From 88d5ee3c40e6e3fde865ae06b1b837eed9ff34de Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Pawe=C5=82=20Sk=C3=B3rzewski?= <pawel.skorzewski@amu.edu.pl>
Date: Thu, 3 Nov 2022 15:24:35 +0100
Subject: [PATCH] =?UTF-8?q?Wyk=C5=82ad=204.=20Regresja=20logistyczna?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 wyk/03_Regresja_liniowa_2.ipynb   |    2 +-
 wyk/04_Regresja_logistyczna.ipynb | 9779 +++++++++++++++--------------
 2 files changed, 4970 insertions(+), 4811 deletions(-)

diff --git a/wyk/03_Regresja_liniowa_2.ipynb b/wyk/03_Regresja_liniowa_2.ipynb
index 605ad58..4d849ae 100644
--- a/wyk/03_Regresja_liniowa_2.ipynb
+++ b/wyk/03_Regresja_liniowa_2.ipynb
@@ -1496,7 +1496,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.4"
+   "version": "3.10.6"
   },
   "livereveal": {
    "start_slideshow_at": "selected",
diff --git a/wyk/04_Regresja_logistyczna.ipynb b/wyk/04_Regresja_logistyczna.ipynb
index b61990d..ceeabc6 100644
--- a/wyk/04_Regresja_logistyczna.ipynb
+++ b/wyk/04_Regresja_logistyczna.ipynb
@@ -8,8 +8,8 @@
     }
    },
    "source": [
-    "### AITech — Uczenie maszynowe\n",
-    "# 3. Regresja logistyczna"
+    "### Uczenie maszynowe\n",
+    "# 4. Regresja logistyczna"
    ]
   },
   {
@@ -86,7 +86,7 @@
     }
    },
    "source": [
-    "## 3.1. Dwuklasowa regresja logistyczna"
+    "## 4.1. Dwuklasowa regresja logistyczna"
    ]
   },
   {
@@ -115,7 +115,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 147,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -127,7 +127,7 @@
     "\n",
     "import numpy as np\n",
     "import matplotlib\n",
-    "import matplotlib.pyplot as pl\n",
+    "import matplotlib.pyplot as plt\n",
     "import pandas\n",
     "import ipywidgets as widgets\n",
     "\n",
@@ -138,8 +138,8 @@
     "\n",
     "# Przydatne funkcje\n",
     "\n",
-    "# Wyświetlanie macierzy w LaTeX-u\n",
     "def LatexMatrix(matrix):\n",
+    "    \"\"\"Wyświetlanie macierzy w LaTeX-u\"\"\"\n",
     "    ltx = r'\\left[\\begin{array}'\n",
     "    m, n = matrix.shape\n",
     "    ltx += '{' + (\"r\" * n) + '}'\n",
@@ -148,13 +148,13 @@
     "    ltx += r'\\end{array}\\right]'\n",
     "    return ltx\n",
     "\n",
-    "# Hipoteza (wersja macierzowa)\n",
-    "def hMx(theta, X):\n",
+    "def h(theta, X):\n",
+    "    \"\"\"Hipoteza (wersja macierzowa)\"\"\"\n",
     "    return X * theta\n",
     "\n",
-    "# Wykres danych (wersja macierzowa)\n",
-    "def regdotsMx(X, y, xlabel, ylabel):    \n",
-    "    fig = pl.figure(figsize=(16*.6, 9*.6))\n",
+    "def regdots(X, y, xlabel, ylabel):\n",
+    "    \"\"\"Wykres danych (wersja macierzowa)\"\"\"\n",
+    "    fig = plt.figure(figsize=(16*.6, 9*.6))\n",
     "    ax = fig.add_subplot(111)\n",
     "    fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n",
     "    ax.scatter([X[:, 1]], [y], c='r', s=50, label='Dane')\n",
@@ -162,12 +162,12 @@
     "    ax.set_xlabel(xlabel)\n",
     "    ax.set_ylabel(ylabel)\n",
     "    ax.margins(.05, .05)\n",
-    "    pl.ylim(y.min() - 1, y.max() + 1)\n",
-    "    pl.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n",
+    "    plt.ylim(y.min() - 1, y.max() + 1)\n",
+    "    plt.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n",
     "    return fig\n",
     "\n",
-    "# Wykres krzywej regresji (wersja macierzowa)\n",
-    "def reglineMx(fig, fun, theta, X):\n",
+    "def regline(fig, fun, theta, X):\n",
+    "    \"\"\"Wykres krzywej regresji (wersja macierzowa)\"\"\"\n",
     "    ax = fig.axes[0]\n",
     "    x0 = np.min(X[:, 1]) - 1.0\n",
     "    x1 = np.max(X[:, 1]) + 1.0\n",
@@ -179,8 +179,8 @@
     "                theta1=(float(theta[1][0]) if theta[1][0] >= 0 else float(-theta[1][0])),\n",
     "                op='+' if theta[1][0] >= 0 else '-')))\n",
     "\n",
-    "# Legenda wykresu\n",
     "def legend(fig):\n",
+    "    \"\"\"Legenda wykresu\"\"\"\n",
     "    ax = fig.axes[0]\n",
     "    handles, labels = ax.get_legend_handles_labels()\n",
     "    # try-except block is a fix for a bug in Poly3DCollection\n",
@@ -189,20 +189,19 @@
     "    except AttributeError:\n",
     "        pass\n",
     "\n",
-    "# Wersja macierzowa funkcji kosztu\n",
-    "def JMx(theta,X,y):\n",
+    "def J(theta,X,y):\n",
+    "    \"\"\"Wersja macierzowa funkcji kosztu\"\"\"\n",
     "    m = len(y)\n",
     "    J = 1.0 / (2.0 * m) * ((X * theta - y).T * ( X * theta - y))\n",
     "    return J.item()\n",
     "\n",
