Make push-pages

Author: mvdoc

_sources/notebooks/shortclips/02_download_shortclips.ipynb

@@ -51,9 +51,8 @@
         "download more subjects.\n",
         "\n",
         "We also skip the stimuli files, since the dataset provides two preprocessed\n",
-        "feature spaces to perform voxelwise modeling without requiring the original\n",
-        "stimuli.\n",
-        "\n"
+        "feature spaces to fit voxelwise encoding models without requiring the original\n",
+        "stimuli."
       ]
     },
     {

_sources/notebooks/shortclips/03_compute_explainable_variance.ipynb

@@ -15,9 +15,10 @@
         "stimulus-dependent signal and noise. If we present the same stimulus multiple\n",
         "times and we record brain activity for each repetition, the stimulus-dependent\n",
         "signal will be the same across repetitions while the noise will vary across\n",
-        "repetitions. In voxelwise modeling, the features used to model brain activity\n",
-        "are the same for each repetition of the stimulus. Thus, encoding models will\n",
-        "predict only the repeatable stimulus-dependent signal.\n",
+        "repetitions. In the Voxelwise Encoding Model framework, \n",
+        "the features used to model brain activity are the same for each repetition of the \n",
+        "stimulus. Thus, encoding models will predict only the repeatable stimulus-dependent \n",
+        "signal.\n",
         "\n",
         "The stimulus-dependent signal can be estimated by taking the mean of brain\n",
         "responses over repeats of the same stimulus or experiment. The variance of the\n",

_sources/notebooks/shortclips/README.md

@@ -1,6 +1,6 @@
 # Shortclips tutorial
 
-This tutorial describes how to use the Voxelwise Encoding Model framework on a visual
+This tutorial describes how to use the Voxelwise Encoding Model framework in a visual
 imaging experiment.
 
 ## Dataset

_sources/notebooks/vim2/README.md

@@ -7,7 +7,7 @@ lobe, and with no mappers to plot the data on flatmaps.
 Using the "Shortclips tutorial" with full brain responses is recommended.
 :::
 
-This tutorial describes how to perform voxelwise modeling on a visual
+This tutorial describes how to use the Voxelwise Encoding Model framework in a visual
 imaging experiment.
 
 ## Data set

_sources/pages/index.md

@@ -5,7 +5,7 @@ Welcome to the tutorials on the Voxelwise Encoding Model framework from the
 
 If you use these tutorials for your work, consider citing the corresponding paper:
 
-> T. Dupré La Tour, M. Visconti di Oleggio Castello, and J. L. Gallant. The voxelwise modeling framework: a tutorial introduction to fitting encoding models to fMRI data. PsyArXiv, 2024. [doi:10.31234/osf.io/t975e.](https://doi.org/10.31234/osf.io/t975e)
+> T. Dupré La Tour, M. Visconti di Oleggio Castello, and J. L. Gallant. The Voxelwise Encoding Model framework: a tutorial introduction to fitting encoding models to fMRI data. PsyArXiv, 2024. [doi:10.31234/osf.io/t975e.](https://doi.org/10.31234/osf.io/t975e)
 
 You can find a copy of the paper [here](https://github.com/gallantlab/voxelwise_tutorials/blob/main/paper/voxelwise_tutorials_paper.pdf).
 

notebooks/shortclips/02_download_shortclips.html

@@ -442,7 +442,7 @@ <h2>Download<a class="headerlink" href="#download" title="Link to this heading">
 analysis on the four other subjects. Uncomment the lines in <code class="docutils literal notranslate"><span class="pre">DATAFILES</span></code> to
 download more subjects.</p>
 <p>We also skip the stimuli files, since the dataset provides two preprocessed
-feature spaces to perform voxelwise modeling without requiring the original
+feature spaces to fit voxelwise encoding models without requiring the original
 stimuli.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">

