"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# code for loading the format for the notebook\n",
"import os\n",
"\n",
"# path : store the current path to convert back to it later\n",
"path = os.getcwd()\n",
"os.chdir(os.path.join('..', 'notebook_format'))\n",
"\n",
"from formats import load_style\n",
"load_style(plot_style = False)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ethen 2018-09-15 15:15:16 \n",
"\n",
"CPython 3.6.4\n",
"IPython 6.4.0\n",
"\n",
"numpy 1.14.1\n",
"pandas 0.23.0\n",
"matplotlib 2.2.2\n",
"sklearn 0.19.1\n"
]
}
],
"source": [
"os.chdir(path)\n",
"\n",
"# 1. magic for inline plot\n",
"# 2. magic to print version\n",
"# 3. magic so that the notebook will reload external python modules\n",
"# 4. magic to enable retina (high resolution) plots\n",
"# https://gist.github.com/minrk/3301035\n",
"%matplotlib inline\n",
"%load_ext watermark\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"%config InlineBackend.figure_format = 'retina'\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from sklearn import datasets\n",
"from sklearn.metrics import accuracy_score\n",
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn.linear_model import LogisticRegression\n",
"\n",
"%watermark -a 'Ethen' -d -t -v -p numpy,pandas,matplotlib,sklearn"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Softmax Regression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Softmax Regression** is a generalization of logistic regression that we can use for multi-class classification. If we want to assign probabilities to an object being one of several different things, softmax is the thing to do. Even later on, when we start training neural network models, the final step will be a layer of softmax.\n",
"\n",
"A softmax regression has two steps: first we add up the evidence of our input being in certain classes, and then we convert that evidence into probabilities.\n",
"\n",
"In **Softmax Regression**, we replace the sigmoid logistic function by the so-called *softmax* function $\\phi(\\cdot)$.\n",
"\n",
"$$P(y=j \\mid z^{(i)}) = \\phi(z^{(i)}) = \\frac{e^{z^{(i)}}}{\\sum_{j=1}^{k} e^{z_{j}^{(i)}}}$$\n",
"\n",
"where we define the net input *z* as \n",
"\n",
"$$z = w_1x_1 + ... + w_mx_m + b= \\sum_{l=1}^{m} w_l x_l + b= \\mathbf{w}^T\\mathbf{x} + b$$ \n",
"\n",
"(**w** is the weight vector, $\\mathbf{x}$ is the feature vector of 1 training sample. Each $w$ corresponds to a feature $x$ and there're $m$ of them in total. $b$ is the bias unit. $k$ denotes the total number of classes.) \n",
"\n",
"Now, this softmax function computes the probability that the $i_{th}$ training sample $\\mathbf{x}^{(i)}$ belongs to class $l$ given the weight and net input $z^{(i)}$. So given the obtained weight $w$, we're basically compute the probability, $p(y = j \\mid \\mathbf{x^{(i)}; w}_j)$, the probability of the training sample belonging to class $j$ for each class label in $j = 1, \\ldots, k$. Note the normalization term in the denominator which causes these class probabilities to sum up to one.\n",
"\n",
"We can picture our softmax regression as looking something like the following, although with a lot more $x_s$. For each output, we compute a weighted sum of the $x_s$, add a bias, and then apply softmax.\n",
"\n",
"\n",
"\n",
"If we write that out as equations, we get:\n",
"\n",
"\n",
"\n",
"We can \"vectorize\" this procedure, turning it into a matrix multiplication and vector addition. This is helpful for computational efficiency. (It's also a useful way to think.)\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To illustrate the concept of softmax, let us walk through a concrete example. Suppose we have a training set consisting of 4 samples from 3 different classes (0, 1, and 2)\n",
"\n",
"- $x_0 \\rightarrow \\text{class }0$\n",
"- $x_1 \\rightarrow \\text{class }1$\n",
"- $x_2 \\rightarrow \\text{class }2$\n",
"- $x_3 \\rightarrow \\text{class }2$\n",
"\n",
"First, we apply one-hot encoding to encode the class labels into a format that we can more easily work with."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1., 0., 0.],\n",
" [0., 1., 0.],\n",
" [0., 0., 1.],\n",
" [0., 0., 1.]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y = np.array([0, 1, 2, 2])\n",
"\n",
"def one_hot_encode(y):\n",
" n_class = np.unique(y).shape[0]\n",
" y_encode = np.zeros((y.shape[0], n_class))\n",
" for idx, val in enumerate(y):\n",
" y_encode[idx, val] = 1.0\n",
" \n",
" return y_encode\n",
"\n",
"y_encode = one_hot_encode(y)\n",
"y_encode"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A sample that belongs to class 0 (the first row) has a 1 in the first cell, a sample that belongs to class 1 has a 1 in the second cell of its row, and so forth.\n",
"\n",
"Next, let us define the feature matrix of our 4 training samples. Here, we assume that our dataset consists of 2 features; thus, we create a 4x2 dimensional matrix of our samples and features.\n",
