juliaL32a.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural networks: predict\n",
    "\n",
    "CPSC 340: Machine Learning and Data Mining\n",
    "\n",
    "2018 Winter Term 1\n",
    "\n",
    "By Mike Gelbart (converted to Julia by Jason Chau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject <module 'sklearn.neural_network' from 'C:\\\\Users\\\\jasonsyc.STUDENTS.000\\\\.julia\\\\conda\\\\3\\\\lib\\\\site-packages\\\\sklearn\\\\neural_network\\\\__init__.py'>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using PyCall,PyPlot\n",
    "plt = pyimport(\"matplotlib.pyplot\")\n",
    "using Random\n",
    "SkNeural = pyimport(\"sklearn.neural_network\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Back to supervised learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider 1-D regression..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(0, 5)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,3,4,  5,5.2,6]\n",
    "y = [1,2,2.3,3,3.5,4.8]\n",
    "function plot_pts(x,y)\n",
    "    plt.plot(x,y, \".\", markersize=15)\n",
    "    plt.xlim([0, 7])\n",
    "    plt.ylim([0, 5])\n",
    "end\n",
    "plot_pts(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider various fits... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pts(x,y)\n",
    "grid = range(0,stop=7,length=100)\n",
    "plt.plot(grid,0.7.*grid)\n",
    "plt.title(\"Linear fit: y=ax+b (2 parameters)\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pts(x,y)\n",
    "plt.plot(grid,0.4.*grid+0.05.*grid.^2)\n",
    "plt.title(\"Quadratic fit: y=ax^2+bx+c (3 parameters)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can fit various functions from the _polynomial family_. But each polynomial **has a different number of parameters**. Note that the polynomial family always maps from $\\mathbb{R}^d\\rightarrow \\mathbb{R}$.\n",
    "\n",
    "- Model: has parameters that we fit\n",
    "- Family: a set of models that are linked by some theme, but may have different numbers of parameters\n",
    "- **\"Neural network\" is a family of functions just like this.**\n",
    "  - The class includes linear functions like we saw above, but also insanely nonlinear ones.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Formal definition\n",
    "\n",
    "$$ z^{(l+1)} = f\\left( W^{(l)} z^{(l)} + b^{(l)}\\right) $$\n",
    "\n",
    "where $W^{(l)}$ is a matrix of parameters, $b^{(l)}$ is a vector of parameters, $f(\\cdot)$ is an elementwise nonlinearity, $l=0,\\ldots,L$ where $L$ is the number of \"hidden layers\", $z^{(0)}=x$, and $z^{(L)}=y$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function example_1_layer_nn(x,W,f) # x is a vector, W is a matrix\n",
    "    return f(W*x)\n",
    "end\n",
    "\n",
    "x = rand(5)\n",
    "W = rand(2,5)\n",
    "f(x) = 1 ./(1 .+broadcast(exp,-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Float64,1}:\n",
       " 0.9157297476037178\n",
       " 0.7337367668979993\n",
       " 0.9969456860128165\n",
       " 0.4172460109822467\n",
       " 0.9353576574466758"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×5 Array{Float64,2}:\n",
       " 0.546711  0.983584   0.698272  0.3275    0.0871148\n",
       " 0.945891  0.0580299  0.818601  0.617023  0.669145 "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.8944101490628004\n",
       " 0.9313874303096188"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example_1_layer_nn(x,W,f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Above: the size of the input is 5 and the size of the output is 2.\n",
    "- Below: the size of the input is 5 and the size of the output is 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-element Array{Float64,1}:\n",
       " 0.6737636108088411"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function example_nn(x,W,f) # x is a vector, W is a _list of matrices_\n",
    "    for W_l in W\n",
