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August 27, 2018 16:52
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"/anaconda3/envs/py35/lib/python3.5/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", | |
" from ._conv import register_converters as _register_converters\n" | |
] | |
} | |
], | |
"source": [ | |
"import numpy as np\n", | |
"import seaborn as sns\n", | |
"import matplotlib.pyplot as plt\n", | |
"%matplotlib inline\n", | |
"import pymc3 as pm\n", | |
"sns.set_context('talk')\n", | |
"sns.set_style('whitegrid')\n", | |
"import statsmodels.formula.api as smf\n", | |
"import statsmodels.api as sm\n", | |
"import pandas as pd\n", | |
"np.random.seed(1)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Kernel regression\n", | |
"\n", | |
"In the post I'm going to introduce *Kernel* regression as a precurser to Gaussian Processes regression. To start with we'll review linear regression and then introduce a very simple extension using a limited number kernels, which we'll think of as just like multivariate regression. A complicated picture will arise when we let the number of kernels being used equal the number of data. Finally we'll abandon ordinary least squares regression and show kernel regression proper as a way of averaging data. \n", | |
"\n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Linear regression uses the multivariate normal distribution\n", | |
"\n", | |
"Our data are $N$ observations of a reponse and independent variable: $(y_i, X_i)\\ i = 1, ..., N$. The $X_i$ could be vectors (for multivariate linear regression) of could be realisations of a single variable. Initially we'll keep things simple and assume the latter. \n", | |
"\n", | |
"The main model assumptions are that each $y_i$ is normally distributed, with a mean given by a linear function of the dependent variable, $\\mu_i = \\beta_0 + \\beta_1x_i$ and a common variance, $\\sigma^2$. In other words: \n", | |
"\n", | |
"$$\n", | |
"\\begin{align}\n", | |
"y_i \\sim & \\mathcal{N}(\\mu, \\sigma^2)\\\\\n", | |
"\\sim & \\mathcal{N}(\\beta_0 + \\beta_1X_i, \\sigma^2)\n", | |
"\\end{align}\n", | |
"$$\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Our task is to estimate the $\\beta$'s by minimizing the squared errors (alternatively maximimizing the log-likelihood) between the estimated mean values $\\hat{\\beta}_0 + \\hat{\\beta}_1 X_i$ the true values $y_i$ (the hats denote an estimated quantity). \n", | |
"\n", | |
"An example is shown below in graphical format. We're using the OLS model from the python module [`statsmodels`](https://www.statsmodels.org/stable/index.html). Here the true values of the parameters are $\\beta_0 = 2$ and $\\beta_1 = 0.5$. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"x = np.linspace(-1,1,20)\n", | |
"y = 2 + 0.5*x + np.random.normal(0, 0.1, len(x))\n", | |
"df = pd.DataFrame({'x': x, 'y': y})\n", | |
"result = smf.ols('y ~ x', data=df).fit()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x111a71278>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.scatter(x, y, label='data')\n", | |
"plt.plot(x, result.fittedvalues, \n", | |
" label='Fitted line:\\n$y = {0:4.2f} + {1:4.2f}X$'.format(*result.params))\n", | |
"_ = plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## If the data are non-linear we can add polynomial terms\n", | |
"\n", | |
"If the data are non-linear in $X$ then we could add a $X^2$ term to the regression. i.e. \n", | |
"$$\n", | |
"Y = \\beta_0 + \\beta_1 X + \\beta_2 X^2 + \\epsilon\n", | |
"$$\n", | |
"\n", | |
"This is known as [polynomial regression](https://en.wikipedia.org/wiki/Polynomial_regression). \n", | |
"\n", | |
"An example of this is shown below, where we've just added a $\\beta_2 = -1$ term to the previous equation. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"x = np.linspace(-1,1,20)\n", | |
"y = 2 + 0.5*x - x**2 + np.random.normal(0, 0.1, len(x))\n", | |
"df = pd.DataFrame({'x': x, 'y': y})\n", | |
"result = smf.ols('y ~ x + np.power(x, 2)', data=df).fit()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c1e43bf60>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.scatter(x, y, label='data')\n", | |
"plt.plot(x, result.fittedvalues, \n", | |
