notebooks/9 Fitovanje podataka.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitovanje podataka"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> U ovoj svesci ćemo demostrirati fitovanje podataka, pokazati smisao srednjeg kvadratnog odstupanja kao mere kvaliteta fita i pokazati šta znači da model premalo ili previše dobro fituje (_under-_ i _over-fitting_).  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ukoliko za empirijske podatke postoji teorijski model, onda sigurno znamo i jednačinu koja povezuje zavisno i nezavisno promenljivu. To je tipičan slučaj kada u istraživanju imamo sve elemente naučnog metoda uključujući posmatranje, postavljanje hipoteze i dizajniranje eksperimenta. Međutim, nauka o podacima i mašinsko učenje su primene analize podataka na podacima za koje ne moramo da znamo teorijski okvir. Najbolji model mašinskog učenja ne pretenduje da bude naučno objašnjenje pojave već samo model koji u konkretnom slučaju daje dobru predikciju rezultata.\n",
    "\n",
    "Fitovanje podataka u slučajevima kada znamo jednačinu koja povezuje zavisno i nezavisno promeljivu je jednoznačno određeno. Bez teorijskog modela, odnosno poznavanja te veze za fitovanje podatka možemo da koristimo različite modele i vidimo koji je najverodostojniji. Svakako prvo počinjemo od najjednostavnijeg modela, linearnog."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearni model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linearni model je najčešće korišćen model predikcije, ne samo u mašinskom učenju već u nauci uopšte. Pomoću ovog modela se određuju parametri linearne funkcije koja opisuje zavisnost jedne kontinualne promenljive od druge. Ovaj model se često naziva i linearna regresija. Postoji nekoliko načina za pravljenje linearnih modela. Mi ćemo ovde pokušati da prikažemo najjednostavniji, tj. onaj koji ne učitava biblioteku za mašinsko učenje samo zato da bi uradio linearan fit. Biblioteka __numpy__ ima funkcije koje mogu da nam pomognu."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za potrebe ove vežbe koristićemo prvo veštački generisane, odnosno simulirane podatke. Uzećemo tačno određenu vezu između nezavisne (x) i zavisno promenljive (y). Da bi zadatak bio malo realniji dodaćemo i malo šuma. U toj situaciji znamo šta treba da dobijemo pa ćemo tačno znati koliko pri fitovanju grešimo. Potom ćemo fitovanje uraditi za empirijske podatke gde ne znamo funkciju zavisnosti između promenljivih."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulacija "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za potrebe simulacije bazirane na pseudo-slučajnim brojevima potreban nam je modul __random__ iz biblioteke __numpy__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da bi podaci sa kojima radimo u ovoj svesci bili isti bez obzira gde i kada pokrenemo kôd, potrebno je da generator slučajnih brojeva uvek počne od iste vrednosti. To ćemo obezbediti tako što na početku zadamo uvek istu vrednost \"klice\" random generatora pomoću funkcije `random.seed()`. Vrednost u zagradama može biti bilo koji nenegativan ceo broj. Važno je da ga ne menjamo kako bi rezultati bili ponovljivi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pomoću funkcije `random.random()` ovog modula ćemo generisati niz od `n=12` slučajnih _float_ brojeva između 0 i 3. Primetite da ovaj niz nije lista nego niz tipa _array_ jer takve generiše __numpy__. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=12\n",
