From 1653feeda6f377c8dcb38dcaead476eea8f188ee Mon Sep 17 00:00:00 2001
From: Jake Crawford <jjc2718@gmail.com>
Date: Thu, 17 Aug 2023 16:06:59 -0400
Subject: [PATCH 1/3] add penn template and edit metadata

---
 .github/workflows/manubot.yaml                |   1 +
 build/pandoc/defaults/docx.yaml               |   2 +-
 build/themes/upenn-dissertation-template.docx | Bin 0 -> 33277 bytes
 content/02.delete-me.md                       | 295 ------------------
 content/02.introduction.md                    |   7 +
 content/metadata.yaml                         |  37 +--
 6 files changed, 22 insertions(+), 320 deletions(-)
 create mode 100644 build/themes/upenn-dissertation-template.docx
 delete mode 100644 content/02.delete-me.md
 create mode 100644 content/02.introduction.md

diff --git a/.github/workflows/manubot.yaml b/.github/workflows/manubot.yaml
index 1ef5e98..4e93327 100644
--- a/.github/workflows/manubot.yaml
+++ b/.github/workflows/manubot.yaml
@@ -45,6 +45,7 @@ jobs:
       # Set SPELLCHECK to true/false for whether to check spelling in this action.
       # For workflow dispatch jobs, this SPELLCHECK setting will be overridden by the user input.
       SPELLCHECK: true
+      BUILD_DOCX: true
     defaults:
       run:
         shell: bash --login {0}
diff --git a/build/pandoc/defaults/docx.yaml b/build/pandoc/defaults/docx.yaml
index b8f2f93..9a4ff0b 100644
--- a/build/pandoc/defaults/docx.yaml
+++ b/build/pandoc/defaults/docx.yaml
@@ -2,7 +2,7 @@
 # Load on top of common defaults.
 to: docx
 output-file: output/manuscript.docx
-reference-doc: build/themes/default.docx
+reference-doc: build/themes/upenn-dissertation-template.docx
 resource-path:
  - '.'
  - content
diff --git a/build/themes/upenn-dissertation-template.docx b/build/themes/upenn-dissertation-template.docx
new file mode 100644
index 0000000000000000000000000000000000000000..095ba564fed699abd55dc75177aec4664e9e5539
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diff --git a/content/02.delete-me.md b/content/02.delete-me.md
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@@ -1,295 +0,0 @@
-This manuscript is a template (aka "rootstock") for [Manubot](https://manubot.org/ "Manubot"), a tool for writing scholarly manuscripts.
-Use this template as a starting point for your manuscript.
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-> I took the one less traveled by,  
-> And that has made all the difference.
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-
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-    # a string too long to fit within page:
-    assert doi == "10.25313/2524-2695-2018-3-vliyanie-enhansera-copia-i-insulyatora-gypsy-na-sintez-ernk-modifikatsii-hromatina-i-svyazyvanie-insulyatornyh-belkov-vtransfetsirovannyh-geneticheskih-konstruktsiyah"
-```
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-Exporting PDF manuscript
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-## Figures
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-
-![
-**An image too wide to fit within page at full size.**
-Loaded from a specific (hashed) version of the image on GitHub.
-](https://github.com/manubot/resources/raw/15493970f8882fce22bef829619d3fb37a613ba5/test/wide.png "Wide image"){#fig:wide-image}
-
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-Loaded from a specific (hashed) version of the image on GitHub.
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-
-![
-**A vector `.svg` image loaded from GitHub.**
-The parameter `sanitize=true` is necessary to properly load SVGs hosted via GitHub URLs.
-White background specified to serve as a backdrop for transparent sections of the image.
-Note that if you want to export to Word (`.docx`), you need to download the image and reference it locally (e.g. `content/images/vector.svg`) instead of using a URL.
-](https://raw.githubusercontent.com/manubot/resources/main/test/vector.svg?sanitize=true "Vector image"){#fig:vector-image height=2.5in .white}
-
-## Tables
-
-| *Bowling Scores* | Jane          | John          | Alice         | Bob           |
-|:-----------------|:-------------:|:-------------:|:-------------:|:-------------:|
-| Game 1 | 150 | 187 | 210 | 105 |
-| Game 2 |  98 | 202 | 197 | 102 |
-| Game 3 | 123 | 180 | 238 | 134 |
-
-Table: A table with a top caption and specified relative column widths.
-{#tbl:bowling-scores}
-
-|         | Digits 1-33                        | Digits 34-66                      | Digits 67-99                      | Ref.                                                        |
-|:--------|:-----------------------------------|:----------------------------------|:----------------------------------|:------------------------------------------------------------|
-| pi      | 3.14159265358979323846264338327950 | 288419716939937510582097494459230 | 781640628620899862803482534211706 | [`piday.org`](https://www.piday.org/million/)               |
-| e       | 2.71828182845904523536028747135266 | 249775724709369995957496696762772 | 407663035354759457138217852516642 | [`nasa.gov`](https://apod.nasa.gov/htmltest/gifcity/e.2mil) |
-
-Table: A table too wide to fit within page.
-{#tbl:constant-digits}
-
-|          | **Colors** <!-- $colspan="2" --> |                      |
-|:--------:|:--------------------------------:|:--------------------:|
-| **Size** | **Text Color**                   | **Background Color** |
-| big      | blue                             | orange               |
-| small    | black                            | white                |
-
-Table: A table with merged cells using the `attributes` plugin.
