From ba85c3581c2474368c02349b431d9aecfbd5c0d6 Mon Sep 17 00:00:00 2001 From: Eduardo Cueto Mendoza Date: Tue, 28 Apr 2020 10:42:58 -0600 Subject: [PATCH] [MOD] Added backpropagation function --- Numpy_NN.ipynb | 114 ++++++++++++++++++++++++++++++++++--------------- 1 file changed, 80 insertions(+), 34 deletions(-) diff --git a/Numpy_NN.ipynb b/Numpy_NN.ipynb index 82a47f9..2b9ab5a 100644 --- a/Numpy_NN.ipynb +++ b/Numpy_NN.ipynb @@ -1,21 +1,14 @@ { "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np" - ] - }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ - "import matplotlib.pyplot as plt" + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import sklearn.datasets" ] }, { @@ -23,37 +16,28 @@ "execution_count": 3, "metadata": {}, "outputs": [], - "source": [ - "import sklearn.datasets" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], "source": [ "X,y = sklearn.datasets.make_moons(200,noise=0.15)" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 12, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -70,7 +54,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -79,7 +63,7 @@ "(200, 2)" ] }, - "execution_count": 13, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -90,7 +74,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -104,16 +88,28 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'W1' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmodel_dic\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m'W1'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mW1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'b1'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mb1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'W2'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mW2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'b2'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mb2\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mNameError\u001b[0m: name 'W1' is not defined" + ] + } + ], "source": [ "model_dic = {'W1': W1, 'b1': b1,'W2': W2, 'b2': b2}" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -127,7 +123,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -139,13 +135,13 @@ " a2 = np.tanh(z2)\n", " exp_scores = np.exp(a2)\n", " softmax = exp_scores / np.sum(exp_scores, dim=1, keepdims=True)\n", - " return softmax\n", + " return z1,a1,softmax\n", " " ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -164,12 +160,62 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ - "softmax = np.random.randn(200,2)\n" + "def predict(x, model_dict):\n", + " W1,b1,W2,b2 = retrieve(model_dict)\n", + " z1 = x.dot(W1) + b1\n", + " a1 = np.tanh(z1)\n", + " z2 = a1.dot(W2) + b2\n", + " a2 = np.tanh(z2)\n", + " exp_scores = np.exp(a2)\n", + " softmax = exp_scores / np.sum(exp_scores, dim=1, keepdims=True)\n", + " return np.argmax(softmax, axis=1)\n" ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "def backpropagation(x,y,model_dict,epochs):\n", + " for i in range(epochs):\n", + " W1,b1,W2,b2 = retrieve(model_dict)\n", + " z1,a1,probs = forward(x,model_dict)\n", + " delta3 = np.copy(probs)\n", + " delta3[range(x.shaape[0]),y] -= 1\n", + " dW2 = (a1.T).dot(delta3)\n", + " db2 = np.sum(delta3,axis=0,keepdims=True)\n", + " delta2 = delta3.dot(W2.T) * (1-np.power(np.tanh(z1),2))\n", + " dW1 = np.dot(x.T,delta2)\n", + " db1 = np.sum(delta2,axis=0,keepdims=True)\n", + " # Add regularization terms\n", + " dW2 += lambda_reg * np.sum(W2)\n", + " dW1 += lambda_reg * np.sum(W1)\n", + " # Update weights\n", + " W1 += -learning_rate * dW1\n", + " b1 += -learning_rate * db1\n", + " W2 += -learning_rate * dW2\n", + " b2 += -learning_rate * db2\n", + " # Update the model dictionary\n", + " model_dict = {'W1': W1, 'b1': b1,'W2': W2, 'b2': b2}\n", + " # Print loss every 50 epochs\n", + " if i%50 == 0:\n", + " print(\"Loss at epoch {} is: {}\".format(i,loss(probs,y,model_dict)))\n", + " \n", + " return model_dict\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": {