{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parameter Estimation\n",
    "\n",
    "The following was a rewrite of the book (Deep Learnign with PyTorch's) jupyter notebook. Instead of using Torch and Tensors I decided to use pure Numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We two thermometers in front of us. One that measures in celcius the other in unknown units. We want to know what units the measurements are in so we'll use machine learning to help us figure out the relationship between the two."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem Statement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_c = np.array([0.5,  14.0, 15.0, 28.0, 11.0,  8.0,  3.0, -4.0,  6.0, 13.0, 21.0])\n",
    "t_u = np.array([35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll use a Linear model.\n",
    "\n",
    "> Linearity doesn?t necessarily imply that the curve connecting the mean of Y conditional on values of X is a straight line (though that is often what we impose), but that the parameters that describe the function relating Y to the Xs are linear. The equation is additive ? the weights aren?t multipled or raised to a power other than 1. [1]\n",
    "\n",
    "We'll start with the slope intercept equation we all once learned. \n",
    "\n",
    "$y = m * x + b$ \n",
    "\n",
    "but we'll slightly modify how we walk about it, so it scales to more variables than just one (x).\n",
    "\n",
    "$y = b_1 * x + b_0$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $y$ = our prediction of measurements in celsius\n",
    "- $x$ = our measurements of unknown \n",
    "- $b_1$ = some fractional number to scale our measurements of unknown This number will be learned.\n",
    "- $b_0$ = some fractional number to add to our measurements of unknown. This number will be learned."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining Machine Learning Functions\n",
    "\n",
    "The follow three equations are equivalent for our simple lienar regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$y = mx + b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$y = b_1 * x + b_0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$t_c = w* t_u + b$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(t_u: np.array, w: float, b: float):\n",
    "    \"\"\"Our model. \n",
    "    Makes predictions. 'Converting' measurements of unknown units\n",
    "    into a celcius measurements.\"\"\"\n",
    "    return w * t_u + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\text{loss_fn} = \\frac{1}{n} \\sum_{i=1}^{n}(y_i - \\hat{y_i})^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I really liked this snippet from the [Wikipedia entry](https://en.wikipedia.org/wiki/Mean_squared_error) on the mean squared error forumula:\n",
    "\n",
    "> The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_fn(t_p: np.array, t_c: np.array):\n",
    "    \"\"\"Our loss function.\n",
    "    Computes how close we are to reality. Our goal is to minimize this.\"\"\"\n",
    "    squared_diffs = (t_p - t_c)**2\n",
    "    return squared_diffs.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\text{dloss_fn} = 2* \\frac{1}{n} \\sum_{i=1}^{n} (y_i - \\hat{y_i})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dloss_fn(t_p: np.array, t_c: np.array):\n",
    "    \"\"\"Loss function derivative.\n",
    "    \"\"\"\n",
    "    dsq_diffs = 2 * (t_p - t_c) / t_p.size  # <1>\n",
    "    return dsq_diffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dmodel_dw(t_u: np.array, w: float, b: float):\n",
    "    \"\"\"Model function partial derivative w.r.t w\"\"\"\n",
    "    return t_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dmodel_db(t_u: np.array, w: float, b: float):\n",
    "    \"\"\"Model function partial derivative w.r.t b\"\"\"\n",
    "    return 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grad_fn(t_u, t_c, t_p, w, b):\n",
    "    \"\"\"Gradient function.\n",
    "    Computes the gradient of the loss with respect to w and b.\"\"\"\n",
    "    dloss_dtp = dloss_fn(t_p, t_c)  # compute the loss\n",
    "    dloss_dw = dloss_dtp * dmodel_dw(t_u, w, b)  # how much of that loss can be described by `b_1`\n",
    "    dloss_db = dloss_dtp * dmodel_db(t_u, w, b)  # how much of that loss can be described by `b_0`\n",
    "    return np.array([dloss_dw.sum(), dloss_db.sum()])  # <1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![gradient descent appropriate learning rate](gradient_descent_appropriate_learning_rate.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point we have all the building blocks we need to learn our paremeters `w` and `b`. We're going to write our `training_loop` which will:\n",
    "\n",
    "- iterate over our data set `n_epoch` times\n",
    "- compute the loss for our current `w` and `b`\n",
    "- compute the gradient of the loss with respect to `w` and `b` (`grad`)\n",
    "- update `w` and `b` using our gradient of the loss (`grad`) and our `learning_rate`\n",
    "- print out some metrics every now and then"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def training_loop(\n",
