labs/regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A quick tour through Gluon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "import math\n",
    "from mxnet import nd, gluon, autograd\n",
    "\n",
    "import mxnet as mx\n",
    "import seaborn\n",
    "import matplotlib.pyplot as plt\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "ctx = mx.gpu()\n",
    "batch_size=10\n",
    "sample_size = 10000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Crearting Synthetic Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 2) (10000,)\n"
     ]
    }
   ],
   "source": [
    "X = nd.random_normal(loc=0, scale=1, shape=(sample_size,2))\n",
    "def fn(X, noise=.001):\n",
    "    noise_term = noise * nd.random_normal(loc=0, scale=1, shape=(sample_size,))\n",
    "    return (2 * X[:, 0] + 3.1 * X[:, 1] + math.pi) + noise\n",
    "y = fn(X)\n",
    "print(X.shape, y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X.asnumpy(),y.asnumpy())\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "train_data = gluon.data.DataLoader(gluon.data.ArrayDataset(X,y), shuffle=True, batch_size=batch_size, last_batch='keep')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Define a Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def define_net():\n",
    "    net = gluon.nn.Sequential()\n",
    "    with net.name_scope():\n",
    "        net.add(gluon.nn.Dense(1))\n",
    "    return net"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sequential2_ (\n",
       "  Parameter sequential2_dense0_weight (shape=(1, 0), dtype=float32)\n",
       "  Parameter sequential2_dense0_bias (shape=(1,), dtype=float32)\n",
       ")"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net = define_net()\n",
    "net.collect_params()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Initialzie Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "net.collect_params().initialize(mx.init.Normal(), ctx=ctx, force_reinit=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## More initialization algorithms and parameters\n",
    "for further information check the [API documentation](https://mxnet.incubator.apache.org/api/python/optimization/optimization.html)\n",
    "\n",
    "|Function|Description|notes|\n",
    "|:---|:---|:---|\n",
    "|Uniform|Initializes weights with random values uniformly sampled from a given range.|![dd](http://mathworld.wolfram.com/images/eps-gif/UniformDistribution_651.gif)A uniform distribution has constant probability|\n",
    "|Normal|Initializes weights with random values sampled from a normal distribution with a mean of zero and standard deviation of sigma.|![](http://mathworld.wolfram.com/images/eps-gif/NormalDistribution_651.gif)A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function P(x)|\n",
    "|Load|Initializes variables by loading data from file or dict.||\n",
    "|Mixed|Initialize parameters using multiple initializers.||\n",
    "|Zero|Initializes weights to zero.||\n",
    "|One|Initializes weights to one.||\n",
    "|Constant|Initializes the weights to a given value.||\n",
    "|Orthogonal|Initialize weight as orthogonal matrix.|A Matrix A is orthagonal if $AA^T=I\\ or\\ A^{-1}=A^T$. Intentions is to use initialize conditions to benefit from depth independent finite delay in learning|\n",
    "|Xavier|Returns an initializer performing “Xavier” initialization for weights.|This initializer is designed to keep the scale of gradients roughly the same in all layers. Randomizarion can be Uniform or Average|\n",
    "|MSRAPrelu|Initialize the weight according to a MSRA paper.|[paper](https://arxiv.org/pdf/1502.01852.pdf)|\n",
    "|Bilinear|Initialize weight for upsampling layers.|\n",
