David Watson

David S. Watson, Joshua O'Hara, Niek Tax et al.

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has received relatively little attention. We adapt the popular Shapley value framework to explain various types of predictive uncertainty, quantifying each feature's contribution to the conditional entropy of individual model outputs. We consider games with modified characteristic functions and find deep connections between the resulting Shapley values and fundamental quantities from information theory and conditional independence testing. We outline inference procedures for finite sample error rate control with provable guarantees, and implement efficient algorithms that perform well in a range of experiments on real and simulated data. Our method has applications to covariate shift detection, active learning, feature selection, and active feature-value acquisition.

Jakob Mokander, Prathm Juneja, David Watson et al.

On the whole, the U.S. Algorithmic Accountability Act of 2022 (US AAA) is a pragmatic approach to balancing the benefits and risks of automated decision systems. Yet there is still room for improvement. This commentary highlights how the US AAA can both inform and learn from the European Artificial Intelligence Act (EU AIA).

Jakob Mokander, Margi Sheth, David Watson et al.

Organisations that design and deploy artificial intelligence (AI) systems increasingly commit themselves to high-level, ethical principles. However, there still exists a gap between principles and practices in AI ethics. One major obstacle organisations face when attempting to operationalise AI Ethics is the lack of a well-defined material scope. Put differently, the question to which systems and processes AI ethics principles ought to apply remains unanswered. Of course, there exists no universally accepted definition of AI, and different systems pose different ethical challenges. Nevertheless, pragmatic problem-solving demands that things should be sorted so that their grouping will promote successful actions for some specific end. In this article, we review and compare previous attempts to classify AI systems for the purpose of implementing AI governance in practice. We find that attempts to classify AI systems found in previous literature use one of three mental model. The Switch, i.e., a binary approach according to which systems either are or are not considered AI systems depending on their characteristics. The Ladder, i.e., a risk-based approach that classifies systems according to the ethical risks they pose. And the Matrix, i.e., a multi-dimensional classification of systems that take various aspects into account, such as context, data input, and decision-model. Each of these models for classifying AI systems comes with its own set of strengths and weaknesses. By conceptualising different ways of classifying AI systems into simple mental models, we hope to provide organisations that design, deploy, or regulate AI systems with the conceptual tools needed to operationalise AI governance in practice.

David S. Watson, Kristin Blesch, Jan Kapar et al.

We propose methods for density estimation and data synthesis using a novel form of unsupervised random forests. Inspired by generative adversarial networks, we implement a recursive procedure in which trees gradually learn structural properties of the data through alternating rounds of generation and discrimination. The method is provably consistent under minimal assumptions. Unlike classic tree-based alternatives, our approach provides smooth (un)conditional densities and allows for fully synthetic data generation. We achieve comparable or superior performance to state-of-the-art probabilistic circuits and deep learning models on various tabular data benchmarks while executing about two orders of magnitude faster on average. An accompanying $\texttt{R}$ package, $\texttt{arf}$, is available on $\texttt{CRAN}$.

Kristin Blesch, David S. Watson, Marvin N. Wright

Despite the popularity of feature importance (FI) measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analyzing a variable's importance before and after adjusting for covariates - i.e., between $\textit{marginal}$ and $\textit{conditional}$ measures. Our work draws attention to this rarely acknowledged, yet crucial distinction and showcases its implications. Further, we reveal that for testing conditional FI, only few methods are available and practitioners have hitherto been severely restricted in method application due to mismatching data requirements. Most real-world data exhibits complex feature dependencies and incorporates both continuous and categorical data (mixed data). Both properties are oftentimes neglected by conditional FI measures. To fill this gap, we propose to combine the conditional predictive impact (CPI) framework with sequential knockoff sampling. The CPI enables conditional FI measurement that controls for any feature dependencies by sampling valid knockoffs - hence, generating synthetic data with similar statistical properties - for the data to be analyzed. Sequential knockoffs were deliberately designed to handle mixed data and thus allow us to extend the CPI approach to such datasets. We demonstrate through numerous simulations and a real-world example that our proposed workflow controls type I error, achieves high power and is in line with results given by other conditional FI measures, whereas marginal FI metrics result in misleading interpretations. Our findings highlight the necessity of developing statistically adequate, specialized methods for mixed data.

Gecia Bravo-Hermsdorff, David S. Watson, Jialin Yu et al.