-{#tbl: merged-cells}
-
-## Equations
-
-A LaTeX equation:
-
-$$\int_0^\infty e^{-x^2} dx=\frac{\sqrt{\pi}}{2}$$ {#eq:regular-equation}
-
-An equation too long to fit within page:
-
-$$x = a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s + t + u + v + w + x + y + z + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9$$ {#eq:long-equation}
-
-## Special
-
-<i class="fas fa-exclamation-triangle"></i> [WARNING]{.semibold} _The following features are only supported and intended for `.html` and `.pdf` exports._
-_Journals are not likely to support them, and they may not display correctly when converted to other formats such as `.docx`._
-
-[Link styled as a button](https://manubot.org "Manubot Homepage"){.button}
-
-Adding arbitrary HTML attributes to an element using Pandoc's attribute syntax:
-
-::: {#some_id_1 .some_class style="background: #ad1457; color: white; margin-left: 40px;" title="a paragraph of text" data-color="white" disabled="true"}
-Manubot Manubot Manubot Manubot Manubot.
-Manubot Manubot Manubot Manubot.
-Manubot Manubot Manubot.
-Manubot Manubot.
-Manubot.
-:::
-
-Adding arbitrary HTML attributes to an element with the Manubot `attributes` plugin (more flexible than Pandoc's method in terms of which elements you can add attributes to):
-
-Manubot Manubot Manubot Manubot Manubot.
-Manubot Manubot Manubot Manubot.
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-Manubot Manubot.
-Manubot.
-<!-- $id="element_id" class="some_class" $style="color: #ad1457; margin-left: 40px;" $disabled="true" $title="a paragraph of text" $data-color="red" -->
-
-Available background colors for text, images, code, banners, etc:  
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-Using the [Font Awesome](https://fontawesome.com/) icon set:
-
-<!-- include the Font Awesome library, per: https://fontawesome.com/start -->
-<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.7.2/css/all.css">
-
-<i class="fas fa-check"></i> <i class="fas fa-question"></i> <i class="fas fa-star"></i> <i class="fas fa-bell"></i> <i class="fas fa-times-circle"></i> <i class="fas fa-ellipsis-h"></i>
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-<i class="fas fa-scroll fa-lg"></i> **Light Grey Banner**<br>
-useful for *general information* - [manubot.org](https://manubot.org/)
-]{.banner .lightgrey}
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-useful for *important information* - [manubot.org](https://manubot.org/)
-]{.banner .lightblue}
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-[
-<i class="fas fa-ban fa-lg"></i> **Light Red Banner**<br>
-useful for *warnings* - [manubot.org](https://manubot.org/)
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diff --git a/content/02.introduction.md b/content/02.introduction.md
new file mode 100644
index 0000000..17a75ff
--- /dev/null
+++ b/content/02.introduction.md
@@ -0,0 +1,7 @@
+## Chapter 1
+
+* Modeling strategies (copy existing review)
+
+* Machine learning for cancer transcriptomics (add some new text)
+
+## Test section
diff --git a/content/metadata.yaml b/content/metadata.yaml
index ccf8d55..685ea1b 100644
--- a/content/metadata.yaml
+++ b/content/metadata.yaml
@@ -1,30 +1,19 @@
 ---
-title: "Manuscript Title"
+title: "Jake Crawford dissertation title"
 date: null  # Defaults to date generated, but can specify like '2022-10-31'.
 keywords:
-  - markdown
-  - publishing
-  - manubot
+  - gene-expression
+  - cancer-genomics
+  - machine-learning
+  - optimization
+  - domain-adaptation
 lang: en-US
 authors:
-  - github: johndoe
-    name: John Doe
-    initials: JD
-    orcid: XXXX-XXXX-XXXX-XXXX
-    twitter: johndoe
-    mastodon: johndoe
-    mastodon-server: mastodon.social
-    email: john.doe@something.com
+  - github: jjc2718
+    name: Jake Crawford
+    initials: JC
+    orcid: 0000-0001-6207-0782
+    twitter: jjc2718
+    email: jcra@pennmedicine.upenn.edu
     affiliations:
-      - Department of Something, University of Whatever
-    funders:
-      - Grant XXXXXXXX
-  - github: janeroe
-    name: Jane Roe
-    initials: JR
-    orcid: XXXX-XXXX-XXXX-XXXX
-    email: jane.roe@whatever.edu
-    affiliations:
-      - Department of Something, University of Whatever
-      - Department of Whatever, University of Something
-    corresponding: true
+      - Genomics and Computational Biology Graduate Group, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA

From 1169dfff7c1a37a18349a154275b95faf1ee068a Mon Sep 17 00:00:00 2001
From: Jake Crawford <jjc2718@gmail.com>
Date: Mon, 28 Aug 2023 10:00:18 -0400
Subject: [PATCH 2/3] add optimizers paper

---
 content/02.introduction.md      |  2 -
 content/20.header.md            |  6 +++
 content/21.abstract.md          | 19 ++++++++++
 content/22.introduction.md      | 17 +++++++++
 content/23.methods.md           | 66 +++++++++++++++++++++++++++++++++
 content/24.results.md           | 66 +++++++++++++++++++++++++++++++++
 content/25.discussion.md        | 23 ++++++++++++
 content/26.data_availability.md |  7 ++++
 content/27.supp_info.md         | 11 ++++++
 content/images/optimizers       |  1 +
 content/manual-references.json  | 52 ++++++++++++++++++++++++++
 11 files changed, 268 insertions(+), 2 deletions(-)
 create mode 100644 content/20.header.md
 create mode 100644 content/21.abstract.md
 create mode 100644 content/22.introduction.md
 create mode 100644 content/23.methods.md
 create mode 100644 content/24.results.md
 create mode 100644 content/25.discussion.md
 create mode 100644 content/26.data_availability.md
 create mode 100644 content/27.supp_info.md
 create mode 120000 content/images/optimizers

diff --git a/content/02.introduction.md b/content/02.introduction.md
index 17a75ff..9cf392f 100644
--- a/content/02.introduction.md
+++ b/content/02.introduction.md
@@ -3,5 +3,3 @@
 * Modeling strategies (copy existing review)
 
 * Machine learning for cancer transcriptomics (add some new text)
-
-## Test section
diff --git a/content/20.header.md b/content/20.header.md
new file mode 100644
index 0000000..6d65052
--- /dev/null
+++ b/content/20.header.md
@@ -0,0 +1,6 @@
+## Chapter 2: optimization strongly influences model selection in transcriptomic prediction
+
+This chapter has been posted as a preprint on bioRxiv (https://www.biorxiv.org/content/10.1101/2023.06.26.546586v1) and submitted for publication at Bioinformatics Advances as "Optimizer’s dilemma: optimization strongly influences model selection in transcriptomic prediction".