    "x=random.random(n)*3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.63021483, 0.83510816, 1.27355277, 2.5343284 , 0.01415657,\n",
       "       0.36470736, 2.01224725, 2.47755827, 0.41011977, 1.72527999,\n",
       "       2.67396586, 0.62760637])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za dalji rad će nam biti potrebno da ovaj niz bude uređen, odnosno sortiran od najmanje vrednosti. Funkcija `sort()` sortira niz i modifikuje ga. Dovoljno je da aktiviramo `x.sort()` pa da niz __x__ bude sortiran."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x.sort()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uzećemo da kvadratna funkcija povezuje x i y, tj. da je $y=2x^2-2x+5$. Da zavisnost ne bi bila sasvim očigledna generisaćemo šum, odnosno niz __noise__ kao niz slučajnih brojeva između 0 i 1,5. Vrednost tog šuma ćemo dodati na vrednost dobijenu kvadratnom funkcijom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise=np.random.rand(n)*1.5\n",
    "y = 2*(x**2) - 2*x - 5 + noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sada pošto imamo i __x__ i __y__ možemo da fitujemo podatke linearnom funkcijom. To ćemo uraditi pomoću funkcije `polyfit()` koja služi za fitovanje polinomom bilo kog reda. Ako stavimo kao argument broj 1, taj polinom će biti prvog reda, odnosno linearna funkcija. Koeficijenti linearne funkcije će biti sačuvani u objektu koji smo nazvali __model1__. Sa tim koeficijentima možemo da, pomoću funkcije `poly1d()` koja od koeficijenata polinoma pravi polinom, da definišemo pomoćnu funkciju `model1_fn()` koja će nam biti potrebna kasnije. Ta funkcija će za svaku vrednost promenljive __x__ davati predikciju vrednosti promenljive __y__. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1=np.polyfit(x,y,1)\n",
    "model1_fn=np.poly1d(model1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Biće potrebno da nacrtamo i tačke (__x__,__y__) i krivu __model1_fn__ da bismo videli kako traženi model fituje podatke. Da bi bilo lakše da ocenimo kvalitet fita, ovom grafiku ćemo dodati i reziduale, odnosno razlike između stvarnih vrednosti za __y__ i vrednosti koje smo prognozirali pomoću modela."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pomoćne promenljive __xfit__ i __yfit__ su uvedene da bi se funkcija prikazala kao linija, odnosno da bi rezolucija pri crtanju krive bila bolja. Interval od 0 do 3 smo podelili na 100 intervala pomoću funkcije `linspace()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "\n",
    "xfit = np.linspace(0, 3, 100)\n",
    "yfit = model1_fn(xfit)\n",
    "plt.plot(xfit,yfit,color=\"gray\")\n",
    "\n",
    "plt.vlines(x=x, ymin=y, ymax=model1_fn(x), colors='red');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kvalitet fita možemo da opišemo na mnogo načina. Često se za to koristi koeficijent korelacije. Ovde nam je zgodnije da koristimo srednji kvadrat odstupanja (MSE od eng. _mean square error_) kao meru koja može lepo da se vizuelizuje. Što je vrednost MSE manja, to je fit bolji. Vidimo na grafiku kolike su vrednosti odstupanja za svaku tačku (crvene linije). Sve te vrednosti treba kvadrirati, sabrati i podeliti sa n. Konkretno za ovaj linearni fit, srednje kvadratno odstupanje je:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5325787013593561"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rez=np.poly1d(model1)(x)-y\n",