    "        x = f(W_l*x)\n",
    "    end\n",
    "    return x\n",
    "end\n",
    "\n",
    "x = rand(5)\n",
    "W1 = rand(2,5)\n",
    "W2 = rand(1,2)\n",
    "example_nn(x, [W1,W2], f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Regression: end with the prediction (output has $1$ dimension)\n",
    "- Classification: end with a softmax (output has $c$ dimensions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1D neural net example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate synthetic data\n",
    "Random.seed!(3)\n",
    "n = 200\n",
    "X = rand(n,1)\n",
    "y = broadcast(sin,2 .*X[:,1]) + randn(n).*0.03\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(X,y,\".\",markersize=10);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nn = SkNeural.MLPRegressor(solver=\"lbfgs\")\n",
    "nn.fit(X,y);\n",
    "\n",
    "plt.plot(X,y,\".\",markersize=10);\n",
    "grid = reshape(range(0,stop=1,length=1000),1000,1)\n",
    "\n",
    "plt.plot(grid, nn.predict(grid),linewidth=5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### random weights\n",
    "\n",
    "To build intuition about the types of functions we can represent, let's explore what happens with random weights using different architectures. Again, this is all within the confines of $\\mathbb{R}\\rightarrow\\mathbb{R}$ which isn't the real deal.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jasonsyc.STUDENTS.000\\.julia\\conda\\3\\lib\\site-packages\\sklearn\\neural_network\\multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1) reached and the optimization hasn't converged yet.\r\n",
      "  % self.max_iter, ConvergenceWarning)\r\n"
     ]
    }
   ],
   "source": [
    "nn = SkNeural.MLPRegressor(hidden_layer_sizes=(), activation=\"logistic\", max_iter=1)\n",
    "\n",
    "# change hidden_layer_sizes to, e.g. 10,\n",
    "# change activation to relu\n",
    "\n",
    "nn.fit(zeros(1,1),[0])\n",
    "grid = reshape(range(-10,stop=10,length=1000),1000,1)\n",
    "plt.plot(grid, nn.predict(grid),linewidth=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regression example with $d=2$ (again, change hidden layer sizes and nonlinearity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jasonsyc.STUDENTS.000\\.julia\\conda\\3\\lib\\site-packages\\sklearn\\neural_network\\multilayer_perceptron.py:566: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (1) reached and the optimization hasn't converged yet.\r\n",
      "  % self.max_iter, ConvergenceWarning)\r\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject <mpl_toolkits.mplot3d.art3d.Poly3DCollection object at 0x000000003BB7C588>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn = SkNeural.MLPRegressor(hidden_layer_sizes=(), max_iter=1)\n",
    "\n",
    "nn.fit(zeros(1,2),[0])\n",
    "\n",
    "ngrid = 20\n",
    "X = repeat(range(-5, stop=5, length=ngrid)',ngrid,1)\n",
    "Y = repeat(range(-5, stop=5, length=ngrid),1,ngrid)\n",
    "\n",
    "inputs = hcat(X'[:], Y'[:])\n",
    "outputs = nn.predict(inputs)\n",
    "Z = reshape(outputs, ngrid, ngrid)\n",
    "\n",
    "# Plot the surface.\n",
    "pygui(true)\n",
    "PyPlot.surf(X,Y,Z,antialiased=false,cmap=ColorMap(\"coolwarm\"))\n",
    "# surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm, linewidth=0, antialiased=false)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some deep learning software\n",
    "\n",
    "There's been a lot of software released lately to take care of this for you. Some big players are:\n",
    "\n",
    "| Name   |  Host language  | Released |\n",
    "|--------|-------------|---------------|\n",
    "| [Torch](http://torch.ch) | Lua | 2002 |\n",
    "| [Theano](http://deeplearning.net/software/theano/) | Python | 2007 |\n",
    "| [Caffe](http://caffe.berkeleyvision.org) | Executable with Python wrapper | 2014 |\n",
    "| [TensorFlow](https://www.tensorflow.org) | Python | 2015 |\n",