    "|FusedRNN|Initialize parameters for fused rnn layers.|![](../images/FusedRNN.png)[1]|\n",
    "|LSTMBias|Initialize all biases of an LSTMCell to 0.0 except for the forget gate whose bias is set to custom value.||"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sequential2_ (\n",
       "  Parameter sequential2_dense0_weight (shape=(1, 0), dtype=float32)\n",
       "  Parameter sequential2_dense0_bias (shape=(1,), dtype=float32)\n",
       ")"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net.collect_params()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2) \n",
      "[[ 0.00245928]]\n",
      "<NDArray 1x1 @gpu(0)>\n"
     ]
    }
   ],
   "source": [
    "some_data = nd.array([[1,2]], ctx=ctx)\n",
    "print(some_data.shape, net(some_data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Defining loss function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "loss_fn = gluon.loss.L2Loss()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Further loss functions\n",
    "\n",
    "|Function|Description|Notes|\n",
    "|:-|:-|:-\n",
    "|[L2Loss](https://mxnet.incubator.apache.org/api/python/gluon/loss.html#mxnet.gluon.loss.L2Loss)|Calculates the mean squared error between pred and label.||\n",
    "|[L1Loss](https://mxnet.incubator.apache.org/api/python/gluon/loss.html#mxnet.gluon.loss.L1Loss)|Calculates the mean absolute error between pred and label.||\n",
    "|[SigmoidBinaryCrossEntropyLoss](https://mxnet.incubator.apache.org/api/python/gluon/loss.html#mxnet.gluon.loss.SigmoidBinaryCrossEntropyLoss)|The cross-entropy loss for binary classification.||\n",
    "|[SoftmaxCrossEntropyLoss](https://mxnet.incubator.apache.org/api/python/gluon/loss.html#mxnet.gluon.loss.SoftmaxCrossEntropyLoss)|Computes the softmax cross entropy loss.||\n",
    "|KLDivLoss|The Kullback-Leibler divergence loss.|KLDiv is a measure of divergence between two distributions. $\\mathcal{L}=\\sum^N_{i=1}{y_i}.log\\ \\frac{y_i}{\\hat{y_i}}$ <br> in if `from_logits` is set to `True`, then instead of $\\hat{y_i}$, $softmax(\\hat{y_i})$ is used.|\n",
    "|HuberLoss|Huber Loss is used in Robust Regression. Robust regression performs better in presense of outliers or the model us suspeced to be heteroscedastic, when sub populations have different variabilities.|Calculates smoothed L1 loss that is equal to L1 loss if absolute error exceeds rho but is equal to L2 loss otherwise.  $$\\mathcal{L} = \\sum_i\n",
    "    \\begin{cases} \n",
    "      \\frac{1}{2\\rho}(\\hat{y_i}-y_i)^2 & if\\ |\\hat{y_i}-y_i| < \\rho \\\\\n",
    "       |\\hat{y_i}-y_i| - \\frac{\\rho}{2}& otherwise \n",
    "    \\end{cases}$$|\n",
    "|HingeLoss|Calculates the hinge loss function often used in SVMs||\n",
    "|SquaredHingeLoss|Calculates the soft-margin loss function used in SVMs||\n",
    "|LogisticLoss|Calculates the logistic loss (for binary losses only)||\n",
    "|TripletLoss|Calculates triplet loss given three input tensors and a positive margin.|[paper](https://arxiv.org/pdf/1503.03832.pdf)|\n",
    "|CTCLoss|Connectionist Temporal Classification Loss.|[paper](https://www.cs.toronto.edu/~graves/icml_2006.pdf)|\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Optimization\n",
    "Gluon Trainer applies and optimizer and set parameters for that optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.001, 'momentum': .9})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "ref: [2][3][4][5]\n",
    "\n",
    "# Further optimization algorithms\n",