notebooks/shortclips/03_compute_explainable_variance.html

@@ -422,9 +422,10 @@ <h1>Compute the explainable variance<a class="headerlink" href="#compute-the-exp
 stimulus-dependent signal and noise. If we present the same stimulus multiple
 times and we record brain activity for each repetition, the stimulus-dependent
 signal will be the same across repetitions while the noise will vary across
-repetitions. In voxelwise modeling, the features used to model brain activity
-are the same for each repetition of the stimulus. Thus, encoding models will
-predict only the repeatable stimulus-dependent signal.</p>
+repetitions. In the Voxelwise Encoding Model framework,
+the features used to model brain activity are the same for each repetition of the
+stimulus. Thus, encoding models will predict only the repeatable stimulus-dependent
+signal.</p>
 <p>The stimulus-dependent signal can be estimated by taking the mean of brain
 responses over repeats of the same stimulus or experiment. The variance of the
 estimated stimulus-dependent signal, which we call the explainable variance, is
@@ -436,8 +437,8 @@ <h1>Compute the explainable variance<a class="headerlink" href="#compute-the-exp
 across repetitions. For each repeat, we define the residual timeseries between
 brain response and average brain response as <span class="math notranslate nohighlight">\(r_i = y_i - \bar{y}\)</span>. The
 explainable variance (EV) is estimated as</p>
-<div class="amsmath math notranslate nohighlight" id="equation-8571b8dd-458d-4804-9a62-21ea954a14fe">
-<span class="eqno">(1)<a class="headerlink" href="#equation-8571b8dd-458d-4804-9a62-21ea954a14fe" title="Permalink to this equation">#</a></span>\[\begin{align}\text{EV} = \frac{1}{N}\sum_{i=1}^N\text{Var}(y_i) - \frac{N}{N-1}\sum_{i=1}^N\text{Var}(r_i)\end{align}\]</div>
+<div class="amsmath math notranslate nohighlight" id="equation-636d7741-bd36-4057-88bd-5e66477663ba">
+<span class="eqno">(1)<a class="headerlink" href="#equation-636d7741-bd36-4057-88bd-5e66477663ba" title="Permalink to this equation">#</a></span>\[\begin{align}\text{EV} = \frac{1}{N}\sum_{i=1}^N\text{Var}(y_i) - \frac{N}{N-1}\sum_{i=1}^N\text{Var}(r_i)\end{align}\]</div>
 <p>In the literature, the explainable variance is also known as the <em>signal
 power</em>.</p>
 <p>For more information, see <span id="id1">Sahani and Linden [<a class="reference internal" href="merged_for_colab_model_fitting.html#id130" title="M. Sahani and J. Linden. How linear are auditory cortical responses? Adv. Neural Inf. Process. Syst., 2002.">2002</a>]</span>, <span id="id2">Hsu <em>et al.</em> [<a class="reference internal" href="merged_for_colab_model_fitting.html#id131" title="A. Hsu, A. Borst, and F. E. Theunissen. Quantifying variability in neural responses and its application for the validation of model predictions. Network, 2004.">2004</a>]</span>, and <span id="id3">Schoppe <em>et al.</em> [<a class="reference internal" href="merged_for_colab_model_fitting.html#id132" title="O. Schoppe, N. S. Harper, B. Willmore, A. King, and J. Schnupp. Measuring the performance of neural models. Front. Comput. Neurosci., 2016.">2016</a>]</span>.</p>