One of the goals of causal inference is to generalize from past experiments and observational data to novel conditions. While it is in principle possible to eventually learn a mapping from a novel experimental condition to an outcome of interest, provided a sufficient variety of experiments is available in the training data, coping with a large combinatorial space of possible interventions is hard. Under a typical sparse experimental design, this mapping is ill-posed without relying on heavy regularization or prior distributions. Such assumptions may or may not be reliable, and can be hard to defend or test. In this paper, we take a close look at how to warrant a leap from past experiments to novel conditions based on minimal assumptions about the factorization of the distribution of the manipulated system, communicated in the well-understood language of factor graph models. A postulated $\textit{interventional factor model}$ (IFM) may not always be informative, but it conveniently abstracts away a need for explicitly modeling unmeasured confounding and feedback mechanisms, leading to directly testable claims. Given an IFM and datasets from a collection of experimental regimes, we derive conditions for identifiability of the expected outcomes of new regimes never observed in these training data. We implement our framework using several efficient algorithms, and apply them on a range of semi-synthetic experiments.

David S. Watson, Ricardo Silva

Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or extreme sparsity constraints. We relax these assumptions and focus on an important but more specialized problem, namely recovering the causal order among a subgraph of variables known to descend from some (possibly large) set of confounding covariates, i.e. a $\textit{confounder blanket}$. This is useful in many settings, for example when studying a dynamic biomolecular subsystem with genetic data providing background information. Under a structural assumption called the $\textit{confounder blanket principle}$, which we argue is essential for tractable causal discovery in high dimensions, our method accommodates graphs of low or high sparsity while maintaining polynomial time complexity. We present a structure learning algorithm that is provably sound and complete with respect to a so-called $\textit{lazy oracle}$. We design inference procedures with finite sample error control for linear and nonlinear systems, and demonstrate our approach on a range of simulated and real-world datasets. An accompanying $\texttt{R}$ package, $\texttt{cbl}$, is available from $\texttt{CRAN}$.

David S. Watson, Marvin N. Wright

We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of Candès et al. (2018), we develop a novel testing procedure that works in conjunction with any valid knockoff sampler, supervised learning algorithm, and loss function. The CPI can be efficiently computed for high-dimensional data without any sparsity constraints. We demonstrate convergence criteria for the CPI and develop statistical inference procedures for evaluating its magnitude, significance, and precision. These tests aid in feature and model selection, extending traditional frequentist and Bayesian techniques to general supervised learning tasks. The CPI may also be applied in causal discovery to identify underlying multivariate graph structures. We test our method using various algorithms, including linear regression, neural networks, random forests, and support vector machines. Empirical results show that the CPI compares favorably to alternative variable importance measures and other nonparametric tests of conditional independence on a diverse array of real and simulated datasets. Simulations confirm that our inference procedures successfully control Type I error and achieve nominal coverage probability. Our method has been implemented in an R package, cpi, which can be downloaded from https://github.com/dswatson/cpi.

David S. Watson, Jordan Penn, Lee M. Gunderson et al.

Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the $\textit{exclusion criterion}$, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides $\textit{partial}$ identification in linear systems given a set of $\textit{leaky instruments}$, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art. An accompanying $\texttt{R}$ package, $\texttt{leakyIV}$, is available from $\texttt{CRAN}$.

Matthew Shorvon, Frederik Mallmann-Trenn, David S. Watson

Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard even under many common structural constraints and approximation schemes. We introduce $\mathit{probably\ approximately\ correct}$ (PAC) algorithms for MAP inference that provide provably optimal solutions under variable and fixed computational budgets. We characterize tractability conditions for PAC-MAP using information theoretic measures that can be estimated from finite samples. Our PAC-MAP solvers are efficiently implemented using probabilistic circuits with appropriate architectures. The randomization strategies we develop can be used either as standalone MAP inference techniques or to improve on popular heuristics, fortifying their solutions with rigorous guarantees. Experiments confirm the benefits of our method in a range of benchmarks.

Pegah Golchian, Jan Kapar, David S. Watson et al.

Handling missing values is a common challenge in biostatistical analyses, typically addressed by imputation methods. We propose a novel, fast, and easy-to-use imputation method called missing value imputation with adversarial random forests (MissARF), based on generative machine learning, that provides both single and multiple imputation. MissARF employs adversarial random forest (ARF) for density estimation and data synthesis. To impute a missing value of an observation, we condition on the non-missing values and sample from the estimated conditional distribution generated by ARF. Our experiments demonstrate that MissARF performs comparably to state-of-the-art single and multiple imputation methods in terms of imputation quality and fast runtime with no additional costs for multiple imputation.

Binh Duc Vu, Jan Kapar, Marvin Wright et al.

We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally represents relationships in the data. We provide exact and approximate solutions to the decoding problem via constrained optimization, split relabeling, and nearest neighbors regression. These methods effectively invert the compression pipeline, establishing a map from the embedding space back to the input space using splits learned by the ensemble's constituent trees. The resulting decoders are universally consistent under common regularity assumptions. The procedure works with supervised or unsupervised models, providing a window into conditional or joint distributions. We demonstrate various applications of this autoencoder, including powerful new tools for visualization, compression, clustering, and denoising. Experiments illustrate the ease and utility of our method in a wide range of settings, including tabular, image, and genomic data.