    "Gradient Descent's goal is to minimize the objective fucnction $J(\\theta)$ parameterized by a model's prameters $\\theta$ through updating the parameters in the opposite direction of the gradient of the objective function. learning rate $\\eta$ determines the stize of the step we are taking in the direction of a local minima.\n",
    "\n",
    "\n",
    "\n",
    "|Function|Description|notes|\n",
    "|:---|:---|:---|\n",
    "|SGD|Stochastic Gradient Descent with momentum and weight decay|Applies SGD to each minibatch. A good rule of thump for setting the parameters is learning rate of .001 with momentum of .9. SGD has trouble navigating areas that one one dimention is significantly more steep than others. SGD can get stuck in local minimas. adding a momentum term (fraction $\\lambda$ to previous update term) we can address this problem to some extent|![](http://ruder.io/content/images/2015/12/without_momentum.gif)|\n",
    "|NAG|Nesterov Accelerated Gradient|Momentum does continue down the slope with speed. Knowing where the gradient is headed helps slowing down the descent towards the local minimas. NAG looks ahead to approximate the future position of parameters and adaptively adjust the momentum. NAG first makes a big jump in the direction of the previous accumulated gradient (brown vector), measures the gradient and then makes a correction (red vector), which results in the complete NAG update (green vector). NAG can help with RNN training performance.|![](http://ruder.io/content/images/2016/09/nesterov_update_vector.png)|\n",
    "|RMSProp|RMSProp Optimizer|RMSProp is similar to AdaDelta and saves the same functino of reducing agressiveness of AdaGrad decaying of learning rate.||\n",
    "|adam|Adaptive Moment Estimation|Adam is another adaptive variant of SGD. Adam can be viewed as a combination of RMSprop and momentum. It works better than other adaptive methods in most cases||\n",
    "|AdaGrad|Adaptive Gradinet Descent|Adaptively reducing learning rate to the parameters to perform smaller updates. This results in large updates in the beginning and progressively smaller updates, resulting in faster convergence.||\n",
    "|AdaDelta|An extension of AdaGrad that reduces agressiveness of AdaGrad|Ada Delta tends to use a decaying average of all the past gradients||\n",
    "|Adamax|Generalized case of adam|The vt factor in the Adam update rule scales the gradient inversely proportionally to the $\\mathcal{l}_2$ norm of the past gradients and current gradient. Adamax generalizes this to $\\mathcal{l}_{\\infty}$||\n",
    "|Nadam|Nesterov-accelerated Adaptive Moment Estimation|Nadam combines Nadam and NAG. It improves Adam by using smarter momentum term as oppsoed to vanilla momentum.||\n",
    "|DCASGD [3]|Delay Compensated Asynchronous Stochastic Gradient Descent|ASGD is designed to asynchronously update the gradients, but sufferes from \"delayed gradients\". This is when a worker updates the global model, but the model has already been updated by another worker. DCASGD compensates this delay. This is a useful method for very large and deep models.|![](../images/CIFAR10DCASGD.png)![](../images/ImageNetDCASGD.png)|\n",
    "|SGLD|Stochastic Gradient Langevin Dynamics|[paper](https://arxiv.org/abs/1702.05575)|\n",
    "|Signum[4]|Compressed Optimisation for Non-Convex Problems|Cost of communicating gradients could be a major bottleneck in distributing learning actoss multiple workers. signSGD alleviates this problem by transmitting just the sign of each minibatch stochastic gradient.|![](../images/Signum.png) SGD---Signum---Adam|\n",
    "|FTML[5]|Follow the Moving Leader|Inspired by onlne learning algorithms based on Follow the Regularized Leader provides improved stability over RMSProp and better performance over adam, especially in changing environments|![](../images/FTML.png)  Results on neural conversational model|\n",