-    "# Wersja macierzowa gradientu funkcji kosztu\n",
-    "def dJMx(theta,X,y):\n",
+    "def dJ(theta,X,y):\n",
+    "    \"\"\"Wersja macierzowa gradientu funkcji kosztu\"\"\"\n",
     "    return 1.0 / len(y) * (X.T * (X * theta - y)) \n",
     "\n",
-    "# Implementacja algorytmu gradientu prostego za pomocą numpy i macierzy\n",
-    "def GDMx(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-3):\n",
+    "def GD(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-3):\n",
+    "    \"\"\"Implementacja algorytmu gradientu prostego za pomocą numpy i macierzy\"\"\"\n",
     "    current_cost = fJ(theta, X, y)\n",
-    "    logs = [[current_cost, theta]]\n",
     "    while True:\n",
     "        theta = theta - alpha * fdJ(theta, X, y) # implementacja wzoru\n",
     "        current_cost, prev_cost = fJ(theta, X, y), current_cost\n",
@@ -210,13 +209,12 @@
     "            break\n",
     "        if abs(prev_cost - current_cost) <= eps:\n",
     "            break\n",
-    "        logs.append([current_cost, theta]) \n",
-    "    return theta, logs\n",
+    "    return theta\n",
     "\n",
-    "thetaStartMx = np.matrix([0, 0]).reshape(2, 1)\n",
+    "theta_start = np.matrix([0, 0]).reshape(2, 1)\n",
     "\n",
-    "# Funkcja, która rysuje próg\n",
     "def threshold(fig, theta):\n",
+    "    \"\"\"Funkcja, która rysuje próg\"\"\"\n",
     "    x_thr = (0.5 - theta.item(0)) / theta.item(1)\n",
     "    ax = fig.axes[0]\n",
     "    ax.plot([x_thr, x_thr], [-1, 2],\n",
@@ -226,7 +224,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 148,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -250,13 +248,13 @@
    "source": [
     "# Wczytanie pełnych (oryginalnych) danych\n",
     "\n",
-    "data_iris = pandas.read_csv('iris.csv')\n",
-    "print(data_iris[:6])"
+    "data_iris = pandas.read_csv(\"iris.csv\")\n",
+    "print(data_iris[:6])\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 149,
    "metadata": {
     "scrolled": true,
     "slideshow": {
@@ -282,14 +280,16 @@
     "# Ograniczenie danych do 2 klas i 1 cechy\n",
     "\n",
     "data_iris_setosa = pandas.DataFrame()\n",
-    "data_iris_setosa['dł. płatka'] = data_iris['pl']  # \"pl\" oznacza \"petal length\"\n",
-    "data_iris_setosa['Iris setosa?'] = data_iris['Gatunek'].apply(lambda x: 1 if x=='Iris-setosa' else 0)\n",
-    "print(data_iris_setosa[:6])"
+    "data_iris_setosa[\"dł. płatka\"] = data_iris[\"pl\"]  # \"pl\" oznacza \"petal length\"\n",
+    "data_iris_setosa[\"Iris setosa?\"] = data_iris[\"Gatunek\"].apply(\n",
+    "    lambda x: 1 if x == \"Iris-setosa\" else 0\n",
+    ")\n",
+    "print(data_iris_setosa[:6])\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 150,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -304,16 +304,16 @@
     "n = n_plus_1 - 1\n",
     "Xn = data_iris_setosa.values[:, 0:n].reshape(m, n)\n",
     "\n",
-    "XMx3 = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
-    "yMx3 = np.matrix(data_iris_setosa.values[:, 1]).reshape(m, 1)\n",
+    "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
+    "y = np.matrix(data_iris_setosa.values[:, 1]).reshape(m, 1)\n",
     "\n",
     "# Regresja liniowa\n",
-    "theta_e3, logs3 = GDMx(JMx, dJMx, thetaStartMx, XMx3, yMx3, alpha=0.03, eps=0.000001)"
+    "theta_lin = GD(J, dJ, theta_start, X, y, alpha=0.03, eps=0.000001)\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 151,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -323,969 +323,997 @@
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       "text/plain": [
-       "<Figure size 691.2x388.8 with 1 Axes>"
+       "<Figure size 960x540 with 1 Axes>"
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      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
-    "fig = regdotsMx(XMx3, yMx3, 'x', 'Iris setosa?')\n",
-    "legend(fig)"
+    "fig = regdots(X, y, \"x\", \"Iris setosa?\")\n",
+    "legend(fig)\n"
    ]
   },
   {
@@ -1303,7 +1331,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 152,
    "metadata": {
     "slideshow": {
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       "text/plain": [
-       "<Figure size 691.2x388.8 with 1 Axes>"
+       "<Figure size 960x540 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
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    ],
    "source": [
-    "fig = regdotsMx(XMx3, yMx3, 'x', 'Iris setosa?')\n",
-    "reglineMx(fig, hMx, theta_e3, XMx3)\n",
-    "legend(fig)"
+    "fig = regdots(X, y, \"x\", \"Iris setosa?\")\n",