notebooks/shortclips/04_understand_ridge_regression.html

@@ -422,13 +422,13 @@ <h1>Understand ridge regression and cross-validation<a class="headerlink" href="
 variable <span class="math notranslate nohighlight">\(y \in \mathbb{R}^{n}\)</span> (the target). Specifically, linear
 regression uses a vector of coefficient <span class="math notranslate nohighlight">\(w \in \mathbb{R}^{p}\)</span> to
 predict the output</p>
-<div class="amsmath math notranslate nohighlight" id="equation-010741a2-76d5-4c9c-9869-185c0d3cb2c4">
-<span class="eqno">(2)<a class="headerlink" href="#equation-010741a2-76d5-4c9c-9869-185c0d3cb2c4" title="Permalink to this equation">#</a></span>\[\begin{align}\hat{y} = Xw\end{align}\]</div>
+<div class="amsmath math notranslate nohighlight" id="equation-da76a1fe-87f6-46bd-9e9c-e09383d7cce8">
+<span class="eqno">(2)<a class="headerlink" href="#equation-da76a1fe-87f6-46bd-9e9c-e09383d7cce8" title="Permalink to this equation">#</a></span>\[\begin{align}\hat{y} = Xw\end{align}\]</div>
 <p>The model is considered accurate if the predictions <span class="math notranslate nohighlight">\(\hat{y}\)</span> are close
 to the true output values <span class="math notranslate nohighlight">\(y\)</span>. Therefore,  a good linear regression model
 is given by the vector <span class="math notranslate nohighlight">\(w\)</span> that minimizes the sum of squared errors:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-04e7999a-297e-4b03-8416-a103d7ff49bf">
-<span class="eqno">(3)<a class="headerlink" href="#equation-04e7999a-297e-4b03-8416-a103d7ff49bf" title="Permalink to this equation">#</a></span>\[\begin{align}w = \arg\min_w ||Xw - y||^2\end{align}\]</div>
+<div class="amsmath math notranslate nohighlight" id="equation-6da7fe0e-54ba-48f4-9aa1-d9bf075b11ab">
+<span class="eqno">(3)<a class="headerlink" href="#equation-6da7fe0e-54ba-48f4-9aa1-d9bf075b11ab" title="Permalink to this equation">#</a></span>\[\begin{align}w = \arg\min_w ||Xw - y||^2\end{align}\]</div>
 <p>This is the simplest model for linear regression, and it is known as <em>ordinary
 least squares</em> (OLS).</p>
 <section id="ordinary-least-squares-ols">
@@ -480,8 +480,8 @@ <h2>Ordinary least squares (OLS)<a class="headerlink" href="#ordinary-least-squa
 </div>
 <p>The linear coefficient leading to the minimum squared loss can be found
 analytically with the formula:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-08541323-7db5-4c17-bea4-760241648a56">
-<span class="eqno">(4)<a class="headerlink" href="#equation-08541323-7db5-4c17-bea4-760241648a56" title="Permalink to this equation">#</a></span>\[\begin{align}w = (X^\top X)^{-1}  X^\top y\end{align}\]</div>
+<div class="amsmath math notranslate nohighlight" id="equation-f012e063-7522-4b05-8e49-064f95b614c7">
+<span class="eqno">(4)<a class="headerlink" href="#equation-f012e063-7522-4b05-8e49-064f95b614c7" title="Permalink to this equation">#</a></span>\[\begin{align}w = (X^\top X)^{-1}  X^\top y\end{align}\]</div>
 <p>This is the OLS solution.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -621,8 +621,8 @@ <h2>Ridge regression<a class="headerlink" href="#ridge-regression" title="Link t
 <p>To solve the instability and under-determinacy issues of OLS, OLS can be
 extended to <em>ridge regression</em>. Ridge regression considers a different
 optimization problem:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-152e4fe6-61c3-4b05-b6f4-2b165911ccca">
-<span class="eqno">(5)<a class="headerlink" href="#equation-152e4fe6-61c3-4b05-b6f4-2b165911ccca" title="Permalink to this equation">#</a></span>\[\begin{align}w = \arg\min_w ||Xw - y||^2 + \alpha ||w||^2\end{align}\]</div>
+<div class="amsmath math notranslate nohighlight" id="equation-3b3d4e3f-b071-4c3f-a29b-8960c06b9e4d">
+<span class="eqno">(5)<a class="headerlink" href="#equation-3b3d4e3f-b071-4c3f-a29b-8960c06b9e4d" title="Permalink to this equation">#</a></span>\[\begin{align}w = \arg\min_w ||Xw - y||^2 + \alpha ||w||^2\end{align}\]</div>
 <p>This optimization problem contains two terms: (i) a <em>data-fitting term</em>
 <span class="math notranslate nohighlight">\(||Xw - y||^2\)</span>, which ensures the regression correctly fits the
 training data; and (ii) a regularization term <span class="math notranslate nohighlight">\(\alpha||w||^2\)</span>, which
@@ -654,8 +654,8 @@ <h2>Ridge regression<a class="headerlink" href="#ridge-regression" title="Link t
 <p>To understand why the regularization term makes the solution more robust to
 noise, let’s consider the ridge solution. The ridge solution can be found
 analytically with the formula:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-492d00e7-ad9c-4c41-8a51-e718f0553dd4">
-<span class="eqno">(6)<a class="headerlink" href="#equation-492d00e7-ad9c-4c41-8a51-e718f0553dd4" title="Permalink to this equation">#</a></span>\[\begin{align}w = (X^\top X + \alpha I)^{-1}  X^\top y\end{align}\]</div>
+<div class="amsmath math notranslate nohighlight" id="equation-a0efc9cb-9e9a-4048-9b95-83cf0418e6d0">
+<span class="eqno">(6)<a class="headerlink" href="#equation-a0efc9cb-9e9a-4048-9b95-83cf0418e6d0" title="Permalink to this equation">#</a></span>\[\begin{align}w = (X^\top X + \alpha I)^{-1}  X^\top y\end{align}\]</div>
 <p>where <code class="docutils literal notranslate"><span class="pre">I</span></code> is the identity matrix. In this formula, we can see that the
 inverted matrix is now <span class="math notranslate nohighlight">\((X^\top X + \alpha I)\)</span>. Compared to OLS, the
 additional term <span class="math notranslate nohighlight">\(\alpha I\)</span> adds a positive value <code class="docutils literal notranslate"><span class="pre">alpha</span></code> to all