    "sum(rez**2)/n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kvadratna funkcija"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pošto znamo kako smo generisali podatke, znamo i da postoji boji fit od linearnog modela. Kvadratna funkcija će sigurno imati manja odstupanja stvarne i prognozirane vrednosti __y__. Za to ćemo koristiti istu funkciju `polyfit()` samo što će sada argument koji se odnosi na red polinoma biti 2. Na sledećem grafiku ćemo nacrtati krivu dobijenu ovakvim fitom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/n40bN5KRkcHChQt1P3EPU5CL9EBff/0127dv5/HHH2f+/Pla2cfjFOQiPYi1lu3bt7Nnzx6efPJJcnJytMZmCFCQi/QQTU1NbNq0iYMHDzJu3DimT5+u1e5DhIJcpAfw+XysXbuWEydO8MILL/DKK69gjNZMDxWOvBwbY14zxpwyxpw1xnzkRJsi4oyGhgZWrFjBiRMnmDJlCq+++qpCPMQEfEZujAkD/g8wBSgGvjXGrLfWngi0bREJTE1NDZ9//jmlpaXMnj2bZ555xu2SpAs4MbTyHHDWWlsEYIxZCcwGFOQiLqqoqGDZsmXcunWLt956i6ysLLdLki7iRJCnAZfu+rkYeL7tRsaYD4APANLT0x3YrYjcz9WrV2n4yU+YZS3s2qW/uRDnxBh5e4Nt9gcPWLvUWpttrc1OSUlxYLci0p7z58+z9Ne/odFvueaLYeHnZ8k7XOJ2WdKFnDgjLwYG3/XzIKDUgXZF5BEVFBSwdm0eN5uiKG+KpQlDSUUtH68pACBnTJrLFUpXcOKM/FvgcWPMUGNMJLAAWO9AuyLSQdZa9uzZw5o1a7hObzbWZdF015vl2kY/n2w55WKF0pUCPiO31vqMMX8GbAHCgN9aa48HXJmIdMjdF/qMGjWKv8mPwk8vFrz9y3u2K62odalC6WqOXBBkrd0EbHKiLRHpuIaGBnJzczlz5kzrhT7/cnYnJe2E9sDEGBcqlO6g63NFPKqyspJPP/2Us2fPMmPGjNYLfT6clkVMxL33T4mJCOPDaZp+GKp0ib6IB12+fJkVK1ZQX1/PwoULefzxx1ufa/lA85MtpyitqGVgYgwfTsvSB50hTEEu4jGnTp1i9erVxMTE8NOf/pT+/fv/YJucMWkK7h5EQS7iEdZa9u3bx9atWxkwYAALFy7UAskCKMhFPMHv9/PFF19w5MgRnnjiCXJycrQYhLRSkIsEuerqalatWsXFixd58cUXmTx5su5eKPdQkIsEsStXrrBy5Uqqq6uZO3cuTz31lNslSRBSkIsEqcLCQtauXUt0dDTvv/8+AwcOdLskCVIKcpEgY61l165d7N69m0GDBvHmm2/qQ015IAW5SBCpq6tj7dq1nD59mmeeeYYZM2YQHq4/U3kw/Q8RCRJlZWX84Q9/4ObNm7z++us8++yz+lBTOkRBLhIEjh8/zrp164iMjGTJkiUMGTLE7ZLEQxTkIi5qampi27Zt7Nu3j0GDBjF//nz69OnjdlniMQpyEZdUVVWxevVqLly4QHZ2Nq+99hphYWEP/0WRNhTkIi74/vvvyc3NpaGhgTlz5jB69Gi3SxIPU5CLdKOWlXx27NhBUlISS5YsITU11e2yxOMU5CLdpKamhrVr13L27FlGjRrFzJkziYqKcrssCQEKcpEA5B0u6dB9vy9cuMDq1aupqalh+vTpZGdna2qhOEZBLtJJeYdL+HhNAbWNfoB2V6tvamriT3/6E0Pee483w8MJ272bAQMGuFazhCYt9SbSSZ9sOdUa4i3uXq2+qqqKzz77jF27dhEXF8fAAQMU4tIldEYu0kktq9Kv/PwjgNZV60srajl58iTr16/H5/Mxe/ZsknfuRAMp0lUCCnJjzCfATKABOAe8b62tcKAukaA3MDHmB6vVh+HnpbjL/OEP+QwYMIC5c+eSnJzsUoXSUwQ6tLIVeNJaOxo4DXwceEki3tB2tfp+ppqc6EIGN13hJz/5CT/72c8U4tItAjojt9Z+ddeP+4F5gZUj4h0tH2hGLu9FhL+ON6JPEhUdw4L5i8nMzGzdLu9wCekXK2jw+fnLX+7QivbiOCfHyH8K/OF+TxpjPgA+AEhPT3dwtyLueXFIDPWR9dTX1fPUqCeYMWMGMTExrc+3zGz51Hf/mS0igXpokBtjtgGPtfPUL6y165q3+QXgA5bfrx1r7VJgKUB2drbtVLUiQcJaS35+Plu3bqXXe+8xffp0/t1TT/1gbviDZrYoyMUpDw1ya+2rD3reGPMu8AbwirVWAS0h79atW2zYsIFz586RmZnJ7Nmz73vHwpaZLS0zWto+LuKEQGetvAb8DTDJWlvjTEkiwclay6FDh/jqq6+w1nboCs32Zra0PC7ilEDHyP83EAVsbf7PvN9a+/OAqxIJMhUVFWzYsIGioiIyMjKYNWsWffv2fejvfTgt656rPwFiIsL4cFpWV5YrPUygs1Z+5FQhIsGoqamJb7/9lu3bt2OMeeT7pLSMg3fkfiwinaUrO0Xu49q1a2zYsIHi4mJ+9KMfMWPGDBITEx+5nZwxaQpu6VIKcpE2fD4fu3fvZs+ePURFRZGTk8Po0aN1t0IJWgpykbsUFRWxceNGbty4wdNPP83UqVOJjY11uyyRB1KQiwC3b9/mq6++oqCggL59+/LOO+8wbNgwt8sS6RAFufRoLR9m7ty5E5/Px6RJk5gwYQLh4frTEO/Q/1bpsS5evMimTZu4evUqmZmZvP7667rJlXiSglx6nMrKSrZt20ZBQQF9+vRh/vz5jBw5Uh9mimcpyKXHaGxsZN++fXz99dc0NTUxceJEJkyYQGRkpNuliQREQS4hz1rL8ePH2bZtG7du3WLEiBFMnTq1Q1dminiBglxC2qVLl/jqq68oLi7mscceY/bs2QwdOtTtskQcpSCXkHT9+nW2b99OYWEh8fHxzJo1i6effppevbTeuIQeBbmElKqqKnbv3s2hQ4cIDw9n8uTJjB8/XuPgEtIU5BISamtr2bt3L/v376epqYmxY8cyadIk4uPj3S5NpMspyMXT6uvrOXDgAHv37qW+vp4nn3ySl156iaSkJLdLE+k2CnLxpIaGBr755hv27t1LbW0tWVlZTJ48mccea29VQpHQpiAXT6mvr+fbb79tDfBhw4bx0ksvkZam28RKz6UgF0+ora3lwIEDZP70pwxqaiLt7/+eSZMmMWjQILdLE3GdglyCWlVVFfv27ePgwYM0NDTwRHQ0CQkJLFq0yO3SRIKGglyCUnl5OXv37uW7777DWsuoUaOYMGECqTt3ul2aSNBRkEvQsNby/fffs2/fPs6cOUN4eDjjxo1j/Pjxupxe5AEU5OK6xsZGjh07xoEDB7h69SqxsbFMnjyZ7Oxs4uLi3C5PJOg5EuTGmL8CPgFSrLXlTrQp98o7XBJyK7FXVFRw8OBBDh48SG1tLampqcycOZPRo0drYQeRRxDwX4sxZjAwBbgYeDnSnrzDJXy8poDaRj8AJRW1fLymACCgMHfjxaGpqYlz586Rn5/P6dOnMcYwfPhwnn/+eTIyMh54T/C8wyWkX6ygwefnL3+5IyRezESc4MRpz78Afw2sc6AtaccnW061hniL2kY/n2w51ekg66oXh/uprKzk8OHDHDp0iMrKSuLi4pg4cSLjxo0jISGhw/V+6uueekW8JKAgN8bMAkqstd89bHUVY8wHwAcA6enpgey2xymtqAVg5ecfAbDg7V/e83hndMWLQ1s+n49Tp05x+PBhioqKsNaSmZnJtGnTyMrKIiwsLKjqFfGqhwa5MWYb0N51z78A/haY2pEdWWuXAksBsrOz7SPU2OMNTIyhpJ3QHpgY0+k2u+LFAe7MPLl06RJHjx7l+PHj1NXV0adPHyZMmMCYMWM6Pfukpa6WOts+LtKTPTTIrbWvtve4MeYpYCjQcjY+CDhkjHnOWnvF0Sp7uA+nZbUOI7SIiQjjw2lZnW7T6ReHq1evcuzYMY4dO0ZFRQURERGMGDGCp59+mqFDhwZ8H/CueDETCRWdHlqx1hYAqS0/G2O+B7I1a8V5LUMHkcvDaPD5SXPgg8lAXxystZSVlXHixAlOnDhBWVkZxhgyMzOZPHkyI0aMICoqqtP13a/eu4dXAn0xEwkVmuPlETlj0iA9EYA9H73sTHs82ouDtZbS0lJOnjzJyZMnKS+/85qdnp7O9OnTeeKJJ7ps3ndLXaE2BVPECY4FubU2w6m2pHt05MWhoaGB8+fPc/r0ac6cOUNVVRXGGDIyMnjuuecYOXJkty3ekDMmTcEt0g6dkcs9WoZMzp49y7lz57hw4QJ+v5/IyEiGDRtGVlYWw4cPJyZGY9MiwUJB3sNZwO/zUXD4MOfPn+f8+fPcvn0bgOTkZLKzsxk+fDhDhgx5pOmCItJ9FOQ9TMsZ96VLl7h48SLZxcX4fT7Wr19PXFwcQ4cOZejQoQwbNqxDF+qIiPs8FeS7du3imyPHOF0VwYW6aHrFJfHzac8wZ9xgt0sLWlVVVZSWllJSUkJpaSnFxcXU19cDEBcXh+8f/oEhQ4bw8yFDSE1NfeAl8iISnDwV5EW3LOdvNvK3v/sf9MLyu/ff59CGw5zdk8zIzHT69+9P//79SU1NJTo62u1yu5Xf7+f69etcu3aNq1evcuXKFa5cudI6TGKMITU1lVGjRpGens7gwYPp27evglskBHgqyH9TaCmpH867TfGE0cTuhqEk9aphYEUd/mPHOHjwYOu2vXv3JiUlheTkZJKSkujXrx9JSUkkJCR4dqzXAk1+PyUXL3Ljxg1u3LhBeXk55eXlXL9+naamJuBOaKekpDBs2DAee+wxBgwYwIABA4iMjHT3AESkS3gqyH9wmbYfzvn7YRqh6L9Mp7KykqtXr3Lt2jXKy8spKyvjyJEjNDQ0tLZhjKFPnz4kJibSp0+f1q/evXsTHx9PXFwccXFxREZGduvZqs/no6amhurqam7fvs3t27eprKxs/aqoqOCNCxew1vK7Tz9tPZa+ffuSkpLC8OHDSUlJoX///iQnJ+s2sCI9iKf+2h90mbYxhoSEBBISEhg+fHjrc9ZaqquruXHjBtevX6eioqL169KlS1RWVraeyd6tV69exMbGEh0dTXR0NFFRUURFRREREUFERATh4eGEh4cTFhZGWFgYxpjW4LfWYq2lqakJv9+P3+/H5/PR2NhIY2MjDQ0N1NXVUV9fT11dHbW1tfe82NwtLi6O3r17k5yczMlf/YrExETeTkoiKSmJxMREz767EBHneCrIO3OZtjGG+Ph44uPj273rYkvQt5wF3759m5qamtavlsCtra3l1q1brUHs8/nw+/0s/s1vAPjd+++3tvlu8xlzy2MtgR8ZGUlERASRkZFERUWRmJhIVFQUMTExxMbGEhsb21prS4DrzFpEHsZTKdEVl2nfHfSdYbdvB2v5xS9+gbWW9UdKuPm7NdT7mtgaOYG/em2ErkYUkS7lqSCH4LtM2wAYQ3h4OHmHS/jP60/yqe/OUE3xrTotfiAiXc5zQR5M2i49VtPg0+IHItLtFOSd1N7SYy20+IGIdKfA7vbfg7W39Nj9aPEDEelKOiPvpPstPdaWFj8Qka6mM/JOut9ZdmJMBGmJMRggLTGGf5j7lMbHRaRL6Yy8k+43p/2/zRql4BaRbqUg7yQtPSYiwUJBHoBgm9MuIj2TxshFRDxOQS4i4nEKchERj1OQi4h4nIJcRMTjjLW2+3dqTBlwoZO/ngyUO1iOm3QswSdUjgN0LMEqkGMZYq1NafugK0EeCGNMvrU22+06nKBjCT6hchygYwlWXXEsGloREfE4BbmIiMd5MciXul2Ag3QswSdUjgN0LMHK8WPx3Bi5iIjcy4tn5CIichcFuYiIxwVtkBtjXjPGnDLGnDXGfNTO88YY87+anz9qjBnrRp0d0YFjmWyMuWWMOdL89V/dqPNhjDG/NcZcM8Ycu8/znuiTDhyHJ/oDwBgz2Biz0xhTaIw5boz583a28Uq/dORYgr5vjDHRxphvjDHfNR/Hf29nG2f7xFobdF9AGHAOyAQige+AJ9psMx3YDBjgx8ABt+sO4FgmA1+4XWsHjuVFYCxw7D7Pe6VPHnYcnuiP5loHAGObv+8NnPbw30pHjiXo+6b53zm++fsI4ADw467sk2A9I38OOGutLbLWNgArgdlttpkN/N7esR9INMYM6O5CO6Ajx+IJ1trdwI0HbOKJPunAcXiGtfaytfZQ8/dVQCHQ9ib5XumXjhxL0Gv+d77d/GNE81fbWSWO9kmwBnkacOmun4v5YYd2ZJtg0NE6xze/FdtsjBnVPaU5zit90hGe6w9jTAYwhjtngHfzXL884FjAA31jjAkzxhwBrgFbrbVd2ifBukKQaeextq9oHdkmGHSkzkPcuYfCbWPMdCAPeLyrC+sCXumTh/Fcfxhj4oHVwF9YayvbPt3OrwRtvzzkWDzRN9ZaP/CMMSYRWGuMedJae/dnMo72SbCekRcDg+/6eRBQ2oltgsFD67TWVra8FbPWbgIijDHJ3VeiY7zSJw/ktf4wxkRwJ/iWW2vXtLOJZ/rlYcfitb6x1lYAu4DX2jzlaJ8Ea5B/CzxujBlqjIkEFgDr22yzHljS/Onvj4Fb1trL3V1oBzz0WIwxjxljTPP3z3GnX653e6WB80qfPJCX+qO5zt8Ahdbaf77PZp7ol44cixf6xhiT0nwmjjEmBngVONlmM0f7JCiHVqy1PmPMnwFbuDPr47fW2uPGmJ83P/8rYBN3Pvk9C9QA77tV74N08FjmAf/eGOMDaoEFtvmj7WBijFnBnVkDycaYYuDvuPNBjqf6pAPH4Yn+aPYCsBgoaB6TBfhbIB281S907Fi80DcDgN8ZY8K480Kzylr7RVfmly7RFxHxuGAdWhERkQ5SkIuIeJyCXETE4xTkIiIepyAXEfE4BbmIiMcpyEVEPO7/A3RaPFAM6rQzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "\n",
    "model2=np.polyfit(x,y,2)\n",
    "model2_fn=np.poly1d(model2)\n",
    "\n",
    "xfit = np.linspace(0, 3, 100)\n",
    "yfit = model2_fn(xfit)\n",
    "plt.plot(xfit,yfit,color=\"gray\")\n",
    "\n",
    "plt.vlines(x=x, ymin=y, ymax=model2_fn(x), colors='red');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Očekivano, ovde su reziduali mnogo manji tako da se crvene linije jedva primećuju. Srednje kvadratno odstupanje je ovde sigurno manje:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19921483320048403"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rez=np.poly1d(model2)(x)-y\n",
    "sum(rez**2)/n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nije teško zaključiti da je kvadratna funkcija odličan model za podatke koje smo prvobitno generisali koristeći kvadratnu funkciju. U realnom slučaju, to naravno nije tako. Mi ne znamo kakva je prava zavisnost i možemo samo da je pretpostavimo na osnovu fitovanja različitim modelima."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testiranje modela"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "U realnom slučaju fitovanje radimo na poznatom uzorku, a predikcije radimo za nepoznate tačke. To je poenta korišćenja modela. Greška koju načinimo predviđajući vrednosti zavisno promenljive u situacijama gde ne možemo da ih izmerimo ili koje se još nisu dogodile je prava mera uspešnosti modela. Ovde ćemo simulirati upravo takvu situaciju za četiri različita modela. Uporedićemo srednje kvadratne greške kako bismo utvrdili koji je model najbolji."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za početak, podelićemo ceo skup tačaka (__x__,__y__) na dva dela: na uzorak na kom fitujemo funkciju (__learn__) i ostatak skupa koji koristimo za testiranje modela (__test__). Konkretno, koristićemo funkciju `random.choice()` iz biblioteke __numpy__ da dobijemo slučajan uzorak koji čine dve trećine početnog skupa, odnosno 8 od 12 elemenata. Sama funkcija nam daje slučajno izabran skup indeksa od 0 do n-1. Nakon toga biramo podatke iz __x__ i __y__ koji odgovaraju tim indeksima. Parametar `replace=False` predstavlja zahtev da se izabrane vrednosti ne ponavljaju."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "learn=np.random.choice(12, 8, replace=False)\n",
