Resolved inconsistencies in #308

paper/paper.bib

@@ -456,3 +456,24 @@ @article{tikka2017b
   volume       = {18},
 }
 
+@inproceedings{agrawal2024automated,
+  author    = {Agrawal, Raj and Witty, Sam and Zane, Andy and Bingham, Eli},
+  editor    = {Globerson, A. and Mackey, L. and Belgrave, D. and Fan, A. and Paquet, U. and Tomczak, J. and Zhang, C.},
+  publisher = {Curran Associates, Inc.},
+  url       = {https://proceedings.neurips.cc/paper_files/paper/2024/file/1d10fe211f5139de49f94c6f0c7cecbe-Paper-Conference.pdf},
+  booktitle = {Advances in Neural Information Processing Systems},
+  date      = {2024},
+  pages     = {16102--16132},
+  title     = {Automated Efficient Estimation using Monte Carlo Efficient Influence Functions},
+  volume    = {37},
+}
+
+@thesis{wang2023tractable,
+  author  = {Wang, Benjie},
+  url     = {https://ora.ox.ac.uk/objects/uuid:2fafc463-3a9f-40cb-a48c-e33272c691b8},
+  date    = {2023},
+  title   = {Tractable Probabilistic Models for Causal Learning and Reasoning},
+  type    = {Doctoral Dissertation},
+  urldate = {2024-01-16},
+}
+

paper/paper.md

@@ -165,13 +165,13 @@ old adage that correlation does not imply causation.
 A key step in causal inference is **causal identification** during which it is
 determined whether it is theoretically possible to estimate a causal effect from
 available data, given prior knowledge about relationships between variables and
-a causal query, such as a:
+a causal query, such as:
 
-1. **Interventional Query**, which asks: _what would happen if we intervene?_
-   For example, what would be the average effect if everyone received treatment?
-2. **Counterfactual Query**, which asks: _what would have happened to specific
-   individuals in an alternative scenario?_ For example, would a given patient,
-   who did recover, have recovered anyway without treatment?.
+1. **Interventional Query**, which asks: _what will happen if we intervene?_ For
+   example, what would be the average effect if everyone received treatment?
+2. **Counterfactual Query**, which asks: _what would have happened had we done
+   something different?_ For example, would a given patient, who recovered after
+   receiving treatment, have recovered anyway without treatment?.
 3. **Transportability Query**, which asks: _can causal findings from one
    population be validly applied to another, and if so, how can evidence from
    multiple studies or populations be combined to draw conclusions about a
@@ -183,11 +183,13 @@ queries to data from (randomized) controlled trials, observational studies, or
 mixtures thereof. $Y_0$ focuses on the qualitative investigation of causation,
 helping researchers determine _whether_ a causal relationship can be estimated
 from available data before attempting to estimate _how strong_ that relationship
-is. $Y_0$ provides a domain-specific language for expressing causal queries,
-tools for representing and manipulating graphical causal models that represent
-prior knowledge about either single or multiple populations, and implementations
-of numerous identification algorithms from the recent causal inference
-literature.
+is. Furthermore, $Y_0$ provides guidance on how to transform the causal query
+into a symbolic estimand that can be non-parametrically estimated from the
+available data. $Y_0$ provides a domain-specific language for representing
+causal queries and estimands as symbolic probabilistic expressions, tools for
+representing causal graphical models with unobserved confounders, such as
+acyclic directed mixed graphs (ADMGs), and implementations of numerous
+identification algorithms from the recent causal inference literature.
 
 # Statement of Need
 
@@ -228,11 +230,15 @@ future algorithms and workflows.
 **Probabilistic Expressions** $Y_0$ implements an internal domain-specific
 language that can capture variables, counterfactual variables, population
 variables, and probabilistic expressions in which they appear. It covers the
-three levels of Pearl's Causal Hierarchy [@bareinboim2022], including the
-probability of sufficient causation $P(Y_X \mid X^*, Y^*)$, necessary causation
-$P(Y^*_{X^*} \mid X, Y)$, and necessary and sufficient causation
-$P(Y_X, Y^*_{X^*})$. Expressions can be converted to SymPy [@meurer2017sympy] or
-LaTeX expressions and be rendered in Jupyter notebooks.
+three levels of Pearl's Causal Hierarchy [@bareinboim2022], including
+association $P(Y=y \mid
+X=x^\ast)$, represented as \texttt{P(Y | \textasciitilde
+X)}, interventions $P_{do(X=x^\ast)}(Y=y, Z=z)$, represented as
+\texttt{P[\textasciitilde X](Y,Z)} and counterfactuals
+$P(Y_{do(X=x^\ast)}=y^\ast\mid X=x, Y=y)$, represented as
+\texttt{P(\textasciitilde Y @ \textasciitilde X | X, Y)}. Expressions can be
+converted to SymPy [@meurer2017sympy] or LaTeX expressions and be rendered in
+Jupyter notebooks.
 