+    "regline(fig, h, theta_lin, X)\n",
+    "legend(fig)\n"
    ]
   },
   {
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   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 153,
    "metadata": {
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       "text/plain": [
-       "<Figure size 691.2x388.8 with 1 Axes>"
+       "<Figure size 960x540 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
-    "fig = regdotsMx(XMx3, yMx3, 'x', 'Iris setosa?')\n",
-    "theta_e3, logs3 = GDMx(JMx, dJMx, thetaStartMx, XMx3, yMx3, alpha=0.03, eps=0.000001)\n",
-    "reglineMx(fig, hMx, theta_e3, XMx3)\n",
-    "threshold(fig, theta_e3)  # pomarańczowa linia oznacza granicę między klasą \"1\" a klasą \"0\" wyznaczoną przez próg \"h(x) = 0.5\"\n",
-    "legend(fig)"
+    "fig = regdots(X, y, \"x\", \"Iris setosa?\")\n",
+    "theta_lin = GD(J, dJ, theta_start, X, y, alpha=0.03, eps=0.000001)\n",
+    "regline(fig, h, theta_lin, X)\n",
+    "threshold(\n",
+    "    fig, theta_lin\n",
+    ")  # pomarańczowa linia oznacza granicę między klasą \"1\" a klasą \"0\" wyznaczoną przez próg \"h(x) = 0.5\"\n",
+    "legend(fig)\n"
    ]
   },
   {
@@ -3588,7 +3686,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 154,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -3596,15 +3694,14 @@
    },
    "outputs": [],
    "source": [
-    "# Funkjca logistycza\n",
-    "\n",
     "def logistic(x):\n",
-    "    return 1.0 / (1.0 + np.exp(-x))"
+    "    \"\"\"Funkcja logistyczna\"\"\"\n",
+    "    return 1.0 / (1.0 + np.exp(-x))\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 155,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -3613,14 +3710,16 @@
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
-    "def plot_logistic():\n",
-    "    x = np.linspace(-5,5,200)\n",
-    "    y = logistic(x)\n",
     "\n",
-    "    fig = plt.figure(figsize=(7,5))\n",
+    "\n",
+    "def plot_logistic():\n",
+    "    \"\"\"Wykres funkcji logistycznej\"\"\"\n",
+    "    x = np.linspace(-5, 5, 200)\n",
+    "    y = logistic(x)\n",
+    "    fig = plt.figure(figsize=(7, 5))\n",
     "    ax = fig.add_subplot(111)\n",
-    "    plt.ylim(-.1,1.1)\n",
-    "    ax.plot(x, y, linewidth='2')"
+    "    plt.ylim(-0.1, 1.1)\n",
+    "    ax.plot(x, y, linewidth=\"2\")\n"
    ]
   },
   {
@@ -3636,7 +3735,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 156,
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+       "  </clipPath>\n",
+       " </defs>\n",
+       "</svg>\n"
       ],
       "text/plain": [
-       "<Figure size 504x360 with 1 Axes>"
+       "<Figure size 700x500 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
-    "plot_logistic()"
+    "plot_logistic()\n"
    ]
   },
   {
@@ -4163,7 +4276,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 157,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4171,9 +4284,9 @@
    },
    "outputs": [],
    "source": [
-    "# Funkcja regresji logistcznej\n",
     "def h(theta, X):\n",
-    "    return 1.0/(1.0 + np.exp(-X * theta))"
+    "    \"\"\"Funkcja regresji logistcznej\"\"\"\n",
+    "    return 1.0 / (1.0 + np.exp(-X * theta))\n"
    ]
   },
   {
@@ -4206,7 +4319,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 158,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -4214,18 +4327,18 @@
    },
    "outputs": [],
    "source": [
-    "# Funkcja kosztu dla regresji logistycznej\n",
     "def J(h, theta, X, y):\n",
+    "    \"\"\"Funkcja kosztu dla regresji logistycznej\"\"\"\n",
     "    m = len(y)\n",
     "    h_val = h(theta, X)\n",
     "    s1 = np.multiply(y, np.log(h_val))\n",
     "    s2 = np.multiply((1 - y), np.log(1 - h_val))\n",
-    "    return -np.sum(s1 + s2, axis=0) / m"
+    "    return -np.sum(s1 + s2, axis=0) / m\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 159,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4233,14 +4346,14 @@
    },
    "outputs": [],
    "source": [
-    "# Gradient dla regresji logistycznej\n",
     "def dJ(h, theta, X, y):\n",
-    "    return 1.0 / len(y) * (X.T * (h(theta, X) - y))"
+    "    \"\"\"Gradient dla regresji logistycznej\"\"\"\n",
+    "    return 1.0 / len(y) * (X.T * (h(theta, X) - y))\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 160,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -4248,27 +4361,28 @@
    },
    "outputs": [],
    "source": [
-    "# Metoda gradientu prostego dla regresji logistycznej\n",
