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Identifying causal parameters from observational data is fraught with subtleties due to the issues of selection bias and confounding. In addition, more complex questions of interest, such as effects of treatment on the treated and mediated…
Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number…
Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…
Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions --…
We study the problem of selecting covariates for unbiased estimation of the total causal effect.Existing approaches typically rely on global causal structure learning over all variables, or on strong assumptions such as causal sufficiency -…
Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose…
Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual…
The work demonstrates that brain might reflect the external world causal relationships in the form of a logically consistent and prognostic model of reality, which shows up as consciousness. The paper analyses and solves the problem of…
Structural Causal Models (SCM) are a powerful framework for describing complicated dynamics across the natural sciences. A particularly elegant way of interpreting SCMs is do-Shapley, a game-theoretic method of quantifying the average…
Causal inference is at the heart of empirical research in natural and social sciences and is critical for scientific discovery and informed decision making. The gold standard in causal inference is performing randomized controlled trials;…
Pearl observes that causal knowledge enables predicting the effects of interventions, such as actions, whereas descriptive knowledge only permits drawing conclusions from observation. This paper extends Pearl's approach to causality and…
This paper introduces Attribution Projection Calculus (AP-Calculus), a novel mathematical framework for determining causal relationships in structured Bayesian networks. We investigate a specific network architecture with source nodes…
We propose a formal language for describing and explaining statistical causality. Concretely, we define Statistical Causality Language (StaCL) for expressing causal effects and specifying the requirements for causal inference. StaCL…
Multimodal classifiers function as opaque black box models. While several techniques exist to interpret their predictions, very few of them are as intuitive and accessible as natural language explanations (NLEs). To build trust, such…
The class of problems in causal inference which seeks to isolate causal correlations solely from observational data even without interventions has come to the forefront of machine learning, neuroscience and social sciences. As new large…
Causal effect identification considers whether an interventional probability distribution can be uniquely determined without parametric assumptions from measured source distributions and structural knowledge on the generating system. While…
This paper provides a preparatory introduction to sheaves and topoi, written as a conceptual continuation of the author's earlier introduction to torsors and as preparatory background for the author's arXiv paper \emph{Grothendieck…
The ultimate goal of most scientific studies is to understand the underlying causal mechanism between the involved variables. Structural causal models (SCMs) are widely used to represent such causal mechanisms. Given an SCM, causal queries…
Across many scientific domains, practitioners rely on coarse, discretized summaries to track the evolving structure of complex systems under noise, measurement error, and changing system size. Understanding when such summaries are reliable…
A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…