+
+_Contributions_: I designed and ran the experiments, created the figures, wrote the initial draft of the manuscript, and edited the manuscript. Maria Chikina gave feedback on an initial version of the manuscript, gave guidance on experimental design, and edited the manuscript. Casey S. Greene gave feedback and guidance on experiments, and edited the manuscript.
+
diff --git a/content/21.abstract.md b/content/21.abstract.md
new file mode 100644
index 0000000..f29189c
--- /dev/null
+++ b/content/21.abstract.md
@@ -0,0 +1,19 @@
+### Abstract
+
+#### Motivation
+
+Most models can be fit to data using various optimization approaches.
+While model choice is frequently reported in machine-learning-based research, optimizers are not often noted.
+We applied two different implementations of LASSO logistic regression implemented in Python's scikit-learn package, using two different optimization approaches (coordinate descent and stochastic gradient descent), to predict driver mutation presence or absence from gene expression across 84 pan-cancer driver genes.
+Across varying levels of regularization, we compared performance and model sparsity between optimizers.
+
+#### Results
+
+After model selection and tuning, we found that coordinate descent (implemented in the `liblinear` library) and SGD tended to perform comparably.
+`liblinear` models required more extensive tuning of regularization strength, performing best for high model sparsities (more nonzero coefficients), but did not require selection of a learning rate parameter.
+SGD models required tuning of the learning rate to perform well, but generally performed more robustly across different model sparsities as regularization strength decreased.
+Given these tradeoffs, we believe that the choice of optimizers should be clearly reported as a part of the model selection and validation process, to allow readers and reviewers to better understand the context in which results have been generated.
+
+#### Availability and implementation
+
+The code used to carry out the analyses in this study is available at <https://github.com/greenelab/pancancer-evaluation/tree/master/01_stratified_classification>. Performance/regularization strength curves for all genes in the Vogelstein et al. 2013 dataset are available at <https://doi.org/10.6084/m9.figshare.22728644>.
diff --git a/content/22.introduction.md b/content/22.introduction.md
new file mode 100644
index 0000000..30f6a22
--- /dev/null
+++ b/content/22.introduction.md
@@ -0,0 +1,17 @@
+### Introduction
+
+Gene expression profiles are widely used to classify samples or patients into relevant groups or categories, both preclinically [@doi:10.1371/journal.pcbi.1009926; @doi:10.1093/bioinformatics/btaa150] and clinically [@doi:10.1200/JCO.2008.18.1370; @doi:10/bp4rtw].
+To extract informative gene features and to perform classification, a diverse array of algorithms exist, and different algorithms perform well across varying datasets and tasks [@doi:10.1371/journal.pcbi.1009926].
+Even within a given model class, multiple optimization methods can often be applied to find well-performing model parameters or to optimize a model's loss function.
+One commonly used example is logistic regression.
+The widely used scikit-learn Python package for machine learning [@url:https://jmlr.org/papers/v12/pedregosa11a.html] provides two modules for fitting logistic regression classifiers: `LogisticRegression`, which uses the `liblinear` coordinate descent method [@url:https://www.jmlr.org/papers/v9/fan08a.html] to find parameters that optimize the logistic loss function, and `SGDClassifier`, which uses stochastic gradient descent [@online-learning] to optimize the same loss function.
+
+Using scikit-learn, we compared the `liblinear` (coordinate descent) and SGD optimization techniques for prediction of driver mutation status in tumor samples, across a wide variety of genes implicated in cancer initiation and development [@doi:10.1126/science.1235122].
+We applied LASSO (L1-regularized) logistic regression, and tuned the strength of the regularization to compare model selection between optimizers.
+We found that across a variety of models (i.e. varying regularization strengths), the training dynamics of the optimizers were considerably different: models fit using `liblinear` tended to perform best at fairly high regularization strengths (100-1000 nonzero features in the model) and overfit easily with low regularization strengths.
+On the other hand, after tuning the learning rate, models fit using SGD tended to perform well across both higher and lower regularization strengths, and overfitting was less common.
+
+Our results caution against viewing optimizer choice as a "black box" component of machine learning modeling.
+The observation that LASSO logistic regression models fit using SGD tended to perform well for low levels of regularization, across diverse driver genes, runs counter to conventional wisdom in machine learning for high-dimensional data which generally states that explicit regularization and/or feature selection is necessary.
+Comparing optimizers or model implementations directly is rare in applications of machine learning for genomics, and our work shows that this choice can affect generalization and interpretation properties of the model significantly.