    "test=list(set(range(n))-set(learn))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 9  4  6  5  8  3 10  1]\n"
     ]
    }
   ],
   "source": [
    "print(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vrednosti __x__ i __y__ za učenje su __xl__ i __yl__, dok su vrednosti za testiranje __xt__ i __yt__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "xl=x[learn]\n",
    "xt=x[test]\n",
    "\n",
    "yl=y[learn]\n",
    "yt=y[test]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za deo skupa koji smo označili sa __learn__ fitovaćemo četiri polinomijalne funkcije prvog, drugog, trećeg i četvrtog reda i tako odrediti koeficijente ovih modela. Potom ćemo za svaki od tih modela konstruisati funkciju koja daje predikciju promenljive __y__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "m1=np.polyfit(xl,yl,1)\n",
    "m2=np.polyfit(xl,yl,2)\n",
    "m3=np.polyfit(xl,yl,3)\n",
    "m4=np.polyfit(xl,yl,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "m1_fn=np.poly1d(m1)\n",
    "m2_fn=np.poly1d(m2)\n",
    "m3_fn=np.poly1d(m3)\n",
    "m4_fn=np.poly1d(m4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zbog jednostavnosti prikaza ovih funkcija uzimamo isti uređen niz vrednosti nezavisno promenljive (__xfit__) i za svaku njenu vrednost izračunavamo vrednost zavisno promenljive po različitim modelima. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "xfit = np.linspace(0, 3, 100)\n",
    "y1fit = m1_fn(xfit)\n",
    "y2fit = m2_fn(xfit)\n",
    "y3fit = m3_fn(xfit)\n",
    "y4fit = m4_fn(xfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reziduale i srednja kvadratna odstupanja računamo samo za tačke iz skupa __test__. Njih želimo da uporedimo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "rez1=np.poly1d(m1)(xt)-yt\n",
    "r1=sum(rez1**2)/len(xt)\n",
    "rez2=np.poly1d(m2)(xt)-yt\n",
    "r2=sum(rez2**2)/len(xt)\n",
    "rez3=np.poly1d(m3)(xt)-yt\n",
    "r3=sum(rez3**2)/len(xt)\n",
    "rez4=np.poly1d(m4)(xt)-yt\n",
    "r4=sum(rez4**2)/len(xt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na sledećoj slici ćemo prikazati grafike za sva četiri modela, redom od polinoma prvog do polinoma četvrtog stepena. Plave tačke prikadaju skupu __learn__, a narandžaste skupu __test__. Iznad grafika je prikazana odgovarajuća vrednost srednjeg kvadratnog odstupanja, __MSE__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'MSE=4.35')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=1, ncols=4, figsize=(18, 5))\n",
    "ax[0].scatter(xl, yl)\n",
    "ax[0].plot(xfit,y1fit,color=\"gray\")\n",
    "ax[0].scatter(xt,yt,color=\"orange\")\n",
    "ax[0].set_title(f\"MSE={r1:.3}\")\n",
    "\n",
    "ax[1].scatter(xl, yl)\n",
    "ax[1].plot(xfit,y2fit,color=\"gray\")\n",
    "ax[1].scatter(xt,yt,color=\"orange\")\n",
    "ax[1].set_title(f\"MSE={r2:.3}\")\n",
    "\n",
    "ax[2].scatter(xl, yl)\n",
    "ax[2].plot(xfit,y3fit,color=\"gray\")\n",
    "ax[2].scatter(xt,yt,color=\"orange\")\n",
    "ax[2].set_title(f\"MSE={r3:.3}\")\n",
    "\n",
    "ax[3].scatter(xl, yl)\n",
    "ax[3].plot(xfit,y4fit,color=\"gray\")\n",
    "ax[3].scatter(xt,yt,color=\"orange\")\n",