"Similarly, we create a 2x3 dimensional weight matrix (one row per feature and one column for each class)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Inputs X:\n",
" [[ 0.1 0.5]\n",
" [ 1.1 2.3]\n",
" [-1.1 -2.3]\n",
" [-1.5 -2.5]]\n",
"\n",
"Weights W:\n",
" [[0.1 0.2 0.3]\n",
" [0.1 0.2 0.3]]\n",
"\n",
"bias:\n",
" [0.01 0.1 0.1 ]\n"
]
}
],
"source": [
"X = np.array([[0.1, 0.5],\n",
" [1.1, 2.3],\n",
" [-1.1, -2.3],\n",
" [-1.5, -2.5]])\n",
"\n",
"W = np.array([[0.1, 0.2, 0.3],\n",
" [0.1, 0.2, 0.3]])\n",
"\n",
"bias = np.array([0.01, 0.1, 0.1])\n",
"\n",
"print('Inputs X:\\n', X)\n",
"print('\\nWeights W:\\n', W)\n",
"print('\\nbias:\\n', bias)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To compute the net input, we multiply the 4x2 matrix feature matrix `X` with the 2x3 (n_features x n_classes) weight matrix `W`, which yields a 4x3 output matrix (n_samples x n_classes) to which we then add the bias unit: \n",
"\n",
"$$\\mathbf{Z} = \\mathbf{X}\\mathbf{W} + \\mathbf{b}$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"net input:\n",
" [[ 0.07 0.22 0.28]\n",
" [ 0.35 0.78 1.12]\n",
" [-0.33 -0.58 -0.92]\n",
" [-0.39 -0.7 -1.1 ]]\n"
]
}
],
"source": [
"def net_input(X, W, b):\n",
" return X.dot(W) + b\n",
"\n",
"net_in = net_input(X, W, bias)\n",
"print('net input:\\n', net_in)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, it's time to compute the softmax activation that we discussed earlier:\n",
"\n",
"$$P(y=j \\mid z^{(i)}) = \\phi_{softmax}(z^{(i)}) = \\frac{e^{z^{(i)}}}{\\sum_{j=1}^{k} e^{z_{j}^{(i)}}}$$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"softmax:\n",
" [[0.29450637 0.34216758 0.36332605]\n",
" [0.21290077 0.32728332 0.45981591]\n",
" [0.42860913 0.33380113 0.23758974]\n",
" [0.44941979 0.32962558 0.22095463]]\n"
]
}
],
"source": [
"def softmax(z):\n",
" return np.exp(z) / np.sum(np.exp(z), axis = 1, keepdims = True)\n",
"\n",
"smax = softmax(net_in)\n",
"print('softmax:\\n', smax)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see, the values for each sample (row) nicely sum up to 1 now. E.g., we can say that the first sample `[ 0.29450637 0.34216758 0.36332605]` has a 29.45% probability to belong to class 0. Now, in order to turn these probabilities back into class labels, we could simply take the argmax-index position of each row:\n",
"\n",
"[[ 0.29450637 0.34216758 **0.36332605**] -> 2 \n",
"[ 0.21290077 0.32728332 **0.45981591**] -> 2 \n",
"[ **0.42860913** 0.33380113 0.23758974] -> 0 \n",
"[ **0.44941979** 0.32962558 0.22095463]] -> 0 "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"predicted class labels: [2 2 0 0]\n"
]
}
],
"source": [
"def to_classlabel(z):\n",
" return z.argmax(axis = 1)\n",
"\n",
"print('predicted class labels: ', to_classlabel(smax))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see, our predictions are terribly wrong, since the correct class labels are `[0, 1, 2, 2]`. Now, in order to train our model we need to measuring how inefficient our predictions are for describing the truth and then optimize on it. To do so we first need to define a loss/cost function $J(\\cdot)$ that we want to minimize. One very common function is \"cross-entropy\":\n",
"\n",
"$$J(\\mathbf{W}; \\mathbf{b}) = \\frac{1}{n} \\sum_{i=1}^{n} H( T^{(i)}, O^{(i)} )$$\n",
"\n",
"which is the average of all cross-entropies $H$ over our $n$ training samples. The cross-entropy function is defined as:\n",
"\n",
"$$H( T^{(i)}, O^{(i)} ) = -\\sum_k T^{(i)} \\cdot log(O^{(i)})$$\n",
"\n",
"Where:\n",
"\n",
"- $T$ stands for \"target\" (i.e., the *true* class labels) \n",
"- $O$ stands for output -- the computed *probability* via softmax; **not** the predicted class label.\n",
"- $\\sum_k$ denotes adding up the difference between the target and the output for all classes."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cross Entropy Cost: 1.3215978715930938\n"
]
}
],
"source": [
"def cross_entropy_cost(y_target, output):\n",
" return np.mean(-np.sum(y_target * np.log(output), axis = 1))\n",
"\n",
"cost = cross_entropy_cost(y_target = y_encode, output = smax)\n",
"print('Cross Entropy Cost:', cost)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gradient Descent"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our objective in training a neural network is to find a set of weights that gives us the lowest error when we run it against our training data. There are many ways to find these weights and simplest one is so called **gradient descent**. It does this by giving us directions (using derivatives) on how to \"shift\" our weights to an optimum. It tells us whether we should increase or decrease the value of a specific weight in order to lower the error function.\n",
"\n",
"Let's imagine we have a function $f(x) = x^4 - 3x^3 + 2$ and we want to find the minimum of this function using gradient descent. Here's a graph of that function:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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