+Based on our results, we recommend considering the appropriate optimization approach carefully based on the goals of each individual analysis.
diff --git a/content/23.methods.md b/content/23.methods.md
new file mode 100644
index 0000000..f81aa8c
--- /dev/null
+++ b/content/23.methods.md
@@ -0,0 +1,66 @@
+### Methods
+
+#### Data download and preprocessing
+
+To generate binary mutated/non-mutated gene labels for our machine learning model, we used mutation calls for TCGA Pan-Cancer Atlas samples from MC3 [@doi:10.1016/j.cels.2018.03.002] and copy number threshold calls from GISTIC2.0 [@doi:10.1186/gb-2011-12-4-r41].
+MC3 mutation calls were downloaded from the Genomic Data Commons (GDC) of the National Cancer Institute, at <https://gdc.cancer.gov/about-data/publications/pancanatlas>.
+Thresholded copy number calls are from an older version of the GDC data and are available here: <https://figshare.com/articles/dataset/TCGA_PanCanAtlas_Copy_Number_Data/6144122>.
+We removed hypermutated samples, defined as two or more standard deviations above the mean non-silent somatic mutation count, from our dataset to reduce the number of false positives (i.e., non-driver mutations).
+Any sample with either a non-silent somatic variant or a copy number variation (copy number gain in the target gene for oncogenes and copy number loss in the target gene for tumor suppressor genes) was included in the positive set; all remaining samples were considered negative for mutation in the target gene.
+
+RNA sequencing data for TCGA was downloaded from GDC at the same link provided above for the Pan-Cancer Atlas.
+We discarded non-protein-coding genes and genes that failed to map and removed tumors that were measured from multiple sites.
+After filtering to remove hypermutated samples and taking the intersection of samples with both mutation and gene expression data, 9074 total TCGA samples remained.
+
+#### Cancer gene set construction
+
+In order to study mutation status classification for a diverse set of cancer driver genes, we started with the set of 125 frequently altered genes from Vogelstein et al. [@doi:10.1126/science.1235122] (all genes from Table S2A).
+For each target gene, in order to ensure that the training dataset was reasonably balanced (i.e., that there would be enough mutated samples to train an effective classifier), we included only cancer types with at least 15 mutated samples and at least 5% mutated samples, which we refer to here as "valid" cancer types.
+In some cases, this resulted in genes with no valid cancer types, which we dropped from the analysis.
+Out of the 125 genes originally listed in the Vogelstein et al. cancer gene set, we retained 84 target genes after filtering for valid cancer types.
+
+#### Classifier setup and optimizer comparison details
+
+We trained logistic regression classifiers to predict whether or not a given sample had a mutational event in a given target gene using gene expression features as explanatory variables.
+Based on our previous work, gene expression is generally effective for this problem across many target genes, although other -omics types can be equally effective in many cases [@doi:10.1186/s13059-022-02705-y].
+Our model was trained on gene expression data (X) to predict mutation presence or absence (y) in a target gene.
+To control for varying mutation burden per sample and to adjust for potential cancer type-specific expression patterns, we included one-hot encoded cancer type and log~10~(sample mutation count) in the model as covariates.
+Since gene expression datasets tend to have many dimensions and comparatively few samples, we used a LASSO penalty to perform feature selection [@doi:10.1111/j.2517-6161.1996.tb02080.x].
+LASSO logistic regression has the advantage of generating sparse models (some or most coefficients are 0), as well as having a single tunable hyperparameter which can be easily interpreted as an indicator of regularization strength, or model complexity.
+
+To compare model selection across optimizers, we first split the "valid" cancer types into train (75%) and test (25%) sets.
+We then split the training data into "subtrain" (66% of the training set) data to train the model on, and "holdout" (33% of the training set) data to perform model selection, i.e. to use to select the best-performing regularization parameter, and the best-performing learning rate for SGD in the cases where multiple learning rates were considered.
+In each case, these splits were stratified by cancer type, i.e. each split had as close as possible to equal proportions of each cancer type included in the dataset for the given driver gene.
+
+#### LASSO parameter range selection and comparison between optimizers
+
+The scikit-learn implementations of coordinate descent (in `liblinear`/`LogisticRegression`) and stochastic gradient descent (in `SGDClassifier`) use slightly different parameterizations of the LASSO regularization strength parameter. `liblinear`'s logistic regression solver optimizes the following loss function:
+
+$$\hat{w} = \text{argmin}_{w} \ (C \cdot \ell(X, y; w)) + ||w||_1$$
+
+where $\ell(X, y; w)$ denotes the negative log-likelihood of the observed data $(X, y)$ given a particular choice of feature weights $w$.`SGDClassifier` optimizes the following loss function:
+
+$$\hat{w} = \text{argmin}_{w} \ \ell(X, y; w) + \alpha ||w||_1$$
+
+<!--_ -->
+
+which is equivalent with the exception of the LASSO parameter which is formulated slightly differently, as $\alpha = \frac{1}{C}$.
+The result of this slight difference in parameterization is that `liblinear` $C$ values vary inversely with regularization strength (higher values = less regularization, or greater model complexity) and `SGDClassifier` $\alpha$ values vary directly with regularization strength (lower values = less regularization, or greater model complexity).
+
+For the `liblinear` optimizer, we trained models using $C$ values evenly spaced on a logarithmic scale between (10^-3^, 10^7^); i.e. the output of `numpy.logspace(-3, 7, 21)`.
+For the SGD optimizer, we trained models using the inverse range of $\alpha$ values between (10^-7^, 10^3^), or `numpy.logspace(-7, 3, 21)`.
+These hyperparameter ranges were intended to give evenly distributed coverage across genes that included "underfit" models (predicting only the mean or using very few features, poor performance on all datasets), "overfit" models (performing perfectly on training data but comparatively poorly on cross-validation and test data), and a wide variety of models in between that typically included the best fits to the cross-validation and test data.