    "|LBSGD [6][7]|Large Batch SGD with momentum and weight decay|Large batches help increasing training speed, but come at teh cost of loss of stability. There are techniques that allow us to train models on large batches (1000 scale) while performing as well as training the same model on small batch size. The techniques hinge on the idea of adaptive batch size and include warmupss, Linear Scaling, and Batch Normalization|![](https://cdn-images-1.medium.com/max/2000/1*iUXQPXWTHbfPlKIzNq75mQ.png)|\n",
    "|Ftrl|[Ftrl optimizer](https://mxnet.incubator.apache.org/api/python/optimization/optimization.html#mxnet.optimizer.Ftrl)|[paper](http://dl.acm.org/citation.cfm?id=2488200)|\n",
    "\n",
    "\n",
    "|||\n",
    "|---|---|\n",
    "|![](http://ruder.io/content/images/2016/09/contours_evaluation_optimizers.gif)|![](http://ruder.io/content/images/2016/09/saddle_point_evaluation_optimizers.gif)|\n",
    "|SGD optimization on loss surface contours|SGD optimization on saddle point|REF:[2]|\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "for further information please check [MXNet documentation](https://mxnet.incubator.apache.org/api/python/optimization/optimization.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Training Loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0\n",
      "epoch: 1\n"
     ]
    }
   ],
   "source": [
    "epochs = 2\n",
    "for e in range(epochs):\n",
    "    for i, (data, label) in enumerate(train_data):\n",
    "        data = data.as_in_context(ctx)\n",
    "        label = label.as_in_context(ctx)\n",
    "        with autograd.record():\n",
    "            y_hat = net(data)\n",
    "            loss = loss_fn(y_hat, label)\n",
    "        autograd.backward(loss)\n",
    "        trainer.step(batch_size=batch_size)\n",
    "    \n",
    "    print(\"epoch: {}\".format(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Evaluation Metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0; batch: 0; RMSE: 4.797231674194336\n",
      "epoch: 0; batch: 100; RMSE: 4.823262311444424\n",
      "epoch: 0; batch: 200; RMSE: 4.796083604518454\n",
      "epoch: 0; batch: 300; RMSE: 4.80735121137676\n",
      "epoch: 0; batch: 400; RMSE: 4.807119855262395\n",
      "epoch: 0; batch: 500; RMSE: 4.790964190831441\n",
      "epoch: 0; batch: 600; RMSE: 4.75370117035166\n",
      "epoch: 0; batch: 700; RMSE: 4.755704509038558\n",
      "epoch: 0; batch: 800; RMSE: 4.767971026019359\n",
      "epoch: 0; batch: 900; RMSE: 4.757177492886881\n",
      "epoch: 1; batch: 0; RMSE: 6.265623569488525\n",
      "epoch: 1; batch: 100; RMSE: 4.879797260359962\n",
      "epoch: 1; batch: 200; RMSE: 4.780074592846543\n",
      "epoch: 1; batch: 300; RMSE: 4.739668083349335\n",
      "epoch: 1; batch: 400; RMSE: 4.726510347570862\n",
      "epoch: 1; batch: 500; RMSE: 4.76146391147149\n",
      "epoch: 1; batch: 600; RMSE: 4.761130930976741\n",
      "epoch: 1; batch: 700; RMSE: 4.764745098547997\n",
      "epoch: 1; batch: 800; RMSE: 4.753533680489596\n",
      "epoch: 1; batch: 900; RMSE: 4.758493993311426\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "epochs = 2\n",
    "log_interval = 100\n",
    "metrics = mx.metric.RMSE()\n",
    "log = []\n",
    "for e in range(epochs):\n",
    "    metrics.reset()\n",
    "    for i, (data, label) in enumerate(train_data):\n",
    "        data = data.as_in_context(ctx)\n",
    "        label = label.as_in_context(ctx)\n",
    "        with autograd.record():\n",
    "            y_hat = net(data)\n",
    "            loss = loss_fn(y_hat, label)\n",
