Towards Bounding Causal Effects under Markov Equivalence

Predicting the effect of unseen interventions is a fundamental research question across the data sciences. It is well established that, in general, such questions cannot be answered definitively from observational data, e.g., as a consequence of unobserved confounding. A generalization of this task is to determine non-trivial bounds on causal effects induced by the data, also known as the task of partial causal identification. In the literature, several algorithms have been developed for solving this problem. Most, however, require a known parametric form or a fully specified causal diagram as input, which is usually not available in practical applications. In this paper, we assume as input a less informative structure known as a Partial Ancestral Graph, which represents a Markov equivalence class of causal diagrams and is learnable from observational data. In this more "data-driven" setting, we provide a systematic algorithm to derive bounds on causal effects that can be computed analytically

Hypothesis testing and causal inference with heterogeneous medical data

Learning from data which associations hold and are likely to hold in the future is a fundamental part of scientific discovery. With increasingly heterogeneous data collection practices, exemplified by passively collected electronic health records or high-dimensional genetic data with only few observed samples, biases and spurious correlations are prevalent. These are called spurious because they do not contribute to the effect being studied. In this context, the modelling assumptions of existing statistical tests and causal inference methods are often found inadequate and their practical utility diminished even though these models are increasingly used as decision-support tools in practice. This thesis investigates how modern computational techniques may broaden the fields of hypothesis testing and causal inference to handle the subtleties of large heterogeneous data sets, as well as simultaneously improve the robustness and theoretical understanding of machine learning algorithms using insights from causality and statistics. The first part of this thesis is concerned with hypothesis testing. We develop a framework for hypothesis testing on set-valued data, a representation that faithfully describes many real-world phenomena including patient biomarker trajectories in the hospital. Using similar techniques, we develop next a two-sample test for making inference on selection-biased data, in the sense that not all individuals are equally likely to be included in the study, a fact that biases tests if not accounted for and if the desideratum is to obtain conclusions that are generally applicable. We conclude this section with an investigation of conditional independence in high-dimensional data, such as found in gene expression data, and propose a test using generative adversarial networks. The second part of this thesis is concerned with causal inference and discovery, with a special focus on the influence of unobserved confounders that distort the observed associations between variables and yet may not be ruled out or adjusted for using data alone. We start by demonstrating that unobserved confounders may bias substantially the generalization performance of machine learning algorithms trained with conventional learning paradigms such as empirical risk minimization. Acknowledging this spurious effect, we develop a new learning principle inspired by causal insights that provably generalizes to test data sampled from a larger set of distributions different from the training distribution. In the last chapter we consider the influence of unobserved confounders for causal discovery. We show that with some assumptions on the type and influence on the nature of unobserved confounding one may develop provably consistent causal discovery algorithms, formulated as a solution to a continuous optimization program

Functional Causal Bayesian Optimization

We propose functional causal Bayesian optimization (fCBO), a method for finding interventions that optimize a target variable in a known causal graph. fCBO extends the CBO family of methods to enable functional interventions, which set a variable to be a deterministic function of other variables in the graph. fCBO models the unknown objectives with Gaussian processes whose inputs are defined in a reproducing kernel Hilbert space, thus allowing to compute distances among vector-valued functions. In turn, this enables to sequentially select functions to explore by maximizing an expected improvement acquisition functional while keeping the typical computational tractability of standard BO settings. We introduce graphical criteria that establish when considering functional interventions allows attaining better target effects, and conditions under which selected interventions are also optimal for conditional target effects. We demonstrate the benefits of the method in a synthetic and in a real-world causal graph

Navigating distance learning technologies using team teaching

In 2004, the American Association of Colleges of Nursing (AACN) adopted the position to move the current level of preparation necessary for advanced practice nurse (APN) roles from the master\u27s degree to the doctoral level. AACN also called for educating APNs and other nurses seeking top leadership and clinical roles in Doctor of Nursing Practice (DNP) Programs. In September 2007, the Jefferson School of Nursing welcomed its first cohort of 18 DNP students. Students represented a wide variety of practice specialties including acute care, primary care, healthcare administration, population health, education and industry. Twenty students comprise the second cohort entering in September 2008. Nationwide, Jefferson is one of 79 schools of nursing offering a DNP degree