+
+For ease of visual comparison in our figures, we plot the SGD $\alpha$ parameter directly, and the `liblinear` $C$ parameter inversely (i.e. $\frac{1}{C}$).
+This orients the x-axes of the relevant plots in the same direction: lower values represent lower regularization strength or higher model complexity, and higher values represent higher regularization strength or lower model complexity, for both optimizers.
+
+#### SGD learning rate selection
+
+scikit-learn's `SGDClassifier` provides four built-in approaches to learning rate scheduling: `constant` (a single, constant learning rate), `optimal` (a learning rate with an initial value selected using a heuristic based on the regularization parameter and the data loss, that decreases across epochs), `invscaling` (a learning rate that decreases exponentially by epoch), and `adaptive` (a learning rate that starts at a constant value, which is divided by 5 each time the training loss fails to decrease for 5 straight epochs).
+The `optimal` learning rate schedule is used by default.
+
+When we compared these four approaches, we used a constant learning rate of 0.0005, and an initial learning rate of 0.1 for the `adaptive` and `invscaling` schedules.
+We also tested a fifth approach that we called "`constant_search`", in which we tested a range of constant learning rates in a grid search on a validation dataset, then evaluated the model on the test data using the best-performing constant learning rate by validation AUPR.
+For the grid search, we used the following range of constant learning rates: {0.000005, 0.00001, 0.00005, 0.0001, 0.0005, 0.001, 0.01}.
+Unless otherwise specified, results for SGD in the main paper figures used the `constant_search` approach, which performed the best in our comparison between schedulers.
+
diff --git a/content/24.results.md b/content/24.results.md
new file mode 100644
index 0000000..4e7dcb9
--- /dev/null
+++ b/content/24.results.md
@@ -0,0 +1,66 @@
+### Results
+
+#### `liblinear` and SGD LASSO models perform comparably, but `liblinear` is sensitive to regularization strength
+
+For each of the 125 driver genes from the Vogelstein et al. 2013 paper, we trained models to predict mutation status (presence or absence) from RNA-seq data, derived from the TCGA Pan-Cancer Atlas.
+For each optimizer, we trained LASSO logistic regression models across a variety of regularization parameters (see Methods for parameter range details), achieving a variety of different levels of model sparsity (Supplementary Figure {@fig:compare_sparsity}).
+We repeated model fitting/evaluation across 4 cross-validation splits x 2 replicates (random seeds) for a total of 8 different models per parameter.
+Cross-validation splits were stratified by cancer type.
+
+Previous work has shown that pan-cancer classifiers of Ras mutation status are accurate and biologically informative [@doi:10.1016/j.celrep.2018.03.046].
+We first evaluated models for KRAS mutation prediction.
+As model complexity increases (more nonzero coefficients) for the `liblinear` optimizer, we observed that performance increases then decreases, corresponding to overfitting for high model complexities/numbers of nonzero coefficients (Figure {@fig:optimizer_compare_mutations}A).
+On the other hand, for the SGD optimizer, we observed consistent performance as model complexity increases, with models having no nonzero coefficients performing comparably to the best (Figure {@fig:optimizer_compare_mutations}B).
+In this case, top performance for SGD (a regularization parameter of 10^-1^) is slightly better than top performance for `liblinear` (a regularization parameter of 1 / 3.16 x 10^2^): we observed a mean test AUPR of 0.722 for SGD vs. mean AUPR of 0.692 for `liblinear`.
+
+To determine how relative performance trends with `liblinear` tend to compare across the genes in the Vogelstein dataset at large, we looked at the difference in performance between optimizers for the best-performing models for each gene (Figure {@fig:optimizer_compare_mutations}C).
+The distribution is centered around 0 and more or less symmetrical, suggesting that across the gene set, `liblinear` and SGD tend to perform comparably to one another.
+We saw that for 52/84 genes, performance for the best-performing model was better using SGD than `liblinear`, and for the other 32 genes performance was better using `liblinear`.
+In order to quantify whether the overfitting tendencies (or lack thereof) also hold across the gene set, we plotted the difference in performance between the best-performing model and the largest (least regularized) model; classifiers with a large difference in performance exhibit strong overfitting, and classifiers with a small difference in performance do not overfit (Figure {@fig:optimizer_compare_mutations}D).
+For SGD, the least regularized models tend to perform comparably to the best-performing models, whereas for `liblinear` the distribution is wider suggesting that overfitting is more common.
+
+![
+**A.** Performance vs. inverse regularization parameter for KRAS mutation status prediction, using the `liblinear` coordinate descent optimizer. Dotted lines indicate top performance value of the opposite optimizer.
+**B.** Performance vs. regularization parameter for KRAS mutation status prediction, using the SGD optimizer. "Holdout" dataset is used for SGD learning rate selection, "test" data is completely held out from model selection and used for evaluation.
+**C.** Distribution of performance difference between best-performing model for `liblinear` and SGD optimizers, across all 84 genes in Vogelstein driver gene set. Positive numbers on the x-axis indicate better performance using `liblinear`, and negative numbers indicate better performance using SGD.
+**D.** Distribution of performance difference between best-performing model and largest (least regularized) model, for `liblinear` and SGD, across all 84 genes. Smaller numbers on the y-axis indicate less overfitting, and larger numbers indicate more overfitting.
+](images/optimizers/figure_1.png){#fig:optimizer_compare_mutations width="100%"}
+
+#### SGD is sensitive to learning rate selection
+
+The SGD results shown in Figure {@fig:optimizer_compare_mutations} select the best-performing learning rate using a grid search on the holdout dataset, independently for each regularization parameter.