    "        autograd.backward(loss)\n",
    "        trainer.step(batch_size=batch_size)\n",
    "        metrics.update(labels=loss, preds=y_hat)\n",
    "        log.append(metrics.get()[1])\n",
    "        if not(i % log_interval):\n",
    "            print(\"epoch: {}; batch: {}; RMSE: {}\".format(e,i,metrics.get()[1]))\n",
    "plt.plot(log)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## More supported Evaluation Metrics\n",
    "|Function|Description|notes|\n",
    "|:---|:---|:---|\n",
    "|Accuracy|Computes accuracy classification score.|$Accuracy(y, \\hat{y})=\\frac{1}{n}\\sum_{i=0}^{n-1}1(y_i==\\hat{y_i}))$|\n",
    "|TopKAccuracy|Computes top k predictions accuracy.||\n",
    "|F1|Computes the F1 score of a binary classification problem.|best value is 1.0 and the worst value is 0.0. The F1 score only support binary classification problems<br>`F1 = 2 * (precision * recall) / (precision + recall)`<br>`precision = true_positives / (true_positives + false_positives)`<br>`recall = true_positives / (true_positives + false_negatives)`|\n",
    "|MCC|Computed Matthews Correlation Coefficient|Supports only binary classification and is slower than F1 but provided more insight by including TN. 1 is completely correlated, 0 is uncorrelated, and -1 is negatively correlated<br><br>$MCC=\\frac{TP \\times TN - FP \\times FN}{\\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}$\n",
    "|Perplexity|Computes perplexity. Perplexity is a measurement of how well a probability distribution or model predicts a sample. A low perplexity indicates the model is good at predicting the sample.|$perplexity(q)=e^{-\\frac{1}{N}\\sum{_{i=1}^N}log(q(x_i))}$|\n",
    "|MAE|Computes MAE (Mean Absolute Error) Loss|is a measure of difference between two continuous variables.. <br>$$MAE=\\frac{1}{N}\\sum_i^n|y_i-\\hat{y_i}|$$|\n",
    "|MSE|Computes Mean Squared Error Loss|The MSE is a measure of the quality of an estimator—it is always non-negative, and values closer to zero are better. MSE captures both varince and bias of an estimtor.<br>$$MSE=\\frac{\\sum_{i=1}^n(y_i-\\hat{y_i})^2}{n}$$<br> Source: Wikipedia|\n",
    "|RMSE|Computes Root Mean Squred Error (RMSE) loss.|RMSE measures accuracy of a forecae within a dataset. <br>$$RMSE=\\sqrt{\\frac{\\sum_{i=1}^{n}(y_i-\\hat{y_i})^2}{n}}$$Compared to MSE, RMSE penalized lirge errors for aggressively by squaring them.[8]![8](https://cdn-images-1.medium.com/max/1600/1*YTxb8K2XZIisC944v6rERw.png)|\n",
    "|CrossEntropy|Computes cross-entropy loss.|Cross-Entropy loss is a measure of performance in classification models where output is a propability value. The closer probability of a prediction is to an associated observation, the smaller the loss will be. Cross-Entropy loss is alternatively called log loss. <br> $$\\mathcal{L} = -\\sum_{n=1}^{N}{\\sum_{k=1}^{K}{t_{nk}log(y_{nk})}}$$ $$N:sample size; K:num classes, y_{nk}: P(y\\ blowongs to class\\ k); t_{nk}=1\\Leftrightarrow n\\ belongs\\ to\\ k$$|\n",
    "|PearsonCorrelation|Computes Pearson correlation.|PCC measures linear correlation between two populations with values between -1 and 1. 1 is positive correlation, 0 is no correlation, and -1 expresses that the two populations are negatively correlated.<br> $$\\rho_{X,Y} = \\frac{cov(X,Y)}{\\sigma_X\\sigma_y}\\ where cov(X,Y)=\\mathbb{E}[(X-\\mu_x)(Y-\\mu_y)]$$ |\n",
    "|CustomMetrics|Computes a customized evaluation metric that can be passed to the fucntion as a parameter|`fval = lambda x,y: (x + y).mean()`<br>`eval_metrics = mx.metric.CustomMetric(feval=feval)`|\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Using multiple metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0; batch: 0; RMSE: [('rmse', 4.3657245635986328), ('accuracy', 1.0), ('perplexity', 3.276986972323656), ('Nonsensical', 3.5193841457366943)]\n",