-    "def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, maxSteps=10000):\n",
-    "    errorCurr = fJ(h, theta, X, y)\n",
-    "    errors = [[errorCurr, theta]]\n",
+    "def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, max_steps=10000):\n",
+    "    \"\"\"Metoda gradientu prostego dla regresji logistycznej\"\"\"\n",
+    "    curr_cost = fJ(h, theta, X, y)\n",
+    "    history = [[curr_cost, theta]]\n",
     "    while True:\n",
     "        # oblicz nowe theta\n",
     "        theta = theta - alpha * fdJ(h, theta, X, y)\n",
     "        # raportuj poziom błędu\n",
-    "        errorCurr, errorPrev = fJ(h, theta, X, y), errorCurr\n",
+    "        prev_cost = curr_cost\n",
+    "        curr_cost = fJ(h, theta, X, y)\n",
     "        # kryteria stopu\n",
-    "        if abs(errorPrev - errorCurr) <= eps:\n",
+    "        if abs(prev_cost - curr_cost) <= eps:\n",
     "            break\n",
-    "        if len(errors) > maxSteps:\n",
+    "        if len(history) > max_steps:\n",
     "            break\n",
-    "        errors.append([errorCurr, theta]) \n",
-    "    return theta, errors"
+    "        history.append([curr_cost, theta])\n",
+    "    return theta, history\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 161,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -4279,7 +4393,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "error = [[0.05755617]]\n",
+      "Koszt: [[0.05755617]]\n",
       "theta = [[ 5.02530461]\n",
       " [-1.99174803]]\n"
      ]
@@ -4287,15 +4401,16 @@
    ],
    "source": [
     "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n",
-    "thetaBest, errors = GD(h, J, dJ, thetaStartMx, XMx3, yMx3, \n",
-    "                       alpha=0.1, eps=10**-7, maxSteps=1000)\n",
-    "print(\"error =\", errors[-1][0])\n",
-    "print(\"theta =\", thetaBest)"
+    "theta_best, history = GD(\n",
+    "    h, J, dJ, theta_start, X, y, alpha=0.1, eps=10**-7, max_steps=1000\n",
+    ")\n",
+    "print(f\"Koszt: {history[-1][0]}\")\n",
+    "print(f\"theta = {theta_best}\")\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 162,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -4303,30 +4418,36 @@
    },
    "outputs": [],
    "source": [
-    "# Funkcja regresji logistycznej (wersja skalarna)\n",
     "def scalar_logistic_regression_function(theta, x):\n",
-    "    return 1.0/(1.0 + np.exp(-(theta.item(0) + theta.item(1) * x)))\n",
+    "    \"\"\"Funkcja regresji logistycznej (wersja skalarna)\"\"\"\n",
+    "    return 1.0 / (1.0 + np.exp(-(theta.item(0) + theta.item(1) * x)))\n",
+    "\n",
     "\n",
-    "# Rysowanie progu\n",
     "def threshold_val(fig, x_thr):\n",
+    "    \"\"\"Rysowanie progu\"\"\"\n",
     "    ax = fig.axes[0]\n",
-    "    ax.plot([x_thr, x_thr], [-1, 2],\n",
-    "            color='orange', linestyle='dashed',\n",
-    "            label=u'próg: $x={:.2F}$'.format(x_thr))\n",
+    "    ax.plot(\n",
+    "        [x_thr, x_thr],\n",
+    "        [-1, 2],\n",
+    "        color=\"orange\",\n",
+    "        linestyle=\"dashed\",\n",
+    "        label=\"próg: $x={:.2F}$\".format(x_thr),\n",
+    "    )\n",
+    "\n",
     "\n",
-    "# Wykres krzywej regresji logistycznej\n",
     "def logistic_regline(fig, theta, X):\n",
+    "    \"\"\"Wykres krzywej regresji logistycznej\"\"\"\n",
     "    ax = fig.axes[0]\n",
     "    x0 = np.min(X[:, 1]) - 1.0\n",
     "    x1 = np.max(X[:, 1]) + 1.0\n",
     "    Arg = np.arange(x0, x1, 0.1)\n",
     "    Val = scalar_logistic_regression_function(theta, Arg)\n",
-    "    ax.plot(Arg, Val, linewidth='2')"
+    "    ax.plot(Arg, Val, linewidth=\"2\")\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 163,
    "metadata": {
     "scrolled": true,
     "slideshow": {
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       "text/plain": [
-       "<Figure size 691.2x388.8 with 1 Axes>"
+       "<Figure size 960x540 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
-    "fig = regdotsMx(XMx3, yMx3, xlabel='x', ylabel='Iris setosa?')\n",
-    "logistic_regline(fig, thetaBest, XMx3)\n",
-    "threshold_val(fig, 2.5)"
+    "fig = regdots(X, y, xlabel=\"x\", ylabel=\"Iris setosa?\")\n",
+    "logistic_regline(fig, theta_best, X)\n",
+    "threshold_val(fig, 2.5)\n"
    ]
   },
   {
@@ -5382,12 +5529,16 @@
    "source": [
     "Jak postąpić, jeżeli będziemy mieli więcej niż jedną cechę $x$?\n",
     "\n",
-    "Weźmy teraz wszystkie cechy występujące w zbiorze *Iris*."
