The study of causal abstractions bridges two integral components of human intelligence: the ability to determine cause and effect, and the ability to interpret complex patterns into abstract concepts. Formally, causal abstraction frameworks define connections between complicated low-level causal models and simple high-level ones. One major limitation of most existing definitions is that they are not well-defined when considering lossy abstraction functions in which multiple low-level interventions can have different effects while mapping to the same high-level intervention (an assumption called the abstract invariance condition). In this paper, we introduce a new type of abstractions called projected abstractions that generalize existing definitions to accommodate lossy representations. We show how to construct a projected abstraction from the low-level model and how it translates equivalent observational, interventional, and counterfactual causal queries from low to high-level. Given that the true model is rarely available in practice we prove a new graphical criteria for identifying and estimating high-level causal queries from limited low-level data. Finally, we experimentally show the effectiveness of projected abstraction models in high-dimensional image settings.

The ability of humans to understand the world in terms of cause and effect relationships, as well as their ability to compress information into abstract concepts, are two hallmark features of human intelligence. These two topics have been studied in tandem under the theory of causal abstractions, but it is an open problem how to best leverage abstraction theory in real-world causal inference tasks, where the true model is not known, and limited data is available in most practical settings. In this paper, we focus on a family of causal abstractions constructed by clustering variables and their domains, redefining abstractions to be amenable to individual causal distributions. We show that such abstractions can be learned in practice using Neural Causal Models, allowing us to utilize the deep learning toolkit to solve causal tasks (identification, estimation, sampling) at different levels of abstraction granularity. Finally, we show how representation learning can be used to learn abstractions, which we apply in our experiments to scale causal inferences to high dimensional settings such as with image data.

Visual representations underlie object recognition tasks, but they often contain both robust and non-robust features. Our main observation is that image classifiers may perform poorly on out-of-distribution samples because spurious correlations between non-robust features and labels can be changed in a new environment. By analyzing procedures for out-of-distribution generalization with a causal graph, we show that standard classifiers fail because the association between images and labels is not transportable across settings. However, we then show that the causal effect, which severs all sources of confounding, remains invariant across domains. This motivates us to develop an algorithm to estimate the causal effect for image classification, which is transportable (i.e., invariant) across source and target environments. Without observing additional variables, we show that we can derive an estimand for the causal effect under empirical assumptions using representations in deep models as proxies. Theoretical analysis, empirical results, and visualizations show that our approach captures causal invariances and improves overall generalization.

One of the central elements of any causal inference is an object called structural causal model (SCM), which represents a collection of mechanisms and exogenous sources of random variation of the system under investigation (Pearl, 2000). An important property of many kinds of neural networks is universal approximability: the ability to approximate any function to arbitrary precision. Given this property, one may be tempted to surmise that a collection of neural nets is capable of learning any SCM by training on data generated by that SCM. In this paper, we show this is not the case by disentangling the notions of expressivity and learnability. Specifically, we show that the causal hierarchy theorem (Thm. 1, Bareinboim et al., 2020), which describes the limits of what can be learned from data, still holds for neural models. For instance, an arbitrarily complex and expressive neural net is unable to predict the effects of interventions given observational data alone. Given this result, we introduce a special type of SCM called a neural causal model (NCM), and formalize a new type of inductive bias to encode structural constraints necessary for performing causal inferences. Building on this new class of models, we focus on solving two canonical tasks found in the literature known as causal identification and estimation. Leveraging the neural toolbox, we develop an algorithm that is both sufficient and necessary to determine whether a causal effect can be learned from data (i.e., causal identifiability); it then estimates the effect whenever identifiability holds (causal estimation). Simulations corroborate the proposed approach.

BACKGROUND: MicroRNAs (miRNAs) are approximately 22-nucleotide long regulatory RNA that mediate RNA interference by binding to cognate mRNA target regions. Here, we present a distributed kernel SVM-based binary classification scheme to predict miRNA targets. It captures the spatial profile of miRNA-mRNA interactions via smooth B-spline curves. This is accomplished separately for various input features, such as thermodynamic and sequence-based features. Further, we use a principled approach to uniformly model both canonical and non-canonical seed matches, using a novel seed enrichment metric. Finally, we verify our miRNA-mRNA pairings using an Elastic Net-based regression model on TCGA expression data for four cancer types to estimate the miRNAs that together regulate any given mRNA. RESULTS: We present a suite of algorithms for miRNA target prediction, under the banner Avishkar, with superior prediction performance over the competition. Specifically, our final kernel SVM model, with an Apache Spark backend, achieves an average true positive rate (TPR) of more than 75 percent, when keeping the false positive rate of 20 percent, for non-canonical human miRNA target sites. This is an improvement of over 150 percent in the TPR for non-canonical sites, over the best-in-class algorithm. We are able to achieve such superior performance by representing the thermodynamic and sequence profiles of miRNA-mRNA interaction as curves, devising a novel seed enrichment metric, and learning an ensemble of miRNA family-specific kernel SVM classifiers. We provide an easy-to-use system for large-scale interactive analysis and prediction of miRNA targets. All operations in our system, namely candidate set generation, feature generation and transformation, training, prediction, and computing performance metrics are fully distributed and are scalable. CONCLUSIONS: We have developed an efficient SVM-based model for miRNA target prediction using recent CLIP-seq data, demonstrating superior performance, evaluated using ROC curves for different species (human or mouse), or different target types (canonical or non-canonical). We analyzed the agreement between the target pairings using CLIP-seq data and using expression data from four cancer types. To the best of our knowledge, we provide the first distributed framework for miRNA target prediction based on Apache Hadoop and Spark. AVAILABILITY: All source code and sample data are publicly available at https://bitbucket.org/cellsandmachines/avishkar. Our scalable implementation of kernel SVM using Apache Spark, which can be used to solve large-scale non-linear binary classification problems, is available at https://bitbucket.org/cellsandmachines/kernelsvmspark.