notebooks/shortclips/06_visualize_hemodynamic_response.html

@@ -1660,8 +1660,8 @@ <h2>Visualize the HRF<a class="headerlink" href="#visualize-the-hrf" title="Link
 coefficients <span class="math notranslate nohighlight">\(\beta\)</span> obtained with a ridge regression, but the primal
 coefficients can be computed from the dual coefficients using the training
 features <span class="math notranslate nohighlight">\(X\)</span>:</p>
-<div class="amsmath math notranslate nohighlight" id="equation-679d04fd-27f8-45fb-895d-39c2b830da09">
-<span class="eqno">(7)<a class="headerlink" href="#equation-679d04fd-27f8-45fb-895d-39c2b830da09" title="Permalink to this equation">#</a></span>\[\begin{align}\beta = X^\top w\end{align}\]</div>
+<div class="amsmath math notranslate nohighlight" id="equation-7cf49575-3efa-49ea-87a4-318dc69a1259">
+<span class="eqno">(7)<a class="headerlink" href="#equation-7cf49575-3efa-49ea-87a4-318dc69a1259" title="Permalink to this equation">#</a></span>\[\begin{align}\beta = X^\top w\end{align}\]</div>
 <p>To better visualize the HRF, we will refit a model with more delays, but only
 on a selection of voxels to speed up the computations.</p>
 <div class="cell docutils container">

notebooks/shortclips/09_fit_banded_ridge_model.html

@@ -2827,8 +2827,8 @@ <h2>Plot the banded ridge split<a class="headerlink" href="#plot-the-banded-ridg
 take the kernel weights and the ridge (dual) weights corresponding to each
 feature space, and use them to compute the prediction from each feature space
 separately.</p>
-<div class="amsmath math notranslate nohighlight" id="equation-7b30bc1c-345f-4f87-b7b1-398ba820b074">
-<span class="eqno">(8)<a class="headerlink" href="#equation-7b30bc1c-345f-4f87-b7b1-398ba820b074" title="Permalink to this equation">#</a></span>\[\begin{align}\hat{y} = \sum_i^m \hat{y}_i = \sum_i^m \gamma_i K_i \hat{w}\end{align}\]</div>
+<div class="amsmath math notranslate nohighlight" id="equation-bc87ddee-f7f6-4477-8700-93c7c9d2f516">
+<span class="eqno">(8)<a class="headerlink" href="#equation-bc87ddee-f7f6-4477-8700-93c7c9d2f516" title="Permalink to this equation">#</a></span>\[\begin{align}\hat{y} = \sum_i^m \hat{y}_i = \sum_i^m \gamma_i K_i \hat{w}\end{align}\]</div>
 <p>Then, we use these split predictions to compute split <span class="math notranslate nohighlight">\(\tilde{R}^2_i\)</span>
 scores. These scores are corrected so that their sum is equal to the
 <span class="math notranslate nohighlight">\(R^2\)</span> score of the full prediction <span class="math notranslate nohighlight">\(\hat{y}\)</span>.</p>