    "| [Keras](https://keras.io) | Python | 2015 |\n",
    "| [PyTorch](http://pytorch.org) | Python | 2017 |\n",
    "| [Caffe 2](https://caffe2.ai/) | Python or C++ | 2017 |\n",
    "\n",
    "There are many others. See for example [Comparison of deep learning software](https://en.wikipedia.org/wiki/Comparison_of_deep_learning_software)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Repeating the examples above in Keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Running `conda install -y keras` in root environment\n",
      "└ @ Conda C:\\Users\\jasonsyc.STUDENTS.000\\.julia\\packages\\Conda\\kLXeC\\src\\Conda.jl:112\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting package metadata (current_repodata.json): ...working... done\n",
      "Solving environment: ...working... failed with current_repodata.json, will retry with next repodata source.\n",
      "Initial quick solve with frozen env failed.  Unfreezing env and trying again.\n",
      "Solving environment: ...working... failed with current_repodata.json, will retry with next repodata source.\n",
      "Collecting package metadata (repodata.json): ...working... done\n",
      "Solving environment: ...working... done\n",
      "\n",
      "## Package Plan ##\n",
      "\n",
      "  environment location: C:\\Users\\jasonsyc.STUDENTS.000\\.julia\\conda\\3\n",
      "\n",
      "  added / updated specs:\n",
      "    - keras\n",
      "\n",
      "\n",
      "The following packages will be downloaded:\n",
      "\n",
      "    package                    |            build\n",
      "    ---------------------------|-----------------\n",
      "    _tflow_select-2.3.0        |              mkl           3 KB\n",
      "    absl-py-0.7.1              |           py36_0         158 KB\n",
      "    astor-0.7.1                |           py36_0          44 KB\n",
      "    certifi-2019.6.16          |           py36_1         156 KB\n",
      "    gast-0.2.2                 |           py36_0         155 KB\n",
      "    grpcio-1.16.1              |   py36h351948d_1         849 KB\n",
      "    h5py-2.9.0                 |   py36h5e291fa_0         779 KB\n",
      "    hdf5-1.10.4                |       h7ebc959_0         7.9 MB\n",
      "    keras-2.2.4                |                0           5 KB\n",
      "    keras-applications-1.0.8   |             py_0          33 KB\n",
      "    keras-base-2.2.4           |           py36_0         413 KB\n",
      "    keras-preprocessing-1.1.0  |             py_1          36 KB\n",
      "    libmklml-2019.0.3          |                0        17.4 MB\n",
      "    libprotobuf-3.8.0          |       h7bd577a_0         1.8 MB\n",
      "    markdown-3.1.1             |           py36_0         132 KB\n",
      "    mock-3.0.5                 |           py36_0          49 KB\n",
      "    protobuf-3.8.0             |   py36h33f27b4_0         526 KB\n",
      "    pyreadline-2.1             |           py36_1         143 KB\n",
      "    pyyaml-5.1.1               |   py36he774522_0         152 KB\n",
      "    tensorboard-1.13.1         |   py36h33f27b4_0         3.2 MB\n",
      "    tensorflow-1.13.1          |mkl_py36hd212fbe_0           4 KB\n",
      "    tensorflow-base-1.13.1     |mkl_py36hcaf7020_0        32.4 MB\n",
      "    tensorflow-estimator-1.13.0|             py_0         205 KB\n",
      "    termcolor-1.1.0            |           py36_1           9 KB\n",
      "    werkzeug-0.15.4            |             py_0         262 KB\n",
      "    ------------------------------------------------------------\n",
      "                                           Total:        66.7 MB\n",
      "\n",
      "The following NEW packages will be INSTALLED:\n",
      "\n",
      "  _tflow_select      pkgs/main/win-64::_tflow_select-2.3.0-mkl\n",
      "  absl-py            pkgs/main/win-64::absl-py-0.7.1-py36_0\n",