    "    n_epochs: int,\n",
    "    learning_rate: float,\n",
    "    params: np.array,\n",
    "    t_u: np.array,\n",
    "    t_c: np.array,\n",
    "    print_params=True\n",
    "):\n",
    "    for epoch in range(1, n_epochs + 1):\n",
    "        w, b = params\n",
    "\n",
    "        t_p = model(t_u, w, b)  # <1>\n",
    "        loss = loss_fn(t_p, t_c)\n",
    "        grad = grad_fn(t_u, t_c, t_p, w, b)  # <2>\n",
    "\n",
    "        params = params - learning_rate * grad\n",
    "\n",
    "        if epoch in {1, 2, 3, 10, 11, 99, 100, 4000, 5000}:  # <3>\n",
    "            print('Epoch %d, Loss %f' % (epoch, float(loss)))\n",
    "            if print_params:\n",
    "                print('    Params:', params)\n",
    "                print('    Grad:  ', grad)\n",
    "        if epoch in {4, 12, 101}:\n",
    "            print('...')\n",
    "\n",
    "        if not np.isfinite(params).all():\n",
    "            break  # <3>\n",
    "            \n",
    "    return params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calling Training\n",
    "\n",
    "This is our first time training. Notice\n",
    "\n",
    "- we will iterate over our data set `5000` times\n",
    "- our learning rate is `1e-2` which is equivalent to `.01`\n",
    "- we initialize our parameters `w` and `b` to `1.0` and `0.0` respectively"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, Loss 1763.884545\n",
      "Epoch 2, Loss 5802485.187568\n",
      "Epoch 3, Loss 19408033028.416103\n",
      "...\n",
      "Epoch 10, Loss 90901091382582138082674597204852736.000000\n",
      "Epoch 11, Loss 304045619786437336534998703719126663168.000000\n",
      "...\n",
      "Epoch 99, Loss inf\n",
      "Epoch 100, Loss inf\n",
      "...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-4-c999438efa6d>:4: RuntimeWarning: overflow encountered in square\n",
      "  squared_diffs = (t_p - t_c)**2\n",
      "/Users/ghilston/Git/dlwpt-code/chapter_5/venv/lib/python3.8/site-packages/numpy/core/_methods.py:47: RuntimeWarning: overflow encountered in reduce\n",
      "  return umr_sum(a, axis, dtype, out, keepdims, initial, where)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([            inf, 5.64015582e+304])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learned_params = training_loop(\n",
    "    n_epochs = 5000, \n",
    "    learning_rate = 1e-2, \n",
    "    params = np.array([1.0, 0.0]), \n",
    "    t_u = t_u, \n",
    "    t_c = t_c,\n",
    "    print_params = False)\n",
    "learned_params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We experience our loss growing to infinitey"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![gradient descent to large learning rate](gradient_descent_to_large_learning_rate.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adjusting Learning Rate\n",
    "\n",
    "We'll keep everything the same except for reducing our learning rate. From `1e-2` to `1e-4`. \n",
    "\n",
    "The idea here is our loss should be reducing and since the above training did not result in a decrease in loss, perhaps our \"steps\" or `learning_rate` was to large."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, Loss 1763.884545\n",
      "Epoch 2, Loss 323.090545\n",
      "Epoch 3, Loss 78.929655\n",
      "...\n",
      "Epoch 10, Loss 29.105249\n",
      "Epoch 11, Loss 29.104166\n",
      "...\n",
      "Epoch 99, Loss 29.023582\n",
      "Epoch 100, Loss 29.022668\n",
      "...\n",
      "Epoch 4000, Loss 25.691168\n",
      "Epoch 5000, Loss 24.907745\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.25772346, -1.46307188])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learned_params = training_loop(\n",
    "    n_epochs = 5000, \n",
    "    learning_rate = 1e-4, \n",
    "    params = np.array([1.0, 0.0]), \n",
    "    t_u = t_u, \n",
    "    t_c = t_c,\n",
    "    print_params = False)\n",
    "learned_params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We end up with a loss of ~25.0. This means\n",
    "\n",
    "> On average our predictions are off by $\\sqrt{25} = 5.0$ degrees celcius"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This error, represented by our loss, comes from the imperfection in our model and the error added to the input data to represent real world measurement errors.\n",
    "\n",
    "Our goal is not to achieve a loss of $0.0$ but rather minimize it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling Input\n",
    "\n",
    "Now that our learned parameters are performing better due to a smaller `learning_rate`, one thing we can do is scale our input data. \n",
    "\n",
    "Notice that `t_u` is much learger than `t_c`. This can cause the `learning_rate` to be approprately large to modify one parameter while not affecting another. We could have multiple `learning_rates`, one for each feature, but an easier approach is to scale our features so a single `learning_rate` can modify their values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_info(name: str, t: np.array):\n",
