WIP

Author: gnthibault

DifferentiatingPerceptron.ipynb

@@ -655,7 +655,7 @@
    "views": {}
   },
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -669,9 +669,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.7"
+   "version": "3.12.1"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 1
+ "nbformat_minor": 4
 }

InformationTheoryOptimization.ipynb

@@ -191,7 +191,7 @@
     "\\end{align*}\n",
     "where $p_1$ and $p_2$ are probability mass functions and $\\lambda \\in [0,1]$\n",
     "\n",
-    "Proof: Let $X$ be a discrete random variable with possible outcomes $\\mathcal{X} := {x_i, i \\in 0,1,\\dots N-1}$ and let $u(x)$ be the probability mass function of a discrete uniform distribution on $X \\in \\mathcal{X}$. Then, the entropy of an arbitrary probability mass function $p(x)$ can be rewritten as\n",
+    "Proof: Let $X$ be a discrete random variable with possible outcomes $\\mathcal{X} := {x_i, i \\in 0,1,\\dots N-1}$ and let $u(x)$ be the probability mass function of a discrete uniform distribution on $X \\in \\mathcal{X}$, ie $u(x_i)=\\frac{1}{N}$. Then, the entropy of an arbitrary probability mass function $p(x)$ can be rewritten as\n",
     "\n",
     "\\begin{align*} \\tag{1.2}\n",
     "    H(X) &= - \\sum_{i=0}^{N-1} p(x_i)log(p(x_i)) \\\\\n",

OptimalTransportWasserteinDistance.ipynb

@@ -559,7 +559,7 @@
    "metadata": {},
    "source": [
     "### OT and statistical concepts\n",
-    "Some of the basics to understand the following statements can be found in the notebook \"InformationTheoryOptimization\" this part is also partly a direct reproduction of Marco Cuturi famous article \"Sinkhorn Distances: Lightspeed Computation of Optimal Transport\"\n",
+    "Some of the basics to understand the following statements can be found in the notebook \"InformationTheoryOptimization\", this part is also partly a direct reproduction of Marco Cuturi famous article \"Sinkhorn Distances: Lightspeed Computation of Optimal Transport\"\n",
     "\n",
     "I would like to stop and mention that as we now interpret $P$ as a joint probability matrix, we can define its entropy, the marginal probabiilty entropy, and KL-divergence between two different transportation matrix. These takes the form of\n",
     "\n",
@@ -579,7 +579,7 @@
     "\\begin{align*} \\tag{1.5}\n",
     "    \\forall r,c \\in \\Sigma_d, \\forall P \\in U(r,c), h(P) \\leq h(r) + h(c)\n",
     "\\end{align*}\n",
-    "ie, by using log-sum inequality, proved in the notebook called InformationTheoryOptimization\n",
+    "ie, by using log-sum inequality, we proved in the notebook called InformationTheoryOptimization\n",
     "\\begin{align*}\\tag{1.6}\n",
     "    \\sum_{i=0}^{N-1} a_i log\\left(\\frac{a_i}{b_i}\\right) &\\geq \\left(\\sum_{i=0}^{N-1} a_i\\right) log\\left(\\frac{\\sum_{i=0}^{N-1}a_i}{\\sum_{i=0}^{N-1}b_i}\\right)\n",
     "\\end{align*}\n",

RegularizationByDenoising.ipynb

@@ -15,7 +15,7 @@
     "\n",
     "## Introduction\n",
     "\n",
-    "This notebook intends to show what are the next steps in terms of regularized image reconstruction. We will try to focus especially in a framework that allows the introduction of deep learning in a proper mathematical framework that allows for prior and data fitting mitigation called: regularization by denoising (RED).\n",
+    "This notebook intends to show what are the next steps in terms of regularized image reconstruction. We will try to focus especially in a framework that allows the introduction of deep learning in a proper mathematical framework that allows for prior and data fitting mitigation called: regularization by denoising (RED) but not only.\n",
     "\n",
     "The following paper guided us to write this notebook:\n",
     "\n",
@@ -38,7 +38,10 @@
     "https://ieeexplore.ieee.org/document/9107406\n",
     "\n",
     "* Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition\n",
-    "https://arxiv.org/abs/2106.03668"
+    "https://arxiv.org/abs/2106.03668\n",
+    "\n",
+    "* Deep inverse\n",
+    "https://github.com/deepinv/deepinv"
    ]
   },
   {
@@ -51,7 +54,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -65,9 +68,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.10"
+   "version": "3.12.1"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }

bayesian_ab_testing.ipynb

@@ -1960,7 +1960,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.6"
+   "version": "3.12.1"
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  "nbformat": 4,