      "  astor              pkgs/main/win-64::astor-0.7.1-py36_0\n",
      "  gast               pkgs/main/win-64::gast-0.2.2-py36_0\n",
      "  grpcio             pkgs/main/win-64::grpcio-1.16.1-py36h351948d_1\n",
      "  h5py               pkgs/main/win-64::h5py-2.9.0-py36h5e291fa_0\n",
      "  hdf5               pkgs/main/win-64::hdf5-1.10.4-h7ebc959_0\n",
      "  keras              pkgs/main/win-64::keras-2.2.4-0\n",
      "  keras-applications pkgs/main/noarch::keras-applications-1.0.8-py_0\n",
      "  keras-base         pkgs/main/win-64::keras-base-2.2.4-py36_0\n",
      "  keras-preprocessi~ pkgs/main/noarch::keras-preprocessing-1.1.0-py_1\n",
      "  libmklml           pkgs/main/win-64::libmklml-2019.0.3-0\n",
      "  libprotobuf        pkgs/main/win-64::libprotobuf-3.8.0-h7bd577a_0\n",
      "  markdown           pkgs/main/win-64::markdown-3.1.1-py36_0\n",
      "  mock               pkgs/main/win-64::mock-3.0.5-py36_0\n",
      "  protobuf           pkgs/main/win-64::protobuf-3.8.0-py36h33f27b4_0\n",
      "  pyreadline         pkgs/main/win-64::pyreadline-2.1-py36_1\n",
      "  pyyaml             pkgs/main/win-64::pyyaml-5.1.1-py36he774522_0\n",
      "  tensorboard        pkgs/main/win-64::tensorboard-1.13.1-py36h33f27b4_0\n",
      "  tensorflow         pkgs/main/win-64::tensorflow-1.13.1-mkl_py36hd212fbe_0\n",
      "  tensorflow-base    pkgs/main/win-64::tensorflow-base-1.13.1-mkl_py36hcaf7020_0\n",
      "  tensorflow-estima~ pkgs/main/noarch::tensorflow-estimator-1.13.0-py_0\n",
      "  termcolor          pkgs/main/win-64::termcolor-1.1.0-py36_1\n",
      "  werkzeug           pkgs/main/noarch::werkzeug-0.15.4-py_0\n",
      "\n",
      "The following packages will be UPDATED:\n",
      "\n",
      "  certifi                                  2019.6.16-py36_0 --> 2019.6.16-py36_1\n",
      "\n",
      "\n",
      "\n",
      "Downloading and Extracting Packages\n",
      "pyyaml-5.1.1         | 152 KB    | ########## | 100% \n",
      "pyreadline-2.1       | 143 KB    | ########## | 100% \n",
      "werkzeug-0.15.4      | 262 KB    | ########## | 100% \n",
      "h5py-2.9.0           | 779 KB    | ########## | 100% \n",
      "_tflow_select-2.3.0  | 3 KB      | ########## | 100% \n",
      "keras-preprocessing- | 36 KB     | ########## | 100% \n",
      "mock-3.0.5           | 49 KB     | ########## | 100% \n",
      "keras-base-2.2.4     | 413 KB    | ########## | 100% \n",
      "tensorboard-1.13.1   | 3.2 MB    | ########## | 100% \n",
      "certifi-2019.6.16    | 156 KB    | ########## | 100% \n",
      "libmklml-2019.0.3    | 17.4 MB   | ########## | 100% \n",
      "keras-applications-1 | 33 KB     | ########## | 100% \n",
      "libprotobuf-3.8.0    | 1.8 MB    | ########## | 100% \n",
      "tensorflow-base-1.13 | 32.4 MB   | ########## | 100% \n",
      "markdown-3.1.1       | 132 KB    | ########## | 100% \n",
      "tensorflow-estimator | 205 KB    | ########## | 100% \n",
      "tensorflow-1.13.1    | 4 KB      | ########## | 100% \n",
      "gast-0.2.2           | 155 KB    | ########## | 100% \n",
      "termcolor-1.1.0      | 9 KB      | ########## | 100% \n",
      "protobuf-3.8.0       | 526 KB    | ########## | 100% \n",
      "grpcio-1.16.1        | 849 KB    | ########## | 100% \n",
      "keras-2.2.4          | 5 KB      | ########## | 100% \n",
      "absl-py-0.7.1        | 158 KB    | ########## | 100% \n",
      "astor-0.7.1          | 44 KB     | ########## | 100% \n",
      "hdf5-1.10.4          | 7.9 MB    | ########## | 100% \n",
      "Preparing transaction: ...working... done\n",
      "Verifying transaction: ...working... done\n",
      "Executing transaction: ...working... done\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\r\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject <module 'keras' from 'C:\\\\Users\\\\jasonsyc.STUDENTS.000\\\\.julia\\\\conda\\\\3\\\\lib\\\\site-packages\\\\keras\\\\__init__.py'>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#=\n",