 **Data Structure** $Y_0$ builds on NetworkX [@hagberg2008networkx] to implement
 an (acyclic) directed mixed graph data structure, used in many identification
@@ -255,9 +261,8 @@ Verma constraints [@tian2012verma].
 algorithms of any causal inference package. It implements `ID`
 [@shpitser2006id], `IDC` [@shpitser2007idc], `ID*` [@shpitser2012idstar], `IDC*`
 [@shpitser2012idstar], surrogate outcomes (`TRSO`) [@tikka2019trso], `tian-ID`
-[@tian2010identifying], transport [@correa2020transport], counterfactual
-transport [@correa2022cftransport], and identification for causal queries over
-hierarchical causal models [@weinstein2024hierarchicalcausalmodels].
+[@tian2010identifying], transport [@correa2020transport], and counterfactual
+transport [@correa2022cftransport].
 
 # Case Study
 
@@ -280,10 +285,13 @@ cigarettes. Therefore, we add a _bidirected_ edge in \autoref{cancer}B.
 Unfortunately, `ID` can not produce an estimand for \autoref{cancer}B, which
 motivates the usage of an alternative algorithm that incorporates observational
 and/or interventional data. For example, if data from an observational study
-($\pi^{\ast}$) and data from an interventional trial on smoking ($\pi_1$) are
-available, the surrogate outcomes algorithm (`TRSO`) [@tikka2019trso] estimates
-the effect of smoking on the risk of cancer in \autoref{cancer}B as
-$\sum_{Tar} P^{\pi^{\ast}}(Cancer | Smoking, Tar) P_{\text{Smoking}}^{{\pi_1}}(Tar)$.
+associating smoking with tar and cancer ($\pi^{\ast}$) and data from a
+randomized trial studying the causal effect of smoking on tar buildup in the
+lungs ($\pi_1$) are available, the surrogate outcomes algorithm (`TRSO`)
+[@tikka2019trso] estimates the effect of smoking on the risk of cancer in
+\autoref{cancer}B as
+$\sum_{Tar} P^{\pi^{\ast}}(Cancer |
+Smoking, Tar) P_{\text{Smoking}}^{{\pi_1}}(Tar)$.
 Code and a more detailed description of this case study can be found in the
 following
 [Jupyter notebook](https://github.com/y0-causal-inference/y0/blob/main/notebooks/Surrogate%20Outcomes.ipynb).
@@ -313,29 +321,32 @@ the future. For example, the cyclic identification algorithm (`ioID`)
 realistic graphs that contain cycles, such as how biomolecular signaling
 pathways often contain feedback loops. Further, missing data identification
 algorithms can account for data that is missing not at random (MNAR) by modeling
-the underlying missingness mechanism [@mohan2021]. Several algorithms noted in
-the review by @JSSv099i05, such as generalized identification (`gID`)
-[@lee2019general] and generalized counterfactual identification (`gID*`)
-[@correa2021counterfactual], can be formulated as special cases of
-counterfactual transportability. Therefore, we plan to improve the user
-experience by exposing more powerful algorithms like counterfactual transport
-through a simplified APIs corresponding to special cases like `gID` and `gID*`.
-Similarly, we plan to implement probabilistic expression simplification
-[@tikka2017b] to improve the consistency of the estimands output from
-identification algorithms.
-
-It remains an open research question how to estimate the causal effect for an
-arbitrary estimand produced by an algorithm more sophisticated than `ID`. Two
-potential avenues for overcoming this might be a combination of the Pyro
-probabilistic programming langauge [@bingham2018pyro] and its causal inference
-extension [ChiRho](https://github.com/BasisResearch/chirho). Tractable circuits
-[@darwiche2022causalinferenceusingtractable] also present a new paradigm for
-generic estimation. Such a generalization would be a lofty achievement and
-enable the automation of downstream applications in experimental design.
+the underlying missingness mechanism [@mohan2021]. Implementing recent
+algorithms that provide sufficient conditions for identification in hierarchical
+causal models [@weinstein2024hierarchicalcausalmodels] would be useful for
+supporting causal identification in probabilistic programming languages, such as
+ChiRho. Several algorithms noted in the review by @JSSv099i05, such as
+generalized identification (`gID`) [@lee2019general] and generalized
+counterfactual identification (`gID*`) [@correa2021counterfactual], can be
+formulated as special cases of counterfactual transportability. Therefore, we
+plan to improve the user experience by exposing more powerful algorithms like
+counterfactual transport through a simplified APIs corresponding to special
+cases like `gID` and `gID*`. Similarly, we plan to implement probabilistic
+expression simplification [@tikka2017b] to improve the consistency of the
+estimands output from identification algorithms.
+
+@agrawal2024automated recently demonstrated automatically generating an
+efficient and robust estimator for causal queries more sophisticated than `ID`
+using [ChiRho](https://basisresearch.github.io/chirho/dr_learner.html), a causal
+extension of the Pyro probabilistic programming language [@bingham2018pyro]
+called. Probabilistic circuits [@darwiche2022causalinferenceusingtractable;
+@wang2023tractable] also present a new paradigm for tractable causal estimation.
+Such a generalization would enable the automation of downstream applications in
+experimental design.
 
 # Availability and Usage
 
-`y0` is available as a package on [PyPI](https://pypi.org/project/y0) with the
+$Y_0$ is available as a package on [PyPI](https://pypi.org/project/y0) with the
 source code available at
 [https://github.com/y0-causal-inference/y0](https://github.com/y0-causal-inference/y0)
 under a BSD 3-clause license, archived to Zenodo at