+    "Weźmy teraz wszystkie cechy występujące w zbiorze *Iris*:\n",
+    "* długość płatków (`pl`, *petal length*)\n",
+    "* szerokość płatków (`pw`, *petal width*)\n",
+    "* długość działek kielicha (`sl`, *sepal length*)\n",
+    "* szerokość działek kielicha (`sw`, *sepal width*)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 164,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -5398,45 +5549,29 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "   dł. płatków  szer. płatków  dł. dz. k.  szer. dz. k.  Iris setosa?\n",
-      "0          1.4            0.2         5.2           3.4             1\n",
-      "1          1.5            0.4         5.1           3.7             1\n",
-      "2          5.6            2.4         6.7           3.1             0\n",
-      "3          5.1            2.0         6.5           3.2             0\n",
-      "4          4.5            1.7         4.9           2.5             0\n",
-      "5          5.1            1.6         6.0           2.7             0\n"
+      "    pl   pw   sl   sw  Iris setosa?\n",
+      "0  1.4  0.2  5.2  3.4             1\n",
+      "1  1.5  0.4  5.1  3.7             1\n",
+      "2  5.6  2.4  6.7  3.1             0\n",
+      "3  5.1  2.0  6.5  3.2             0\n",
+      "4  4.5  1.7  4.9  2.5             0\n",
+      "5  5.1  1.6  6.0  2.7             0\n"
      ]
     }
    ],
    "source": [
     "data_iris_setosa_multi = pandas.DataFrame()\n",
-    "data_iris_setosa_multi['dł. płatków'] = data_iris['pl']  # \"pl\" oznacza \"petal length\" (długość płatków)\n",
-    "data_iris_setosa_multi['szer. płatków'] = data_iris['pw']  # \"pw\" oznacza \"petal width\" (szerokość płatków)\n",
-    "data_iris_setosa_multi['dł. dz. k.'] = data_iris['sl']  # \"sl\" oznacza \"sepal length\" (długość działek kielicha)\n",
-    "data_iris_setosa_multi['szer. dz. k.'] = data_iris['sw']  # \"sw\" oznacza \"sepal width\" (szerokość działek kielicha)\n",
-    "data_iris_setosa_multi['Iris setosa?'] = data_iris['Gatunek'].apply(lambda x: 1 if x=='Iris-setosa' else 0)\n",
-    "print(data_iris_setosa_multi[:6])"
+    "for feature in [\"pl\", \"pw\", \"sl\", \"sw\"]:\n",
+    "    data_iris_setosa_multi[feature] = data_iris[feature]\n",
+    "data_iris_setosa_multi[\"Iris setosa?\"] = data_iris[\"Gatunek\"].apply(\n",
+    "    lambda x: 1 if x == \"Iris-setosa\" else 0\n",
+    ")\n",
+    "print(data_iris_setosa_multi[:6])\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "notes"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "%matplotlib inline\n",
-    "\n",
-    "import matplotlib.pyplot as plt\n",
-    "import seaborn"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 165,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -5468,16 +5603,16 @@
     "n = n_plus_1 - 1\n",
     "Xn = data_iris_setosa_multi.values[:, 0:n].reshape(m, n)\n",
     "\n",
-    "XMx4 = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
-    "yMx4 = np.matrix(data_iris_setosa_multi.values[:, n]).reshape(m, 1)\n",
+    "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
+    "y = np.matrix(data_iris_setosa_multi.values[:, n]).reshape(m, 1)\n",
     "\n",
-    "print(XMx4[:6])\n",
-    "print(yMx4[:6])"
+    "print(X[:6])\n",
+    "print(y[:6])\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 166,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -5486,16 +5621,16 @@
    "outputs": [],
    "source": [
     "# Podział danych na zbiór trenujący i testowy\n",
-    "XTrain, XTest = XMx4[:100], XMx4[100:]\n",
-    "yTrain, yTest = yMx4[:100], yMx4[100:]\n",
+    "XTrain, XTest = X[:100], X[100:]\n",
+    "yTrain, yTest = y[:100], y[100:]\n",
     "\n",
     "# Macierz parametrów początkowych\n",
-    "thetaTemp = np.ones(5).reshape(5,1)"
+    "theta_start = np.ones(5).reshape(5, 1)\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 167,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -5506,7 +5641,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "error = [[0.006797]]\n",
+      "Koszt: [[0.006797]]\n",
       "theta = [[ 1.11414027]\n",
       " [-2.89324615]\n",
       " [-0.66543637]\n",
@@ -5516,10 +5651,11 @@
     }
    ],
    "source": [
-    "thetaBest, errors = GD(h, J, dJ, thetaTemp, XTrain, yTrain, \n",
