docs

Author: felixleopoldo

docs/source/available_structure_learning_algorithms.rst

@@ -30,6 +30,7 @@ Algorithms
     structure_learning_algorithms/bnlearn_sihitonpc
     structure_learning_algorithms/bnlearn_tabu
     structure_learning_algorithms/causaldag_gsp
+    structure_learning_algorithms/causallearn_ges
     structure_learning_algorithms/causallearn_grasp
     structure_learning_algorithms/corr_thresh
     structure_learning_algorithms/dualpc

docs/source/examples.rst

@@ -1,7 +1,7 @@
 .. _examples:
 
-Example studies
-########################
+Causal discovery examples
+#################################
 
 .. include:: example_conf.rst
 

docs/source/structure_learning_algorithms/huge_glasso.rst

@@ -3,7 +3,7 @@
 
     .. meta::
         :title: Graphical lasso 
-        :description: Abstract: We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data in the form of an undirected graph called the unconditional dependence graph. We show that unconditional dependence graphs of Bayesian networks correspond to the graphs having equal independence and intersection numbers. Using this observation, a Gröbner basis for a toric ideal associated to unconditional dependence graphs of Bayesian networks is given and then extended by additional binomial relations to connect the space of all such graphs. An MCMC method, called GrUES (Gröbner-based Unconditional Equivalence Search), is implemented based on the resulting moves and applied to synthetic Gaussian data. GrUES recovers the true marginal independence structure via a penalized maximum likelihood or MAP estimate at a higher rate than simple independence tests while also yielding an estimate of the posterior, for which the 20% HPD credible sets include the true structure at a high rate for data-generating graphs with density at least 0.5.  .. rubric:: Example  Config file: `grues_vs_corr-thresh.json <https://github.com/felixleopoldo/benchpress/blob/master/workflow/rules/structure_learning_algorithms/grues/grues_vs_corr-thresh.json>`_  Command:  .. code:: bash      snakemake --cores all --use-singularity --configfile workflow/rules/structure_learning_algorithms/grues/grues_vs_corr-thresh.json  :numref:`roc_grues_vs_thresh` shows the ROC and :numref:`shd_grues_vs_thresh` shows the SHD comparing GrUES to correlation thresholding for datsets from five different graphs corresponding to a 5-variable random Gaussian SEM whose nodes have average degree of 1 and whose edge weights were allowed to be close to 0. Each dataset contains 300 observations and each Markov chain has 10000 observations. Note that SHD between a learned UDG and true CPDAG is not the most reasonable comparison because an inflated FPR will be reported---see :footcite:t:`grues2023` for discussion and a more reasonable benchmark.  :numref:`adj_grues` shows that GrUES estimates the correct `UDG <https://arxiv.org/pdf/2210.00822.pdf#subsection.2.2>`__ while correlation thresholding (:numref:`adj_thresh`) misses the edge `1---2`.   .. _roc_grues_vs_thresh:  .. figure:: ../../../workflow/rules/structure_learning_algorithms/grues/images/roc.png     :width: 320     :alt: ROC (FPR vs. TPR) GrUES vs corr_thresh example     :align: left      ROC of GrUES vs corr_thresh.  .. _shd_grues_vs_thresh:  .. figure:: ../../../workflow/rules/structure_learning_algorithms/grues/images/shd.png     :width: 320     :alt: SHD GrUES vs corr_thresh example     :align: right      SHD of GrUES vs corr_thresh.  .. _adj_grues:  .. figure:: ../../../workflow/rules/structure_learning_algorithms/grues/images/diffplot_30.png     :width: 320     :alt: adjacency matrix GrUES example     :align: left      Adj mat learned by GrUES.  .. _adj_thresh:  .. figure:: ../../../workflow/rules/structure_learning_algorithms/grues/images/diffplot_15.png     :width: 320     :alt: adjacency matrix corr_thresh example     :align: right      Adj mat learned by corr_thresh. 
+        :description: Abstract: We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm—the graphical lasso—that is remarkably fast: It solves a 1000-node problem (∼500000 parameters) in at most a minute and is 30–4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.
 