    "ax[3].set_title(f\"MSE={r4:.3}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ako pažljivo pogledamo grafike, videćemo da polinom prvog reda, odnosno linearna funkcija, ima najveća odstupanja od tačaka iz skupa __learn__. Najbolje je slaganje za polinom najvišeg reda gde sve plave tačke leže baš na krivoj kojom smo fitovali podatke. Ovde je odstupanje tačaka iz __learn__ uzorka od polinoma četvrtog reda jednaka nuli. Međutim, nas više interesuje koliko će tačke odstupati od funkcije za skup kojim testiramo modele. Narandžaste tačke najmanje odstupaju za polinom drugog reda. \n",
    "\n",
    "Pojava da funkcija ne prati dovoljno dobro trend tačaka iz uzorka zbog čega su odstupanja za testni skup velika naziva se _under-fitting_. To svakako nije dobro, ali ni druga krajnost nije dobra. Kada funkcija previše dobro prati tačke iz uzorka, greške za testni skup opet postaju velike. Ta pojava se naziva _over-fitting_. Mi unapred, bez poznavanja vrednosti za testni skup, ne možemo da znamo koji je model najbolji, ali je očekivano da to najjednostavniji model koji prati trend tačaka. Treba se čuvati obe krajnosti.\n",
    "\n",
    "Složenost modela ne zavisi samo od složenosti funkcije već i od broja nezavisno promenljivih. Mi smo ovde radili samo sa jednom nezavisno promenljivom, __x__, ali kod mašinskog učenja taj broj može biti mnogo veći. U takvim slučajevima moramo da uradimo odabir promenljivih koje uključujemo u model (_feature selection_). Premalo nije dobro, ali nije dobro ni previše. _Under-fitting_ i _over-fitting_ su standarni izazovi za mašinsko učenje. Uvek treba tražiti modele koji uključuju samo zaista važne promenljive i gde su funkcije koje ih povezuju što jednostavnije."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Primer na empirijskim podacima"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Isti postupak koji smo uradili sa simuliranim podacima možemo da ponovimo i sa empirijskim. Za tu svrhu ćemo koristiti stari, poznati skup podataka [cars](https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/cars.html). On sadrži podatke o 50 merenja dužine kočenja u zavisnosti od brzine automobila. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "cars=pd.read_csv(\"data/cars.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 50 entries, 0 to 49\n",
      "Data columns (total 2 columns):\n",
      " #   Column  Non-Null Count  Dtype\n",
      "---  ------  --------------  -----\n",
      " 0   speed   50 non-null     int64\n",
      " 1   dist    50 non-null     int64\n",
      "dtypes: int64(2)\n",
      "memory usage: 928.0 bytes\n"
     ]
    }
   ],
   "source": [
    "cars.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cars.speed,cars.dist)\n",
    "plt.xlabel(\"Brzina automobila [mph]\")\n",
    "plt.ylabel(\"Dužina kočenja [ft]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za analizu možemo da iskoristimo iste linije koda koje smo već koristili za simulirane podatke. Samo Treba izmeniti parametre kod `random.choice()` funkcije (sada imamo 50 elemenata niza i biramo 35 za obučavanje) i kod funkcije `linspace()` gde treba izračunati podatke na intervalu od 0 do 25."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "learn=np.random.choice(50, 35, replace=False)\n",
    "test=list(set(range(50))-set(learn))\n",
    "\n",
    "xl=cars.speed[learn]\n",
    "xt=cars.speed[test]\n",
    "\n",
    "yl=cars.dist[learn]\n",