-    "                       alpha=0.1, eps=10**-7, maxSteps=1000)\n",
-    "print(\"error =\", errors[-1][0])\n",
-    "print(\"theta =\", thetaBest)"
+    "theta_best, history = GD(\n",
+    "    h, J, dJ, theta_start, XTrain, yTrain, alpha=0.1, eps=10**-7, max_steps=1000\n",
+    ")\n",
+    "print(f\"Koszt: {history[-1][0]}\")\n",
+    "print(f\"theta = {theta_best}\")\n"
    ]
   },
   {
@@ -5546,7 +5682,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 168,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -5563,21 +5699,22 @@
       " [ 0.14887292]\n",
       " [ 2.13284493]]\n",
       "x0 = [[1.  6.3 1.8 7.3 2.9]]\n",
-      "h(x0) = 1.6061436959824898e-05\n",
-      "c(x0) = (0, 1.6061436959824898e-05) \n",
-      "\n"
+      "h(x0) = 1.606143695982487e-05\n",
+      "c(x0) = (0, 1.606143695982487e-05)\n"
      ]
     }
    ],
    "source": [
     "def classifyBi(theta, X):\n",
+    "    \"\"\"Funkcja decyzyjna regresji logistycznej\"\"\"\n",
     "    prob = h(theta, X).item()\n",
     "    return (1, prob) if prob > 0.5 else (0, prob)\n",
     "\n",
-    "print(\"theta =\", thetaBest)\n",
-    "print(\"x0 =\", XTest[0])\n",
-    "print(\"h(x0) =\", h(thetaBest, XTest[0]).item())\n",
-    "print(\"c(x0) =\", classifyBi(thetaBest, XTest[0]), \"\\n\")"
+    "\n",
+    "print(f\"theta = {theta_best}\")\n",
+    "print(f\"x0 = {XTest[0]}\")\n",
+    "print(f\"h(x0) = {h(theta_best, XTest[0]).item()}\")\n",
+    "print(f\"c(x0) = {classifyBi(theta_best, XTest[0])}\")\n"
    ]
   },
   {
@@ -5593,7 +5730,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 169,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -5604,7 +5741,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0 <=> 0 -- prob: 0.0\n",
+      "0 <=> 0 -- prob: 0.0000\n",
       "1 <=> 1 -- prob: 0.9816\n",
       "0 <=> 0 -- prob: 0.0001\n",
       "0 <=> 0 -- prob: 0.0005\n",
@@ -5620,14 +5757,15 @@
     }
    ],
    "source": [
-    "acc = 0.0\n",
+    "correct = 0\n",
     "for i, rest in enumerate(yTest):\n",
-    "    cls, prob = classifyBi(thetaBest, XTest[i])\n",
+    "    cls, prob = classifyBi(theta_best, XTest[i])\n",
     "    if i < 10:\n",
-    "        print(int(yTest[i].item()), \"<=>\", cls, \"-- prob:\", round(prob, 4))\n",
-    "    acc += cls == yTest[i].item()\n",
+    "        print(f\"{yTest[i].item():1.0f} <=> {cls} -- prob: {prob:6.4f}\")\n",
+    "    correct += cls == yTest[i].item()\n",
+    "accuracy = correct / len(XTest)\n",
     "\n",
-    "print(\"\\nAccuracy:\", acc / len(XTest))"
+    "print(f\"\\nAccuracy: {accuracy}\")\n"
    ]
   },
   {
@@ -5638,7 +5776,7 @@
     }
    },
    "source": [
-    "## 3.2. Wieloklasowa regresja logistyczna"
+    "## 4.2. Wieloklasowa regresja logistyczna"
    ]
   },
   {
@@ -5654,7 +5792,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 170,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5752,20 +5890,21 @@
        "5  6.0  2.7  5.1  1.6  Iris-versicolor"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 170,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "import pandas\n",
-    "data_iris = pandas.read_csv('iris.csv')\n",
-    "data_iris[:6]"
+    "\n",
+    "data_iris = pandas.read_csv(\"iris.csv\")\n",
+    "data_iris[:6]\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 171,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -5792,7 +5931,7 @@
     "\n",
     "import numpy as np\n",
     "\n",
-    "features = ['sl', 'sw', 'pl', 'pw']\n",
+    "features = [\"sl\", \"sw\", \"pl\", \"pw\"]\n",
     "m = len(data_iris)\n",
     "X = np.matrix(data_iris[features])\n",
     "X0 = np.ones(m).reshape(m, 1)\n",
@@ -5800,7 +5939,7 @@
     "y = np.matrix(data_iris[[\"Gatunek\"]]).reshape(m, 1)\n",
     "\n",
     "print(\"X = \", X[:4])\n",
-    "print(\"y = \", y[:4])"
+    "print(\"y = \", y[:4])\n"
    ]
   },
   {
@@ -5872,7 +6011,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 172,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -5883,9 +6022,10 @@
     "def mapY(y, cls):\n",
     "    m = len(y)\n",
     "    yBi = np.matrix(np.zeros(m)).reshape(m, 1)\n",
-    "    yBi[y == cls] = 1.\n",
+    "    yBi[y == cls] = 1.0\n",
     "    return yBi\n",
     "\n",
+    "\n",
     "def indicatorMatrix(y):\n",