    "    print(f\"\"\"{name}\n",
    "    \\t{t}\n",
    "    \\tmean {t.mean()}\n",
    "    \\tstd {t.std()}\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_u\n",
      "    \t[35.7 55.9 58.2 81.9 56.3 48.9 33.9 21.8 48.4 60.4 68.4]\n",
      "    \tmean 51.8\n",
      "    \tstd 16.048619311896644\n",
      "t_c\n",
      "    \t[ 0.5 14.  15.  28.  11.   8.   3.  -4.   6.  13.  21. ]\n",
      "    \tmean 10.5\n",
      "    \tstd 8.782730989638909\n"
     ]
    }
   ],
   "source": [
    "print_info(\"t_u\", t_u)\n",
    "print_info(\"t_c\", t_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example of blatantly scaling by `0.1` is not generally used. Instead one should look up normalization and standardization.\n",
    "\n",
    "This way you don't introduce a hyper paramater, such as the scale amount of `0.1`. Additionally both normalization and standardization will grant you nice properties such as a common min and max or a known mean and standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_un = 0.1 * t_u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and after:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_un\n",
      "    \t[3.57 5.59 5.82 8.19 5.63 4.89 3.39 2.18 4.84 6.04 6.84]\n",
      "    \tmean 5.180000000000001\n",
      "    \tstd 1.6048619311896644\n",
      "t_c\n",
      "    \t[ 0.5 14.  15.  28.  11.   8.   3.  -4.   6.  13.  21. ]\n",
      "    \tmean 10.5\n",
      "    \tstd 8.782730989638909\n"
     ]
    }
   ],
   "source": [
    "print_info(\"t_un\", t_un)\n",
    "print_info(\"t_c\", t_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point our input features are scaled and we can re train using the new features and our original `learning_rate`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, Loss 80.364345\n",
      "    Params: [1.77614036 0.1064    ]\n",
      "    Grad:   [-77.61403636 -10.64      ]\n",
      "Epoch 2, Loss 37.574914\n",
      "    Params: [2.08476325 0.13026386]\n",
      "    Grad:   [-30.86228896  -2.38638583]\n",
      "Epoch 3, Loss 30.871081\n",
      "    Params: [2.20939432 0.12167711]\n",
      "    Grad:   [-12.46310674   0.85867502]\n",
      "...\n",
      "Epoch 10, Loss 29.030488\n",
      "    Params: [ 2.32320286 -0.07098988]\n",
      "    Grad:   [-0.53550501  2.92951383]\n",
      "Epoch 11, Loss 28.941876\n",
      "    Params: [ 2.32844326 -0.1002539 ]\n",
      "    Grad:   [-0.52404021  2.92640187]\n",
      "...\n",
      "Epoch 99, Loss 22.214183\n",
      "    Params: [ 2.75082953 -2.49104605]\n",
      "    Grad:   [-0.44530376  2.52078408]\n",
      "Epoch 100, Loss 22.148713\n",
      "    Params: [ 2.75527501 -2.51621107]\n",
      "    Grad:   [-0.44454729  2.51650186]\n",
      "...\n",
      "Epoch 4000, Loss 2.927679\n",
      "    Params: [  5.36427313 -17.2852779 ]\n",
      "    Grad:   [-0.0005864   0.00331952]\n",
      "Epoch 5000, Loss 2.927647\n",
      "    Params: [  5.3670898  -17.30122252]\n",
      "    Grad:   [-0.0001071  0.0006063]\n"
     ]
    }
   ],
   "source": [
    "learned_params = training_loop(\n",
    "    n_epochs = 5000, \n",
    "    learning_rate = 1e-2, \n",
    "    params = np.array([1.0, 0.0]), \n",
    "    t_u = t_un, \n",
    "    t_c = t_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x1000 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "t_p = model(t_un, *learned_params)  # <1>\n",
    "\n",
    "fig = plt.figure(dpi=250)\n",
    "plt.xlabel(\"Temperature (?Fahrenheit)\")\n",
    "plt.ylabel(\"Temperature (?Celsius)\")\n",
    "plt.plot(t_u, t_p) # <2>\n",
    "plt.plot(t_u, t_c, 'o')\n",
    "plt.savefig(\"temp_unknown_plot.png\", format=\"png\")  # bookskip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x1000 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "fig = plt.figure(dpi=250)\n",
    "plt.xlabel(\"Measurement\")\n",
    "plt.ylabel(\"Temperature (?Celsius)\")\n",
    "plt.plot(t_u, t_c, 'o')\n",
    "\n",
    "plt.savefig(\"temp_data_plot.png\", format=\"png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "- [1] https://uvastatlab.github.io/phdplus/linearmodel.html\n",
    "- [2] https://ml-cheatsheet.readthedocs.io/en/latest/gradient_descent.html\n",
    "- [3] https://en.wikipedia.org/wiki/Mean_squared_error\n",
    "- [4] https://blog.paperspace.com/intro-to-optimization-in-deep-learning-gradient-descent/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "def update_weights(m, b, X, Y, learning_rate):\n",
    "    m_deriv = 0\n",
    "    b_deriv = 0\n",
    "    N = len(X)\n",
    "    for i in range(N):\n",
    "        # Calculate partial derivatives\n",
    "        # -2x(y - (mx + b))\n",
    "        m_deriv += -2*X[i] * (Y[i] - (m*X[i] + b))\n",
    "\n",
    "        # -2(y - (mx + b))\n",
    "        b_deriv += -2*(Y[i] - (m*X[i] + b))\n",
    "\n",
    "    # We subtract because the derivatives point in direction of steepest ascent\n",
    "    m -= (m_deriv / float(N)) * learning_rate\n",
    "    b -= (b_deriv / float(N)) * learning_rate\n",
    "\n",
    "    return m, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}