+We also compared against other learning rate scheduling approaches implemented in scikit-learn (see Methods for implementation details and grid search specifications).
+For KRAS mutation prediction, we observed that the choice of initial learning rate and scheduling approach affects performance significantly, and other approaches to selecting the learning rate performed poorly relative to `liblinear` (black dotted lines in Figure {@fig:sgd_lr_schedulers}) and to the grid search.
+We did not observe an improvement in performance over `liblinear` or the grid search for learning rate schedulers that decrease across epochs (Figure {@fig:sgd_lr_schedulers}A, C, and D), nor did we see comparable performance when we selected a single constant learning rate for all levels of regularization without the preceding grid search (Figure {@fig:sgd_lr_schedulers}B).
+Notably, scikit-learn's default "optimal" learning rate schedule performed relatively poorly for this problem, suggesting that tuning the learning rate and selecting a well-performing scheduler is a critical component of applying SGD successfully for this problem (Figure {@fig:sgd_lr_schedulers}D).
+We observed similar trends across all genes in the Vogelstein gene set, with other learning rate scheduling approaches performing poorly in aggregate relative to both `liblinear` and SGD with the learning rate grid search (Supplementary Figure {@fig:compare_all_lr}).
+
+![
+**A.** Performance vs. regularization parameter for KRAS mutation prediction, using SGD optimizer with adaptive learning rate scheduler. Dotted line indicates top performance value using `liblinear`, from Figure {@fig:optimizer_compare_mutations}A.
+**B.** Performance vs. regularization parameter, using SGD optimizer with constant learning rate scheduler and a learning rate of 0.0005.
+**C.** Performance vs. regularization parameter, using SGD optimizer with inverse scaling learning rate scheduler.
+**D.** Performance vs. regularization parameter, using SGD optimizer with "optimal" learning rate scheduler.
+](images/optimizers/figure_2.png){#fig:sgd_lr_schedulers width="100%"}
+
+#### `liblinear` and SGD result in different models, with varying loss dynamics
+
+We sought to determine whether there was a difference in the sparsity of the models resulting from the different optimization schemes.
+In general across all genes, the best-performing SGD models mostly tend to have many nonzero coefficients, but with a distinct positive tail, sometimes having few nonzero coefficients.
+By contrast, the `liblinear` models are generally sparser with fewer than 2500 nonzero coefficients, out of ~16100 total input features, and a much narrower tail (Figure {@fig:optimizer_coefs}A).
+The sum of the coefficient magnitudes, however, tends to be smaller on average across all levels of regularization for SGD than for `liblinear` (Figure {@fig:optimizer_coefs}B).
+This effect is less pronounced for the other learning rate schedules shown in Figure {@fig:sgd_lr_schedulers}, with the other options resulting in larger coefficient magnitudes (Supplementary Figure {@fig:coef_weights_lr}).
+These results suggest that the models fit by `liblinear` and SGD navigate the tradeoff between bias and variance in slightly different ways: `liblinear` tends to produce sparser models (more zero coefficients) as regularization increases, but if the learning rate is properly tuned, SGD coefficients tend to have smaller overall magnitudes as regularization increases.
+
+
+We also compared the components of the loss function across different levels of regularization between optimizers.
+The LASSO logistic regression loss function can be broken down into a data-dependent component (the log-loss) and a parameter magnitude dependent component (the L1 penalty), which are added to get the total loss that is minimized by each optimizer; see Methods for additional details.
+As regularization strength decreases for `liblinear`, the data loss collapses to near 0, and the L1 penalty dominates the overall loss (Figure {@fig:optimizer_coefs}C).
+For SGD, on the other hand, the data loss decreases slightly as regularization strength decreases but remains relatively high (Figure {@fig:optimizer_coefs}D).
+Other SGD learning rate schedules have similar loss curves to the `liblinear` results, although this does not result in improved classification performance (Supplementary Figure {@fig:loss_lr}).
+
+![
+**A.** Distribution across genes of the number of nonzero coefficients included in best-performing LASSO logistic regression models. Violin plot density estimations are clipped at the ends of the observed data range, and boxes show the median/IQR.
+**B.** Distribution across genes of the sum of model coefficient weights for best-performing LASSO logistic regression models.
+**C.** Decomposition of loss function for models fit using `liblinear` across regularization levels. 0 values on the y-axis are rounded up to machine epsilon; i.e. 2.22 x 10^-16^.
+**D.** Decomposition of loss function for models fit using SGD across regularization levels. 0 values on the y-axis are rounded up to machine epsilon; i.e. 2.22 x 10^-16^.
+](images/optimizers/figure_3.png){#fig:optimizer_coefs width="100%"}
diff --git a/content/25.discussion.md b/content/25.discussion.md
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--- /dev/null
+++ b/content/25.discussion.md
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+### Discussion
+
+Our work shows that optimizer choice presents tradeoffs in model selection for cancer transcriptomics.
+We observed that LASSO logistic regression models for mutation status prediction fit using stochastic gradient descent were highly sensitive to learning rate tuning, but they tended to perform robustly across diverse levels of regularization and sparsity.
+Coordinate descent implemented in `liblinear` did not require learning rate tuning, but generally performed best for a narrow range of fairly sparse models, overfitting as regularization strength decreased.
+Tuning of regularization strength for `liblinear`, and learning rate (and regularization strength to a lesser degree) for SGD, are critical steps which must be considered as part of analysis pipelines.
+The sensitivity we observed to these details highlights the importance of reporting exactly what optimizer was used, and how the relevant hyperparameters were selected, in studies that use machine learning models for transcriptomic data.