     "    classes = np.unique(y.tolist())\n",
     "    m = len(y)\n",
@@ -5895,13 +6035,14 @@
     "        Y[:, i] = mapY(y, cls)\n",
     "    return Y\n",
     "\n",
-    "# one-hot matrix\n",
-    "Y = indicatorMatrix(y)"
+    "\n",
+    "# Macierz jednostkowa\n",
+    "Y = indicatorMatrix(y)\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 173,
    "metadata": {
     "slideshow": {
      "slide_type": "notes"
@@ -5914,7 +6055,7 @@
     "YTrain, YTest = Y[:100], Y[100:]\n",
     "\n",
     "# Macierz parametrów początkowych - niech skłąda się z samych jedynek\n",
-    "thetaTemp = np.ones(5).reshape(5,1)"
+    "theta_start = np.ones(5).reshape(5, 1)\n"
    ]
   },
   {
@@ -5973,7 +6114,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 174,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -5981,9 +6122,9 @@
    },
    "outputs": [],
    "source": [
-    "# Zapis macierzowy funkcji softmax\n",
     "def softmax(X):\n",
-    "    return np.exp(X) / np.sum(np.exp(X))"
+    "    \"\"\"Funkcja softmax (wersja macierzowa)\"\"\"\n",
+    "    return np.exp(X) / np.sum(np.exp(X))\n"
    ]
   },
   {
@@ -5999,7 +6140,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 175,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6017,12 +6158,35 @@
    "source": [
     "Z = np.matrix([[2.1, 0.5, 0.8, 0.9, 3.2]])\n",
     "P = softmax(Z)\n",
-    "print(np.sum(P)) "
+    "print(np.sum(P))\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 176,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "subslide"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def multiple_binary_classifiers(X, Y):\n",
+    "    n = X.shape[1]\n",
+    "    thetas = []\n",
+    "    # Dla każdej klasy wytrenujmy osobny klasyfikator dwuklasowy.\n",
+    "    for c in range(Y.shape[1]):\n",
+    "        YBi = Y[:, c]\n",
+    "        theta = np.matrix(np.random.random(n)).reshape(n, 1)\n",
+    "        # Macierz parametrów theta obliczona dla każdej klasy osobno.\n",
+    "        theta_best, history = GD(h, J, dJ, theta, X, YBi, alpha=0.1, eps=10**-4)\n",
+    "        thetas.append(theta_best)\n",
+    "    return thetas\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 177,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -6034,48 +6198,34 @@
      "output_type": "stream",
      "text": [
       "Otrzymana macierz parametrów theta dla klasy 0:\n",
-      " [[ 0.68590262]\n",
-      " [ 0.39948964]\n",
-      " [ 1.13312933]\n",
-      " [-2.17550597]\n",
-      " [-0.53088875]] \n",
+      " [[ 0.30877778]\n",
+      " [-0.16504776]\n",
+      " [ 1.92701194]\n",
+      " [-1.83418434]\n",
+      " [-0.50458444]] \n",
       "\n",
       "Otrzymana macierz parametrów theta dla klasy 1:\n",
-      " [[ 0.95431453]\n",
-      " [ 0.07249434]\n",
-      " [-1.07233395]\n",
-      " [ 0.53801787]\n",
-      " [-0.65001214]] \n",
+      " [[ 0.93723385]\n",
+      " [-0.13501701]\n",
+      " [-0.8448612 ]\n",
+      " [ 0.77823106]\n",
+      " [-0.95577092]] \n",
       "\n",
       "Otrzymana macierz parametrów theta dla klasy 2:\n",
-      " [[-0.66101185]\n",
-      " [-1.40133883]\n",
-      " [-2.01776182]\n",
-      " [ 2.18505283]\n",
-      " [ 2.74690482]] \n",
+      " [[-0.72237014]\n",
+      " [-1.56606505]\n",
+      " [-1.71063165]\n",
+      " [ 2.21207268]\n",
+      " [ 2.78489436]] \n",
       "\n"
      ]
     }
    ],
    "source": [
-    "# Dla każdej klasy wytrenujmy osobny klasyfikator dwuklasowy.\n",
-    "\n",
-    "def trainMaxEnt(X, Y):\n",
-    "    n = X.shape[1]\n",
-    "    thetas = []\n",
-    "    for c in range(Y.shape[1]):\n",
-    "        YBi = Y[:,c]\n",
-    "        theta = np.matrix(np.random.random(n)).reshape(n,1)\n",
-    "        # Macierz parametrów theta obliczona dla każdej klasy osobno.\n",
-    "        thetaBest, errors = GD(h, J, dJ, theta, \n",
-    "                               X, YBi, alpha=0.1, eps=10**-4)\n",
-    "        thetas.append(thetaBest)\n",
-    "    return thetas\n",
-    "\n",
     "# Macierze theta dla każdej klasy\n",
-    "thetas = trainMaxEnt(XTrain, YTrain);\n",
+    "thetas = multiple_binary_classifiers(XTrain, YTrain)\n",
     "for c, theta in enumerate(thetas):\n",
-    "    print(f\"Otrzymana macierz parametrów theta dla klasy {c}:\\n\", theta, \"\\n\")"