      "epoch: 0; batch: 100; RMSE: [('rmse', 4.8817102602212739), ('accuracy', 1.0), ('perplexity', 28.200619456904597), ('Nonsensical', 3.323296484085593)]\n",
      "epoch: 0; batch: 200; RMSE: [('rmse', 4.7642668017107459), ('accuracy', 1.0), ('perplexity', 25.91258486783947), ('Nonsensical', 3.2509262471353235)]\n",
      "epoch: 0; batch: 300; RMSE: [('rmse', 4.6829357242267395), ('accuracy', 1.0), ('perplexity', 30.197751950537988), ('Nonsensical', 3.1656336900205706)]\n",
      "epoch: 0; batch: 400; RMSE: [('rmse', 4.6740798058355244), ('accuracy', 1.0), ('perplexity', 29.661004416946568), ('Nonsensical', 3.1558677593520157)]\n",
      "epoch: 0; batch: 500; RMSE: [('rmse', 4.6707300383173775), ('accuracy', 1.0), ('perplexity', 33.44960152325766), ('Nonsensical', 3.145690734871847)]\n",
      "epoch: 0; batch: 600; RMSE: [('rmse', 4.7257885155384232), ('accuracy', 1.0), ('perplexity', 31.496872882900387), ('Nonsensical', 3.1877409523715592)]\n",
      "epoch: 0; batch: 700; RMSE: [('rmse', 4.7411036484591804), ('accuracy', 1.0), ('perplexity', 29.7007893229819), ('Nonsensical', 3.2105942364681126)]\n",
      "epoch: 0; batch: 800; RMSE: [('rmse', 4.7357163396518622), ('accuracy', 1.0), ('perplexity', 30.991649078845892), ('Nonsensical', 3.1937683017438419)]\n",
      "epoch: 0; batch: 900; RMSE: [('rmse', 4.7412616706450166), ('accuracy', 1.0), ('perplexity', 31.522191516040227), ('Nonsensical', 3.1898617124253188)]\n",
      "epoch: 1; batch: 0; RMSE: [('rmse', 5.6357660293579102), ('accuracy', 1.0), ('perplexity', 0.2333197224720777), ('Nonsensical', 4.9820442199707031)]\n",
      "epoch: 1; batch: 100; RMSE: [('rmse', 4.7894600405551415), ('accuracy', 1.0), ('perplexity', 21.730890417916804), ('Nonsensical', 3.2675231189125835)]\n",
      "epoch: 1; batch: 200; RMSE: [('rmse', 4.7568263711027834), ('accuracy', 1.0), ('perplexity', 28.311502174679458), ('Nonsensical', 3.1698451716063629)]\n",
      "epoch: 1; batch: 300; RMSE: [('rmse', 4.7323198017487886), ('accuracy', 1.0), ('perplexity', 33.58970474185288), ('Nonsensical', 3.1182454056617033)]\n",
      "epoch: 1; batch: 400; RMSE: [('rmse', 4.7314389673551718), ('accuracy', 1.0), ('perplexity', 33.91706556385746), ('Nonsensical', 3.1450091481134481)]\n",
      "epoch: 1; batch: 500; RMSE: [('rmse', 4.7242445979051721), ('accuracy', 1.0), ('perplexity', 35.01630976326052), ('Nonsensical', 3.1351622194051743)]\n",
      "epoch: 1; batch: 600; RMSE: [('rmse', 4.7407012604635685), ('accuracy', 1.0), ('perplexity', 33.900786536540444), ('Nonsensical', 3.1589176400677732)]\n",
      "epoch: 1; batch: 700; RMSE: [('rmse', 4.7489290485708588), ('accuracy', 1.0), ('perplexity', 32.01610772458356), ('Nonsensical', 3.1944784164726308)]\n",
      "epoch: 1; batch: 800; RMSE: [('rmse', 4.7548228238852284), ('accuracy', 1.0), ('perplexity', 31.79114304135661), ('Nonsensical', 3.1997500076685355)]\n",
      "epoch: 1; batch: 900; RMSE: [('rmse', 4.767036127065051), ('accuracy', 1.0), ('perplexity', 32.44080851489383), ('Nonsensical', 3.2065614014863968)]\n"
     ]
    }
   ],
   "source": [
    "epochs = 2\n",
    "log_interval = 100\n",
    "eval_fn = lambda x, y: ((x + y).mean())\n",
    "custom_metric = mx.metric.CustomMetric(feval=eval_fn, name='Nonsensical')\n",
    "child_metrics = [mx.metric.RMSE(), mx.metric.Accuracy(), mx.metric.Perplexity(ignore_label=None), custom_metric]\n",
    "metrics = mx.metric.CompositeEvalMetric()\n",
    "for c in child_metrics:\n",
    "    metrics.add(c)\n",
    "\n",