+
+To our knowledge, the phenomenon we observed with SGD has not been documented in other applications of machine learning to genomic or transcriptomic data.
+In recent years, however, the broader machine learning research community has identified and characterized implicit regularization for SGD in many settings, including overparametrized or feature-rich problems as is often the case in transcriptomics [@arxiv:2108.04552; @arxiv:2003.06152; @url:http://proceedings.mlr.press/v134/zou21a.html].
+The resistance we observed of SGD-optimized models to decreased performance on held-out data as model complexity increases is often termed "benign overfitting": overfit models, in the sense that they fit the training data perfectly and perform worse on the test data, can still outperform models that do not fit the training data as well or that have stronger explicit regularization.
+Benign overfitting has been attributed to optimization using SGD [@url:http://proceedings.mlr.press/v134/zou21a.html; @doi:10.1145/3446776], and similar patterns have been observed for both linear models and deep neural networks [@doi:10.1073/pnas.1907378117; @arxiv:1611.03530].
+
+Existing gene expression prediction benchmarks and pipelines typically use a single model implementation, and thus a single optimizer.
+We recommend thinking critically about optimizer choice, but this can be challenging for researchers that are inexperienced with machine learning or unfamiliar with how certain models are fit under the hood.
+For example, R's `glmnet` package uses a cyclical coordinate descent algorithm to fit logistic regression models [@doi:10.18637/jss.v033.i01], which would presumably behave similarly to `liblinear`, but this is somewhat opaque in the `glmnet` documentation itself.
+Increased transparency and documentation in popular machine learning packages with respect to optimization, especially for models that are difficult to fit or sensitive to hyperparameter settings, would benefit new and unfamiliar users.
+
+
+Related to what we see in our SGD-optimized models, there exist other problems in gene expression analysis where using all available features is comparable to, or better than, using a subset.
+For example, using the full gene set improves correlations between preclinical cancer models and their tissue of origin, as compared to selecting genes based on variability or tissue-specificity [@doi:10.1101/2023.04.11.536431].
+On the other hand, when predicting cell line viability from gene expression profiles, selecting features by Pearson correlation improves performance over using all features, similar to our `liblinear` classifiers [@doi:10.1101/2020.02.21.959627].
+In future work, it could be useful to explore if the coefficients found by `liblinear` and SGD emphasize the same pathways or functional gene sets, or if there are patterns to which mutation status classifiers (or other cancer transcriptomics classifiers) perform better with more/fewer nonzero coefficients.
diff --git a/content/26.data_availability.md b/content/26.data_availability.md
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+++ b/content/26.data_availability.md
@@ -0,0 +1,7 @@
+### Data and code availability
+
+The data analyzed during this study were previously published as part of the TCGA Pan-Cancer Atlas project [@doi:10.1038/ng.2764], and are available from the NIH NCI Genomic Data Commons (GDC).
+The scripts used to download and preprocess the datasets for this study are available at <https://github.com/greenelab/pancancer-evaluation/tree/master/00_process_data>, and the code used to carry out the analyses in this study is available at <https://github.com/greenelab/pancancer-evaluation/tree/master/01_stratified_classification>, both under the open-source BSD 3-clause license.
+Equivalent versions of Figure {@fig:optimizer_compare_mutations}A and {@fig:optimizer_compare_mutations}B for all 84 genes in the Vogelstein et al. 2013 gene set are available on Figshare at <https://doi.org/10.6084/m9.figshare.22728644>, under a CC0 license.
+This manuscript was written using Manubot [@doi:10.1371/journal.pcbi.1007128] and is available on GitHub at <https://github.com/greenelab/optimizer-manuscript> under the CC0-1.0 license.
+This research was supported in part by the University of Pittsburgh Center for Research Computing through the resources provided. Specifically, this work used the HTC cluster, which is supported by NIH award number S10OD028483.
diff --git a/content/27.supp_info.md b/content/27.supp_info.md
new file mode 100644
index 0000000..f91a8fa
--- /dev/null
+++ b/content/27.supp_info.md
@@ -0,0 +1,11 @@
+### Supplementary Material
+
+![Number of nonzero coefficients (model sparsity) across varying regularization parameter settings for KRAS mutation prediction using SGD and `liblinear` optimizers.](images/optimizers/supp_figure_1.png){#fig:compare_sparsity width="100%"}
+
+![Distribution of performance difference between best-performing model for `liblinear` and SGD optimizers, across all 84 genes in Vogelstein driver gene set, for varying SGD learning rate schedulers. Positive numbers on the x-axis indicate better performance using `liblinear`, and negative numbers indicate better performance using SGD.](images/optimizers/supp_figure_2.png){#fig:compare_all_lr width="100%" .page_break_before}
+
+![Sum of absolute value of coefficients + 1 for KRAS mutation prediction using SGD and `liblinear` optimizers, with varying learning rate schedules for SGD. Similar to the figures in the main paper, the `liblinear` x-axis represents the inverse of the $C$ regularization parameter; SGD x-axes represent the untransformed $\alpha$ parameter.](images/optimizers/supp_figure_3.png){#fig:coef_weights_lr width="100%" .page_break_before}
+