+    "    print(f\"Otrzymana macierz parametrów theta dla klasy {c}:\\n\", theta, \"\\n\")\n"
    ]
   },
   {
@@ -6093,7 +6243,30 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 178,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "subslide"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def classify(thetas, X, debug=False):\n",
+    "    regs = np.array([(X * theta).item() for theta in thetas])\n",
+    "    if debug:\n",
+    "        print(\"Po zastosowaniu regresji: \", regs)\n",
+    "    probs = softmax(regs)\n",
+    "    if debug:\n",
+    "        print(\"Otrzymane prawdopodobieństwa: \", np.around(probs, decimals=3))\n",
+    "    result = np.argmax(probs)\n",
+    "    if debug:\n",
+    "        print(\"Wybrana klasa: \", result)\n",
+    "    return result\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 179,
    "metadata": {
     "slideshow": {
      "slide_type": "subslide"
@@ -6105,36 +6278,29 @@
      "output_type": "stream",
      "text": [
       "Dla x = [[1.  7.3 2.9 6.3 1.8]]:\n",
-      "Po zastosowaniu regresji:  [-7.77303536  0.59324542  1.96796697]\n",
-      "Otrzymane prawdopodobieństwa:  [0.    0.202 0.798]\n",
+      "Po zastosowaniu regresji:  [-7.77134959  0.68398021  1.83339097]\n",
+      "Otrzymane prawdopodobieństwa:  [0.    0.241 0.759]\n",
       "Wybrana klasa:  2\n",
       "Obliczone y = 2\n",
       "Oczekiwane y = 2\n",
       "\n",
       "Dla x = [[1.  4.8 3.  1.4 0.3]]:\n",
-      "Po zastosowaniu regresji:  [ 2.79786587 -1.35649314 -9.55757825]\n",
-      "Otrzymane prawdopodobieństwa:  [0.985 0.015 0.   ]\n",
+      "Po zastosowaniu regresji:  [ 2.57835094 -1.4426392  -9.43900726]\n",
+      "Otrzymane prawdopodobieństwa:  [0.982 0.018 0.   ]\n",
       "Wybrana klasa:  0\n",
       "Obliczone y = 0\n",
       "Oczekiwane y = 0\n",
       "\n",
       "Dla x = [[1.  7.1 3.  5.9 2.1]]:\n",
-      "Po zastosowaniu regresji:  [-7.02868459  0.06130237  1.99650886]\n",
-      "Otrzymane prawdopodobieństwa:  [0.    0.126 0.874]\n",
+      "Po zastosowaniu regresji:  [-6.96334044  0.0284738   1.92618005]\n",
+      "Otrzymane prawdopodobieństwa:  [0.   0.13 0.87]\n",
       "Wybrana klasa:  2\n",
       "Obliczone y = 2\n",
       "Oczekiwane y = 2\n",
       "\n",
       "Dla x = [[1.  5.9 3.  5.1 1.8]]:\n",
-      "Po zastosowaniu regresji:  [-5.60840075 -0.26110148  1.10600174]\n",
-      "Otrzymane prawdopodobieństwa:  [0.001 0.203 0.796]\n",
-      "Wybrana klasa:  2\n",
-      "Obliczone y = 2\n",
-      "Oczekiwane y = 2\n",
-      "\n",
-      "Dla x = [[1.  6.1 2.6 5.6 1.4]]:\n",
-      "Po zastosowaniu regresji:  [-6.85715204  0.71134476  1.62660319]\n",
-      "Otrzymane prawdopodobieństwa:  [0.    0.286 0.714]\n",
+      "Po zastosowaniu regresji:  [-5.14656032 -0.14535936  1.20033165]\n",
+      "Otrzymane prawdopodobieństwa:  [0.001 0.206 0.792]\n",
       "Wybrana klasa:  2\n",
       "Obliczone y = 2\n",
       "Oczekiwane y = 2\n",
@@ -6143,31 +6309,19 @@
     }
    ],
    "source": [
-    "def classify(thetas, X, debug=False):\n",
-    "    regs = np.array([(X*theta).item() for theta in thetas])\n",
-    "    if debug:\n",
-    "        print(\"Po zastosowaniu regresji: \", regs)\n",
-    "    probs = softmax(regs)\n",
-    "    if debug:\n",
-    "        print(\"Otrzymane prawdopodobieństwa: \", np.around(probs,decimals=3))\n",
-    "    result = np.argmax(probs)\n",
-    "    if debug:\n",
-    "        print(\"Wybrana klasa: \", result)\n",
-    "    return result\n",
-    "\n",
-    "for i in range(5):\n",
+    "for i in range(4):\n",
     "    print(f\"Dla x = {XTest[i]}:\")\n",
     "    YPredicted = classify(thetas, XTest[i], debug=True)\n",
     "    print(f\"Obliczone y = {YPredicted}\")\n",
     "    print(f\"Oczekiwane y = {np.argmax(YTest[i])}\")\n",
-    "    print()"
+    "    print()\n"
    ]
   }
  ],
  "metadata": {
   "celltoolbar": "Slideshow",
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -6181,11 +6335,16 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.3"
+   "version": "3.10.6"
   },
   "livereveal": {
    "start_slideshow_at": "selected",
    "theme": "white"
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
+   }
   }
  },
  "nbformat": 4,