    "log = []\n",
    "for e in range(epochs):\n",
    "    metrics.reset()\n",
    "    for i, (data, label) in enumerate(train_data):\n",
    "        data = data.as_in_context(ctx)\n",
    "        label = label.as_in_context(ctx)\n",
    "        with autograd.record():\n",
    "            y_hat = net(data)\n",
    "            loss = loss_fn(y_hat, label)\n",
    "        autograd.backward(loss)\n",
    "        trainer.step(batch_size=batch_size)\n",
    "        metrics.update(labels=loss, preds=y_hat)\n",
    "        log.append(metrics.get())\n",
    "        \n",
    "        if not(i % log_interval):\n",
    "            print(\"epoch: {}; batch: {}; RMSE: {}\".format(e,i,metrics.get_name_value()))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Plotting the results\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0; batch: 0; RMSE: [('rmse', 3.9852550029754639), ('accuracy', 1.0), ('perplexity', 45.49033794401938), ('Nonsensical', 2.9216949939727783)]\n",
      "epoch: 0; batch: 100; RMSE: [('rmse', 4.7905478217814226), ('accuracy', 1.0), ('perplexity', 41.80278565256689), ('Nonsensical', 3.1357937123220747)]\n",
      "epoch: 0; batch: 200; RMSE: [('rmse', 4.7555478615547297), ('accuracy', 1.0), ('perplexity', 33.498222512961725), ('Nonsensical', 3.212168287207831)]\n",
      "epoch: 0; batch: 300; RMSE: [('rmse', 4.7140792152810338), ('accuracy', 1.0), ('perplexity', 31.735004196731218), ('Nonsensical', 3.1780128445340154)]\n",
      "epoch: 0; batch: 400; RMSE: [('rmse', 4.7118840378121547), ('accuracy', 1.0), ('perplexity', 32.09808434260283), ('Nonsensical', 3.1719642203496283)]\n",
      "epoch: 0; batch: 500; RMSE: [('rmse', 4.7431857883335349), ('accuracy', 1.0), ('perplexity', 30.366661597369028), ('Nonsensical', 3.1964689864964781)]\n",
      "epoch: 0; batch: 600; RMSE: [('rmse', 4.715266219193051), ('accuracy', 1.0), ('perplexity', 29.43009267075859), ('Nonsensical', 3.1877132740472995)]\n",
      "epoch: 0; batch: 700; RMSE: [('rmse', 4.7125444175853541), ('accuracy', 1.0), ('perplexity', 30.765149845662084), ('Nonsensical', 3.1812047358926456)]\n",
      "epoch: 0; batch: 800; RMSE: [('rmse', 4.7096425777070978), ('accuracy', 1.0), ('perplexity', 31.97705928402336), ('Nonsensical', 3.1677776165632126)]\n",
      "epoch: 0; batch: 900; RMSE: [('rmse', 4.7253482594474177), ('accuracy', 1.0), ('perplexity', 31.926462893422563), ('Nonsensical', 3.1837933987180613)]\n",
      "epoch: 1; batch: 0; RMSE: [('rmse', 6.4447674751281738), ('accuracy', 1.0), ('perplexity', 27.622261312289197), ('Nonsensical', 4.0547013282775879)]\n",
      "epoch: 1; batch: 100; RMSE: [('rmse', 4.7876463998662366), ('accuracy', 1.0), ('perplexity', 35.955954951361385), ('Nonsensical', 3.1820864948158216)]\n",
      "epoch: 1; batch: 200; RMSE: [('rmse', 4.7035737286752726), ('accuracy', 1.0), ('perplexity', 32.086252259045615), ('Nonsensical', 3.155315309818556)]\n",
      "epoch: 1; batch: 300; RMSE: [('rmse', 4.7327457420849717), ('accuracy', 1.0), ('perplexity', 32.52878741412676), ('Nonsensical', 3.1758833677442961)]\n",
      "epoch: 1; batch: 400; RMSE: [('rmse', 4.7568223592349117), ('accuracy', 1.0), ('perplexity', 36.14880989440005), ('Nonsensical', 3.1740269887904424)]\n",
      "epoch: 1; batch: 500; RMSE: [('rmse', 4.7360895534237466), ('accuracy', 1.0), ('perplexity', 35.958283864776135), ('Nonsensical', 3.1579917334614995)]\n",
      "epoch: 1; batch: 600; RMSE: [('rmse', 4.7392029280273764), ('accuracy', 1.0), ('perplexity', 31.93322536646495), ('Nonsensical', 3.1931528165105871)]\n",
      "epoch: 1; batch: 700; RMSE: [('rmse', 4.7564269868861588), ('accuracy', 1.0), ('perplexity', 29.84018940896536), ('Nonsensical', 3.2204235877772627)]\n",