 
 .. _huge_glasso: 
@@ -37,60 +37,7 @@ huge_glasso
 
 .. rubric:: Description
 
-Abstract:
-We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data in the form of an undirected graph called the unconditional dependence graph. We show that unconditional dependence graphs of Bayesian networks correspond to the graphs having equal independence and intersection numbers. Using this observation, a Gröbner basis for a toric ideal associated to unconditional dependence graphs of Bayesian networks is given and then extended by additional binomial relations to connect the space of all such graphs. An MCMC method, called GrUES (Gröbner-based Unconditional Equivalence Search), is implemented based on the resulting moves and applied to synthetic Gaussian data. GrUES recovers the true marginal independence structure via a penalized maximum likelihood or MAP estimate at a higher rate than simple independence tests while also yielding an estimate of the posterior, for which the 20% HPD credible sets include the true structure at a high rate for data-generating graphs with density at least 0.5.
-
-.. rubric:: Example
-
-Config file: `grues_vs_corr-thresh.json <https://github.com/felixleopoldo/benchpress/blob/master/workflow/rules/structure_learning_algorithms/grues/grues_vs_corr-thresh.json>`_
-
-Command:
-
-.. code:: bash
-
-    snakemake --cores all --use-singularity --configfile workflow/rules/structure_learning_algorithms/grues/grues_vs_corr-thresh.json
-
-:numref:`roc_grues_vs_thresh` shows the ROC and :numref:`shd_grues_vs_thresh` shows the SHD comparing GrUES to correlation thresholding for datsets from five different graphs corresponding to a 5-variable random Gaussian SEM whose nodes have average degree of 1 and whose edge weights were allowed to be close to 0. Each dataset contains 300 observations and each Markov chain has 10000 observations. Note that SHD between a learned UDG and true CPDAG is not the most reasonable comparison because an inflated FPR will be reported---see :footcite:t:`grues2023` for discussion and a more reasonable benchmark.
-
-:numref:`adj_grues` shows that GrUES estimates the correct `UDG <https://arxiv.org/pdf/2210.00822.pdf#subsection.2.2>`__ while correlation thresholding (:numref:`adj_thresh`) misses the edge `1---2`.
-
-
-.. _roc_grues_vs_thresh:
-
-.. figure:: ../../../workflow/rules/structure_learning_algorithms/grues/images/roc.png
-    :width: 320
-    :alt: ROC (FPR vs. TPR) GrUES vs corr_thresh example
-    :align: left
-
-    ROC of GrUES vs corr_thresh.
-
-.. _shd_grues_vs_thresh:
-
-.. figure:: ../../../workflow/rules/structure_learning_algorithms/grues/images/shd.png
-    :width: 320
-    :alt: SHD GrUES vs corr_thresh example
-    :align: right
-
-    SHD of GrUES vs corr_thresh.
-
-.. _adj_grues:
-
-.. figure:: ../../../workflow/rules/structure_learning_algorithms/grues/images/diffplot_30.png
-    :width: 320
-    :alt: adjacency matrix GrUES example
-    :align: left
-
-    Adj mat learned by GrUES.
-
-.. _adj_thresh:
-
-.. figure:: ../../../workflow/rules/structure_learning_algorithms/grues/images/diffplot_15.png
-    :width: 320
-    :alt: adjacency matrix corr_thresh example
-    :align: right
-
-    Adj mat learned by corr_thresh.
-
+Abstract: We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm—the graphical lasso—that is remarkably fast: It solves a 1000-node problem (∼500000 parameters) in at most a minute and is 30–4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.
 
 .. rubric:: Some fields described 
 * ``lambda`` A positive number to control the regularization. Typical usage is to leave the input lambda: null and have the program compute its own.