    "yt=cars.dist[test]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 34, 38, 39, 8, 10, 13, 45, 46, 47, 17, 18, 48, 49, 30]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c4bb5f4310>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cars.speed,cars.dist)\n",
    "plt.scatter(xt,yt,color=\"orange\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "m1=np.polyfit(xl,yl,1)\n",
    "m2=np.polyfit(xl,yl,2)\n",
    "m3=np.polyfit(xl,yl,3)\n",
    "m4=np.polyfit(xl,yl,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "m1_fn=np.poly1d(m1)\n",
    "m2_fn=np.poly1d(m2)\n",
    "m3_fn=np.poly1d(m3)\n",
    "m4_fn=np.poly1d(m4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "xfit = np.linspace(0, 25, 100)\n",
    "y1fit = m1_fn(xfit)\n",
    "y2fit = m2_fn(xfit)\n",
    "y3fit = m3_fn(xfit)\n",
    "y4fit = m4_fn(xfit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "rez1=np.poly1d(m1)(xt)-yt\n",
    "r1=sum(rez1**2)/len(xt)\n",
    "rez2=np.poly1d(m2)(xt)-yt\n",
    "r2=sum(rez2**2)/len(xt)\n",
    "rez3=np.poly1d(m3)(xt)-yt\n",
    "r3=sum(rez3**2)/len(xt)\n",
    "rez4=np.poly1d(m4)(xt)-yt\n",
    "r4=sum(rez4**2)/len(xt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'MSE=6.14e+02')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=1, ncols=4, figsize=(18, 5))\n",
    "ax[0].scatter(xl, yl)\n",
    "ax[0].plot(xfit,y1fit,color=\"gray\")\n",
    "ax[0].scatter(xt,yt,color=\"orange\")\n",
    "ax[0].set_title(f\"MSE={r1:.3}\")\n",
    "\n",
    "ax[1].scatter(xl, yl)\n",
    "ax[1].plot(xfit,y2fit,color=\"gray\")\n",
    "ax[1].scatter(xt,yt,color=\"orange\")\n",
    "ax[1].set_title(f\"MSE={r2:.3}\")\n",
    "\n",
    "ax[2].scatter(xl, yl)\n",
    "ax[2].plot(xfit,y3fit,color=\"gray\")\n",
    "ax[2].scatter(xt,yt,color=\"orange\")\n",
    "ax[2].set_title(f\"MSE={r3:.3}\")\n",
    "\n",
    "ax[3].scatter(xl, yl)\n",
    "ax[3].plot(xfit,y4fit,color=\"gray\")\n",
    "ax[3].scatter(xt,yt,color=\"orange\")\n",
    "ax[3].set_title(f\"MSE={r4:.3}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Izbor podataka za učenje može mnogo da utiče na kvalitet fita. U ovom konkretnom slučaju, generator slučajnih brojeva je odlučio da u skupu za učenje ne bude ni jedna od pet tačaka sa najvećim brzinama (narandžaste tačke sa desne strane). Iako nam izgleda da bi idealni fit trebalo da \"skreće na gore\" za velike brzine, to se ovde nije desilo jer kod plavih tačaka tog trenda nama. Zbog toga nema značajne razlike između fita linearnom i kvadratnom funkcijom dok krive trećeg i četvrtog stepena pronalaze trend u kontra smeru. Izgleda da su sva četiri modela upotrebljiva i da razlika u vrednosti MSE nije velika. Ipak, treba primetiti da predikcije na krajevima intervala za funkcije višeg reda prilično divergiraju.\n",
    "\n",
    "Da li bi srednje kvadratno odstupanje za kvadratnu funkciju bilo najmanje i u slučaju da je izbor tačaka za učenje bio drugačiji možemo lako da proverimo. Ponovo izvršite sve ćelije počevši od `learn=np.random.choice(50, 35, replace=False)` do iscrtavanja grafika pa ćete videti hoće li rezultati biti drugači i koliko će velika biti razlika među modelima. Ovo možete, naravno, da ponovite više puta. Na taj način možete da proverite pouzdanost svog izbora modela."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}