bias/var plots

Author: fs446

bias_variance_linear_regression.ipynb

@@ -331,7 +331,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 64,
    "id": "7d969206",
    "metadata": {},
    "outputs": [],
@@ -343,7 +343,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 65,
    "id": "f18dc6d5",
    "metadata": {},
    "outputs": [],
@@ -391,7 +391,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 66,
    "id": "5e9a45d9",
    "metadata": {},
    "outputs": [],
@@ -418,15 +418,17 @@
    "source": [
     "# generate 'true' data with the design matrix of 'true' model\n",
     "y = X @ beta\n",
-    "plt.figure(figsize=(5, 3))\n",
+    "plt.figure(figsize=(6, 3))\n",
     "plt.plot(y, \"k-\")\n",
     "plt.xlabel(\"independent features' input variable x\")\n",
     "plt.ylabel((\"dependent variable y, true data\"))\n",
     "plt.title(\"true model data as linear model (x -> 4 features + intercept)\")\n",
     "plt.xlim(0, M)\n",
     "plt.ylim(-2, 8)\n",
     "plt.grid(True)\n",
-    "print(X.shape, y.shape)"
+    "print(X.shape, y.shape)\n",
+    "plt.tight_layout()\n",
+    "plt.savefig('bias_variance_plots/true_data.png', dpi=300)"
    ]
   },
   {
@@ -583,7 +585,9 @@
     "X = np.copy(x)[:, None]\n",
     "fig, axs = plt.subplots(2, 2, figsize=(10, 5))\n",
     "bias_variance_of_model(X)\n",
-    "axs[0, 0].set_title(\"underfit, too low model complexity, high bias, low var\");"
+    "axs[0, 0].set_title(\"underfit, too low model complexity, high bias, low var\");\n",
+    "plt.tight_layout()\n",
+    "plt.savefig('bias_variance_plots/too_simple_model.png', dpi=300)"
    ]
   },
   {
@@ -618,7 +622,9 @@
     "# note  that intercept is only added in function bias_variance_of_model(X)\n",
     "fig, axs = plt.subplots(2, 2, figsize=(10, 5))\n",
     "bias_variance_of_model(X)\n",
-    "axs[0, 0].set_title(\"overfit, too high model complexity, low bias, high var\");"
+    "axs[0, 0].set_title(\"overfit, too high model complexity, low bias, high var\");\n",
+    "plt.tight_layout()\n",
+    "plt.savefig('bias_variance_plots/too_complex_model.png', dpi=300)"
    ]
   },
   {
@@ -652,7 +658,9 @@
     "bias_variance_of_model(X)  # lowest possible bias^2+variance, because we\n",
     "# know the true model (again: which in practice likely never will occur)\n",
     "# the remaining variance is from the added noise\n",
-    "axs[0, 0].set_title(\"true model features, lowest bias, lowest var\");"
+    "axs[0, 0].set_title(\"true model features, lowest bias, lowest var\");\n",
+    "plt.tight_layout()\n",
+    "plt.savefig('bias_variance_plots/true_model.png', dpi=300)"
    ]
   },
   {
@@ -684,7 +692,9 @@
     "# note  that intercept is only added in function bias_variance_of_model(X)\n",
     "fig, axs = plt.subplots(2, 2, figsize=(10, 5))\n",
     "bias_variance_of_model(X)\n",
-    "axs[0, 0].set_title(\"reasonable bias/var trade-off if true model is unknown\");"
+    "axs[0, 0].set_title(\"reasonable bias/var trade-off if true model is unknown\");\n",
+    "plt.tight_layout()\n",
+    "plt.savefig('bias_variance_plots/robust_model.png', dpi=300)"
    ]
   },
   {
@@ -721,7 +731,7 @@
   "kernelspec": {
    "display_name": "myddasp",
    "language": "python",
-   "name": "myddasp"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -733,7 +743,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.6"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,

bias_variance_plots/bias_var_l2_regularisation.png

@@ -24,7 +24,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "id": "c86e15f6",
    "metadata": {},
    "outputs": [],
@@ -174,7 +174,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "id": "6764d6da",
    "metadata": {},
    "outputs": [],
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 16,
    "id": "d8ef032a",
    "metadata": {},
    "outputs": [],
@@ -263,7 +263,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 17,
    "id": "e21f304f",
    "metadata": {},
    "outputs": [],
@@ -295,7 +295,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "id": "9afb4067",
    "metadata": {},
    "outputs": [],
@@ -337,7 +337,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 19,
    "id": "9c3ccf25",
    "metadata": {},
    "outputs": [],
@@ -371,7 +371,7 @@
    "outputs": [],
    "source": [
     "fig, axs = plt.subplots(1, 1, figsize=(8, 4))\n",
-    "axs.plot(alpha2_vec, bias_squared, \"C0\", label=r\"bias$^2$\", lw=2)\n",
+    "axs.plot(alpha2_vec, bias_squared, \"C0\", label=r\"bias$^2$\", lw=3)\n",
     "axs.plot(alpha2_vec, variance, \"C1\", label=r\"var\")\n",
     "axs.plot(alpha2_vec, bias_squared + variance, \"C2\", label=r\"bias$^2$+var\")\n",
     "\n",
@@ -381,12 +381,15 @@
     "\n",
     "axs.set_xscale(\"log\")\n",
     "axs.set_yscale(\"log\")\n",
-    "axs.set_xlabel(r\"regularization value $\\alpha^2$\")\n",
+    "axs.set_xlabel(r\"underfit region                                   regularization value $\\alpha^2$                                   overfit region\")\n",
     "axs.set_title(r\"$\\alpha^2_\\mathrm{opt}$=\" + \"{:4.3f}\".format(alpha2_vec[idx]))\n",
     "axs.legend()\n",
     "axs.set_xlim(10**alpha2_min, 10**alpha2_max)\n",
     "axs.set_ylim(1e-2, 1e1)\n",
-    "axs.grid(True)"
+    "axs.grid(True)\n",
+    "axs.xaxis.set_inverted(True)\n",
+    "plt.tight_layout()\n",
+    "plt.savefig('bias_variance_plots/bias_var_l2_regularisation.png', dpi=600)"
    ]
   },
   {
@@ -668,7 +671,7 @@
   "kernelspec": {
    "display_name": "myddasp",
    "language": "python",
-   "name": "myddasp"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -680,7 +683,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.6"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,