+![Decomposition of loss function into data loss and L1 penalty components for KRAS mutation prediction using SGD optimizer, across regularization levels, using varying learning rate schedulers. 0 values on the y-axis are rounded up to machine epsilon, i.e. 2.22 x 10^-16^.](images/optimizers/supp_figure_4.png){#fig:loss_lr width="100%" .page_break_before}
+
+
diff --git a/content/images/optimizers b/content/images/optimizers
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+/Users/jake/Documents/writing/optimizer-manuscript/content/images
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diff --git a/content/manual-references.json b/content/manual-references.json
index 43c7536..2b7b710 100644
--- a/content/manual-references.json
+++ b/content/manual-references.json
@@ -18,5 +18,57 @@
       "family": "Himmelstein"
     }
   ]
+},
+{
+  "id": "online-learning",
+  "type": "webpage",
+  "URL": "https://wiki.eecs.yorku.ca/course_archive/2012-13/F/6328/_media/bottou-onlinelearning-98.pdf",
+  "title": "Online Learning and Stochastic Approximations",
+  "issued": {
+    "date-parts": [
+      [
+        1998
+      ]
+    ]
+  },
+  "author": [
+    {
+      "given": "Leon",
+      "family": "Bottou"
+    }
+  ]
+},
+{
+  "id": "l1-logistic-regression",
+  "type": "paper-conference",
+  "publisher": "Association for the Advancement of Artificial Intelligence (AAAI)",
+  "container-title": "AAAI 2006",
+  "URL": "https://ai.stanford.edu/~pabbeel//pubs/LeeLeeAbbeelNg_el1rlr_AAAI2006.pdf",
+  "title": "Efficient L1 Regularized Logistic Regression",
+  "issued": {
+    "date-parts": [
+      [
+        2006
+      ]
+    ]
+  },
+  "author": [
+    {
+      "given": "Su-In",
+      "family": "Lee"
+    },
+    {
+      "given": "Honglak",
+      "family": "Lee"
+    },
+    {
+      "given": "Pieter",
+      "family": "Abbeel"
+    },
+    {
+      "given": "Andrew Y.",
+      "family": "Ng"
+    }
+  ]
 }
 ]

From 350dc854ae4550063c56739d3c4e985447031e8e Mon Sep 17 00:00:00 2001
From: Jake Crawford <jjc2718@gmail.com>
Date: Mon, 28 Aug 2023 11:24:40 -0400
Subject: [PATCH 3/3] replace symlink with actual files

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+       <use xlink:href="#ArialMT-6c"/>
+       <use xlink:href="#ArialMT-69" x="22.216797"/>
+       <use xlink:href="#ArialMT-62" x="44.433594"/>
+       <use xlink:href="#ArialMT-6c" x="100.048828"/>
+       <use xlink:href="#ArialMT-69" x="122.265625"/>
+       <use xlink:href="#ArialMT-6e" x="144.482422"/>
+       <use xlink:href="#ArialMT-65" x="200.097656"/>
+       <use xlink:href="#ArialMT-61" x="255.712891"/>
+       <use xlink:href="#ArialMT-72" x="311.328125"/>
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+       <use xlink:href="#ArialMT-53"/>
+       <use xlink:href="#ArialMT-47" x="66.699219"/>
+       <use xlink:href="#ArialMT-44" x="144.482422"/>
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+    </g>
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+     <!-- Optimizer -->
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+      <use xlink:href="#ArialMT-4f"/>
+      <use xlink:href="#ArialMT-70" x="77.783203"/>
+      <use xlink:href="#ArialMT-74" x="133.398438"/>
+      <use xlink:href="#ArialMT-69" x="161.181641"/>
+      <use xlink:href="#ArialMT-6d" x="183.398438"/>
+      <use xlink:href="#ArialMT-69" x="266.699219"/>
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+      <use xlink:href="#ArialMT-65" x="338.916016"/>
+      <use xlink:href="#ArialMT-72" x="394.53125"/>
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+      <!-- 0 -->
+      <g style="fill: #262626" transform="translate(42.589063 192.590531)scale(0.1 -0.1)">
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+    <g id="ytick_2">
+     <g id="line2d_2">
+      <path d="M 55.15 164.392633  L 445.75 164.392633  " clip-path="url(#p1ab99308c7)" style="fill: none; stroke: #cccccc; stroke-width: 0.8; stroke-linecap: round"/>
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+      <!-- 2500 -->
+      <g style="fill: #262626" transform="translate(25.90625 167.971539)scale(0.1 -0.1)">
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+       <use xlink:href="#ArialMT-32"/>
+       <use xlink:href="#ArialMT-35" x="55.615234"/>
+       <use xlink:href="#ArialMT-30" x="111.230469"/>
+       <use xlink:href="#ArialMT-30" x="166.845703"/>
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+      <!-- 5000 -->
+      <g style="fill: #262626" transform="translate(25.90625 143.352548)scale(0.1 -0.1)">
+       <use xlink:href="#ArialMT-35"/>
+       <use xlink:href="#ArialMT-30" x="55.615234"/>
+       <use xlink:href="#ArialMT-30" x="111.230469"/>
+       <use xlink:href="#ArialMT-30" x="166.845703"/>
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+      <!-- 7500 -->
+      <g style="fill: #262626" transform="translate(25.90625 118.733556)scale(0.1 -0.1)">
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+       <use xlink:href="#ArialMT-37"/>
+       <use xlink:href="#ArialMT-35" x="55.615234"/>
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+      <!-- 10000 -->
+      <g style="fill: #262626" transform="translate(20.345313 94.114564)scale(0.1 -0.1)">
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+       <use xlink:href="#ArialMT-30" x="55.615234"/>
+       <use xlink:href="#ArialMT-30" x="111.230469"/>
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+       <use xlink:href="#ArialMT-32" x="55.615234"/>
+       <use xlink:href="#ArialMT-35" x="111.230469"/>
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+       <use xlink:href="#ArialMT-35" x="55.615234"/>
+       <use xlink:href="#ArialMT-30" x="111.230469"/>
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new file mode 100644
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