      "epoch: 1; batch: 800; RMSE: [('rmse', 4.7381346608220269), ('accuracy', 1.0), ('perplexity', 32.30469218252686), ('Nonsensical', 3.1965281242055914)]\n",
      "epoch: 1; batch: 900; RMSE: [('rmse', 4.7470143385123995), ('accuracy', 1.0), ('perplexity', 33.22765392587356), ('Nonsensical', 3.1913612733381105)]\n"
     ]
    }
   ],
   "source": [
    "from gluoncv.utils import TrainingHistory\n",
    "epochs = 2\n",
    "log_interval = 100\n",
    "eval_fn = lambda x, y: ((x + y).mean())\n",
    "custom_metric = mx.metric.CustomMetric(feval=eval_fn, name='Nonsensical')\n",
    "child_metrics = [mx.metric.RMSE(), mx.metric.Accuracy(), mx.metric.Perplexity(ignore_label=None), custom_metric]\n",
    "metrics = mx.metric.CompositeEvalMetric()\n",
    "ths = []    \n",
    "\n",
    "for c in child_metrics:\n",
    "    metrics.add(c)\n",
    "    ths.append(TrainingHistory([c.name, c.name+\"_val\"]))    \n",
    "\n",
    "log = []\n",
    "for e in range(epochs):\n",
    "    metrics.reset()\n",
    "    for i, (data, label) in enumerate(train_data):\n",
    "        data = data.as_in_context(ctx)\n",
    "        label = label.as_in_context(ctx)\n",
    "        with autograd.record():\n",
    "            y_hat = net(data)\n",
    "            loss = loss_fn(y_hat, label)\n",
    "        autograd.backward(loss)\n",
    "        trainer.step(batch_size=batch_size)\n",
    "        metrics.update(labels=loss, preds=y_hat)\n",
    "        log.append(metrics.get())\n",
    "        for j in range(len(metrics.get()[0])):\n",
    "            val = metrics.get()[1][j]\n",
    "            ths[j].update([val, val/2])          \n",
    "        \n",
    "        if not(i % log_interval):\n",
    "            print(\"epoch: {}; batch: {}; RMSE: {}\".format(e,i,metrics.get_name_value()))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "min_val, max_val = 0, 0\n",
    "for th in ths:\n",
    "    min_val =  nd.array(th.history[th.labels[0]]).min().asscalar()\n",
    "    min_val = min(min_val, nd.array(th.history[th.labels[1]]).min().asscalar()) // 2\n",
    "    max_val =  nd.array(th.history[th.labels[0]]).max().asscalar()\n",
    "    max_val =  max(max_val, nd.array(th.history[th.labels[1]]).max().asscalar()) * 2\n",
    "    th.plot(labels=th.labels, y_lim=(min_val, max_val), colors=('red', 'blue'))\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Refrences:\n",
    "1. EcoRNN: Fused LSTM RNN Implementation with Data Layout Optimization Zheng et al.: arXiv:1805.08899\n",
    "2. Sebastian Ruder: [http://ruder.io/optimizing-gradient-descent/](http://ruder.io/optimizing-gradient-descent/)\n",
    "3. Asynchronous Stochastic Gradient Descent with Delay Compensation; Zheng et al.: arXiv:1609.08326 [cs.LG]\n",
    "4. Compressed Optimisation for Non-Convex Problems. Anandkumar et al.: arXiv:1802.04434 [cs.LG]\n",
    "5. Follow the Moving Leader in Deep Learning. Zheng et al.: [paper](http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf)\n",
    "6. Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour, He et al.: arXiv:1706.02677 [cs.CV] \n",
    "7. [Twards Data Science Blog](https://towardsdatascience.com/deep-learning-at-scale-accurate-large-mini-batch-sgd-8207d54bfe02). This is an intuitive version of [6].\n",
    "8. [MAE and RMSE — Which Metric is Better?](https://medium.com/human-in-a-machine-world/mae-and-rmse-which-metric-is-better-e60ac3bde13d)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Environment (conda_mxnet_p36)",
   "language": "python",
   "name": "conda_mxnet_p36"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}