    "using Conda\n",
    "Conda.add(\"keras\")\n",
    "=#\n",
    "KerasModels = pyimport(\"keras.models\") #import Sequential # pip install keras\n",
    "KerasLayers = pyimport(\"keras.layers\") #import Dense\n",
    "Keras = pyimport(\"keras\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "# generate fake data\n",
    "Random.seed!(5)\n",
    "N = 200\n",
    "X = rand(N,1)\n",
    "y = broadcast(sin,2 .*X) + randn(N,1).*0.03;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.2892346668243406\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2019-08-01 09:03:17.655119: I tensorflow/core/platform/cpu_feature_guard.cc:141] Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX\n",
      "2019-08-01 09:03:17.657422: I tensorflow/core/common_runtime/process_util.cc:71] Creating new thread pool with default inter op setting: 4. Tune using inter_op_parallelism_threads for best performance.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From C:\\Users\\jasonsyc.STUDENTS.000\\.julia\\conda\\3\\lib\\site-packages\\tensorflow\\python\\ops\\math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\r\n",
      "Instructions for updating:\r\n",
      "Use tf.cast instead.\r\n",
      "0.001157178720459342\n"
     ]
    }
   ],
   "source": [
    "model = KerasModels.Sequential()\n",
    "model.add(KerasLayers.Dense(10, input_dim=1, activation=\"tanh\", kernel_initializer=\"lecun_uniform\",))\n",
    "model.add(KerasLayers.Dense(1, activation=\"linear\", kernel_initializer=\"lecun_uniform\",))\n",
    "\n",
    "# Compile model\n",
    "sgd = Keras.optimizers.SGD(lr=0.1, momentum=0.0, decay=0.0, nesterov=false)\n",
    "model.compile(loss=\"mean_squared_error\", optimizer=sgd)#'adam')\n",
    "\n",
    "# Fit the model\n",
    "loss=model.evaluate(X, y,verbose=0)\n",
    "println(loss)\n",
    "model.fit(X, y, epochs=1000, verbose=0)\n",
    "\n",
    "# evaluate the model\n",
    "loss=model.evaluate(X, y,verbose=0)\n",
    "println(loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Note that no code is executed in the first few lines.\n",
    "- This is a new paradigm that we're not exactly used to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pygui(false)\n",
    "plt.plot(X,y,\".\",markersize=10)\n",
    "grid = range(0,stop=1,length=1000)\n",
    "plt.plot(grid, model.predict(grid),linewidth=5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject <mpl_toolkits.mplot3d.art3d.Poly3DCollection object at 0x000000003EA87898>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# random weights\n",
    "model = KerasModels.Sequential()\n",
    "model.add(KerasLayers.Dense(50, input_dim=2, activation=\"tanh\", kernel_initializer=\"lecun_uniform\"))\n",
    "model.add(KerasLayers.Dense(1, activation=\"linear\", kernel_initializer=\"lecun_uniform\",))\n",
    "model.compile(loss=\"mean_squared_error\", optimizer=\"sgd\")\n",
    "\n",
    "# fig = plt.figure()\n",
    "# ax = fig.gca(projection='3d')\n",
    "\n",
    "n = 30\n",
    "X = repeat(range(-5, stop=5, length=n)',n,1)\n",
    "Y = repeat(range(-5, stop=5, length=n),1,n)\n",
    "\n",
    "inputs = hcat(X'[:], Y'[:])\n",
    "outputs = model.predict(inputs)\n",
    "Z = reshape(outputs, n,n)\n",
    "\n",
    "# Plot the surface.\n",
    "pygui(true)\n",
    "PyPlot.surf(X,Y,Z,cmap=ColorMap(\"coolwarm\"))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How many parameters do we have?\n",
    "\n",
    "Just the weight matrices: $$dk_1 + k_1k_2 + \\ldots + k_{L-1}k_L + k_Lc$$\n",
    "\n",
    "With the biases: $$(d+1)k_1 + (k_1+1)k_2 + \\ldots + (k_{L-1}+1)k_L + (k_L+1)c$$\n",
    "\n",
    "where $c$ is the dimensionality of the output.\n",
    "  \n",
    "**This is potentially a lot of parameters!!!!**"
   ]
  }
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