach to infer DAGs and properties of the joint distribution from a set of marginal distributions of subsets of variables and derive causal conclusions for toy examples.
Further reading:

• [1] Dominik Janzing: Merging joint distributions via causal model classes with low VC dimension, arxiv:1804.03206
• [2] Sergio Garrido Mejia, Elke Kirschbaum, Dominik Janzing: Obtaining causal information by merging data sets with MaxEnt. AISTATS 2022
• [3] Dominik Janzing: Causal versions of Maximum Entropy and Principle of Insufficient Reason, Journal of Causal Inference 2021.

Title: Towards Causal Deep Generative Models for Sequential Data

One of my research dreams is to build a high-resolution video generation model that enables granularity controls in e.g., the scene appearance and the interactions between objects. I tried, and then realised the need of me inventing deep learning tricks for this goal is due to the issue of non-identifiability in my sequential deep generative models. In this talk I will discuss our research towards developing identifiable deep generative models in sequence modelling, and share some recent and on-going works regarding switching dynamic models. Throughout the talk I will highlight the balance between causality "Theorist" and deep learning "Alchemist", and discuss my opinions on the future of causal deep generative modelling research.

Title: A Cautious Approach To Constraint-Based Causal Model Selection Based on Equivalence Tests

Causal graphical models are used many scientific domains to represent important causal assumptions about the processes that underlie collected data. The focus of this work is on graphical structure learning (a.k.a. causal discovery or model selection) for the “downstream” purpose of using the estimated graph for subsequent causal inference tasks, such as establishing the identifying formula for some causal effect of interest and then estimating it. An obstacle to having confidence in existing procedures in applied health science settings is that they tend to estimate structures that are overly sparse, i.e., missing too many edges. However, statistical “caution” (or “conservativism”) would err on the side of more dense graphs rather than more sparse graphs. This paper proposes to reformulate the conditional independence hypothesis tests of classical constraint-based algorithms as equivalence tests: test the null hypothesis of association greater than some (user-chosen, sample-size dependent) threshold, rather than test the null of no association. We argue this addresses several important statistical issues in applied causal model selection and leads to procedures with desirable behaviors and properties.

Title: Reliable Machine Learning with Instruments

Society is made up of a set of diverse individuals, demographic groups, and institutions. Learning and deploying algorithmic models across these heterogeneous environments face a set of various trade-offs. In order to develop reliable machine learning algorithms that can interact successfully with the real world, it is necessary to deal with such heterogeneity. In this talk, I will focus on how to employ an instrumental variable (IV) to alleviate the impact of unobserved confounders on the credibility of algorithmic decision-making and the reliability of machine learning models that are learned from observational and heterogeneous data. In particular, I will present how we can leverage tools from machine learning, namely, kernel methods and deep learning, to solve potentially ill-posed non-linear IV regression and proxy variable problems. Lastly, I will argue that a better understanding of the ways in which our data are generated and how our models can influence them will be crucial for reliable human-machine interactions, especially when gaining full information about data may not be possible.

Title: Statistical Testing under Distributional Shifts and its Application to Causality

We discuss the problem of statistical testing under distributional shifts. In such problems, we are interested in the hypothesis P in H0 for a target distribution P, but observe data from a different distribution Q. We assume that P is related to Q through a known shift tau and formally introduce hypothesis testing in this setting. We propose a general testing procedure that first resamples from the observed data to construct an auxiliary data set and then applies an existing test in the target domain. This proposal comes with theoretical guarantees. Testing under distributional shifts allows us to tackle a diverse set of problems. We argue that it may prove useful in reinforcement learning and covariate shift, we show how it reduces conditional to unconditional independence testing and we provide example applications in causal inference. This is joint work with Nikolaj Thams, Sorawit Saenkyongam, and Niklas Pfister.

Title: Learning Linear Non-Gaussian Causal Models via Higher Moment Relationships

In this talk we will discuss the problem of learning the directed graph for a linear non-Gaussian causal model. We will specifically address the cases where the graph may have cycles or there might be hidden variables. While ICA methods are able to recover the correct graph, they do not always guarantee to have found the optimal solution. Our methods are based on using specific relationships that hold among the 2nd and 3rd moments of the random vector and can help us characterize the graph. While in the acyclic case, the directed graph can be found uniquely, when cycles are allowed the graph can be learned up to an equivalence class. We give a description of all the graphs that each equivalence class consists of. We then give an algorithm based on relationships among the second and third order moments of the random vector that recovers the equivalence class of the graph, assuming the graph lies in a specific family of cyclic graphs. This is joint work in progress with Mathias Drton, Marina Garrote-Lopez, and Niko Nikov.

Title: Beyond ICA: Causal Disentanglement via Interventions

Traditional methods for representation learning, such as independent component analysis (ICA), seek representations of observed data in terms of a set of independent variables. However, human reasoning relies on variables which are not statistically independent, such as height and weight. The emerging field of causal representation learning takes the view that the variables in a representation should not be statistically independent, but rather that they should be causally autonomous. From a generative modeling perspective, we may view learning such a representation as an inference problem, which we call "causal disentanglement". In this talk, I will outline a research program which aims to build a computational and statistical theory of causal disentanglement. I will discuss initial results in this program, including our own work proving identifiability of causal representations from interventions in a linear setting. I will conclude with an overview of future applications for these methods in biology, healthcare, and human-AI interaction.

Title: Veridical data science with a case study to seek genetic drivers of a heart disease

"AI is like nuclear energy–both promising and dangerous." - Bill Gates, 2019. Data Science is a pillar of AI and has driven most of recent cutting-edge discoveries in biomedical research and beyond. Human judgment calls are ubiquitous at every step of a data science life cycle, e.g., in problem formulation, choosing data cleaning methods, predictive algorithms and data perturbations. Such judgment calls are often responsible for the "dangers" of AI. To mitigate these dangers, we introduce in this talk a framework based on three core principles: Predictability, Computability and Stability (PCS). The PCS framework unifies and expands on the ideas and best practices of statistics and machine learning. It emphasizes reality check through predictability and takes a full account of uncertainty sources in the whole data science life cycle including those from human judgment calls such as those in data curation/cleaning. PCS consists of a workflow and documentation and is supported by our software package veridical or v-flow. Moreover, we illustrate the usefulness of PCS in the development of iterative random forests (iRF) for predictable and stable non-linear interaction discovery (in collaboration with the Brown Lab at LBNL and Berkeley Statistics). Finally, in the pursuit of genetic drivers of a heart disease called hypertrophic cardiomyopathy (HCM) as a CZ Biohub project in collaboration with the Ashley Lab at Stanford Medical School and others, we use iRF and UK Biobank data to recommend gene-gene interaction targets for knock-down experiments. We then analyze the experimental data to show promising findings about genetic drivers for HCM.