Stephen Asiedu, David Watson

Causal discovery in multi-omic datasets is crucial for understanding the bigger picture of gene regulatory mechanisms, but remains challenging due to high dimensionality, differentiation of direct from indirect relationships, and hidden confounders. We introduce GENESIS (GEne Network inference from Expression SIgnals and SNPs), a constraint-based algorithm that leverages the natural causal precedence of genotypes to infer ancestral relationships in transcriptomic data. Unlike traditional causal discovery methods that start with a fully connected graph, GENESIS initialises an empty ancestrality matrix and iteratively populates it with direct, indirect or non-causal relationships using a series of provably sound marginal and conditional independence tests. By integrating genotypes as fixed causal anchors, GENESIS provides a principled ``head start'' to classical causal discovery algorithms, restricting the search space to biologically plausible edges. We test GENESIS on synthetic and real-world genomic datasets. This framework offers a powerful avenue for uncovering causal pathways in complex traits, with promising applications to functional genomics, drug discovery, and precision medicine.

Kirtan Padh, Jakob Zeitler, David Watson et al.

Causal effect estimation is important for many tasks in the natural and social sciences. We design algorithms for the continuous partial identification problem: bounding the effects of multivariate, continuous treatments when unmeasured confounding makes identification impossible. Specifically, we cast causal effects as objective functions within a constrained optimization problem, and minimize/maximize these functions to obtain bounds. We combine flexible learning algorithms with Monte Carlo methods to implement a family of solutions under the name of stochastic causal programming. In particular, we show how the generic framework can be efficiently formulated in settings where auxiliary variables are clustered into pre-treatment and post-treatment sets, where no fine-grained causal graph can be easily specified. In these settings, we can avoid the need for fully specifying the distribution family of hidden common causes. Monte Carlo computation is also much simplified, leading to algorithms which are more computationally stable against alternatives.

David S. Watson

Explaining the predictions of opaque machine learning algorithms is an important and challenging task, especially as complex models are increasingly used to assist in high-stakes decisions such as those arising in healthcare and finance. Most popular tools for post-hoc explainable artificial intelligence (XAI) are either insensitive to context (e.g., feature attributions) or difficult to summarize (e.g., counterfactuals). In this paper, I introduce $\textit{rational Shapley values}$, a novel XAI method that synthesizes and extends these seemingly incompatible approaches in a rigorous, flexible manner. I leverage tools from decision theory and causal modeling to formalize and implement a pragmatic approach that resolves a number of known challenges in XAI. By pairing the distribution of random variables with the appropriate reference class for a given explanation task, I illustrate through theory and experiments how user goals and knowledge can inform and constrain the solution set in an iterative fashion. The method compares favorably to state of the art XAI tools in a range of quantitative and qualitative comparisons.

Limor Gultchin, David S. Watson, Matt J. Kusner et al.

We examine the problem of causal response estimation for complex objects (e.g., text, images, genomics). In this setting, classical \emph{atomic} interventions are often not available (e.g., changes to characters, pixels, DNA base-pairs). Instead, we only have access to indirect or \emph{crude} interventions (e.g., enrolling in a writing program, modifying a scene, applying a gene therapy). In this work, we formalize this problem and provide an initial solution. Given a collection of candidate mediators, we propose (a) a two-step method for predicting the causal responses of crude interventions; and (b) a testing procedure to identify mediators of crude interventions. We demonstrate, on a range of simulated and real-world-inspired examples, that our approach allows us to efficiently estimate the effect of crude interventions with limited data from new treatment regimes.

David Watson, Limor Gultchin, Ankur Taly et al.

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence (XAI), a fast-growing research area that is so far lacking in firm theoretical foundations. Building on work in logic, probability, and causality, we establish the central role of necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We provide a sound and complete algorithm for computing explanatory factors with respect to a given context, and demonstrate its flexibility and competitive performance against state of the art alternatives on various tasks.

David Kinney, David Watson

Discovering high-level causal relations from low-level data is an important and challenging problem that comes up frequently in the natural and social sciences. In a series of papers, Chalupka et al. (2015, 2016a, 2016b, 2017) develop a procedure for causal feature learning (CFL) in an effort to automate this task. We argue that CFL does not recommend coarsening in cases where pragmatic considerations rule in favor of it, and recommends coarsening in cases where pragmatic considerations rule against it. We propose a new technique, pragmatic causal feature learning (PCFL), which extends the original CFL algorithm in useful and intuitive ways. We show that PCFL has the same attractive measure-theoretic properties as the original CFL algorithm. We compare the performance of both methods through theoretical analysis and experiments.