log regression formula update

logistic_regression/logistic_regression.ipynb

@@ -13,6 +13,10 @@
     "\n",
     "$$ w^T x = w_0 + w_1x_1 + w_2x_2 + w_3x_3 $$\n",
     "\n",
+    "$$ w^Tx = \\sum^n_{i=1}{w_i \\cdot x_i} $$\n",
+    "\n",
+    "$$ \\sigma = \\frac{1}{1 + e^{-w^T}} $$\n",
+    "\n",
     "$$ P(y|x) = σ(w^Tx) $$\n",
     "\n",
     "## Given data:\n",
@@ -133,7 +137,7 @@
     "plt.show()\n",
     "\n",
     "plt.plot(x, np.log(fn(x)))\n",
-    "plt.show()\n"
+    "plt.show()"
    ]
   },
   {
@@ -213,7 +217,7 @@
     "labels = np.hstack((np.zeros(num_observations), np.ones(num_observations)))\n",
     "plt.figure(figsize=(12, 8))\n",
     "plt.scatter(features[:,0], features[:,1], alpha=.4, c=labels)\n",
-    "plt.show()\n"
+    "plt.show()"
    ]
   },
   {
@@ -375,8 +379,15 @@
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
    "version": "3.6.1"
+  },
+  "latex_envs": {
+   "bibliofile": "biblio.bib",
+   "cite_by": "apalike",
+   "current_citInitial": 1,
+   "eqLabelWithNumbers": true,
+   "eqNumInitial": 0
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 1
 }