" label='Fitted line:\\n$Y = {0:4.2f} {1:+4.2f}X {2:+4.2f}X^2$'.format(*result.params))\n", | |
"_ = plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The model is still a multivariate normal but the elements of the mean function are now no longer linearly increasing. Like the linear case the covariance matrix still has no off-diagonal non-zero elements. \n", | |
"\n", | |
"We could extend this to any number of cubic, quartic etc. terms. In other words, we would be using a polynomial basis to fit the non-linear relationship between X and Y. The problem with this is that the value of $y$ at $X= -1$ is dependent on the value of $Y$ at $X = 1$. i.e. a polynomial basis is *non-local*. \n", | |
"\n", | |
"To avoid the problem of non-locality we can use a series of *kernels* instead of a the polynomial terms. " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"\n", | |
"## Kernels also allow non-linearities\n", | |
"A [kernel][1] is a symmetric function that takes two inputs and returns a single, positive output. A kernel measures the similarity between the two inputs.\n", | |
"A popular kernel is the *Gaussian* kernel, which is shown below: \n", | |
"\n", | |
"$$\n", | |
"K(x, x') = \\exp\\left(-\\frac{||x - x'||^2}{w}\\right)\n", | |
"$$\n", | |
"\n", | |
"$w$ is known as the bandwidth. This measures the similarity between two points $x$ and $x'$. \n", | |
"[1]: https://en.wikipedia.org/wiki/Kernel_(statistics)#Nonparametric_statistics" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"\n", | |
"In Kernal regression we replace the powers of $X$ in polynomial regression with the values of the kernel at different values of $X$. These values are known as **knots** or **centroids** which we'll label $q$ to highlight the fact they are logically distinct from the covarite $X$. The equation below has three centroids ($q_1,q_2,q_3$): \n", | |
"\n", | |
"$$\n", | |
"y_i = \\gamma_1 K(X_i, q_1) + \\gamma_2 K(X_i, q_2) + \\gamma_3 K(X_i, q_3) + \\epsilon\n", | |
"$$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"To estimate the parameters, $\\gamma$, we can (kind of) still use all the machinery of OLS regression. To demonstrate let's use some highly non-linear data, a noisey sine curve: " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c22b2c358>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"np.random.seed(1)\n", | |
"N = 20\n", | |
"x = np.linspace(0, 10, N)\n", | |
"ytrue = np.sin\n", | |
"y = ytrue(x) + np.random.normal(0,0.1, size=N)\n", | |
"with sns.plotting_context('talk', font_scale=1):\n", | |
" plt.plot(x, y, 'o')\n", | |
" plt.xlabel('$x$')\n", | |
" plt.ylabel('$f(x)$')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
" Let's have 5 knots equally spaced across the $X$ axis each with a bandwidth of 2:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def gauss_kernel(x, knots, w=2):\n", | |
" # Gaussian kernel using predetermined knots. \n", | |
" unnormed = [np.exp(-(x-knot)**2/w) for knot in knots]\n", | |
" normed = unnormed #[x/x.sum() for x in unnormed]\n", | |
" return np.array(normed).T" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"n_knots = 5\n", | |
"knots = np.linspace(np.floor(x.min()), np.ceil(x.max()), n_knots)\n", | |
"w = 2\n", | |
"K = gauss_kernel(x, knots, w=w) " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The variable `K` is a matrix of dimension $N \\times 5$. You can think of it as a design matrix like multivariate linear regression where each column is a different variable. \n", | |
"\n", | |
"For each knot, there is a kernel defined over all the data. i.e. for each knot, there's a value of $K$ for each value of $X$. Let's plot this: " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c22c7e5c0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"with sns.plotting_context('talk'):\n", | |
" sns.set_style('white')\n", | |
" fig, axes = plt.subplots(n_knots, figsize=(5,10), \n", | |
" sharex=True, sharey=True)\n", | |
" cols = sns.color_palette('colorblind')\n", | |
" \n", | |
" for i, ax in enumerate(axes):\n", | |
" \n", | |
" ax.scatter(x, y, color=cols[0], marker='o', label='data')\n", | |
" ax2 = ax.twinx()\n", | |
" \n", | |
" ax2.scatter(x, K.T[i], color=cols[1], alpha=0.7, marker='x')\n", | |
" ax.vlines(knots[i], -2, 2, color=cols[1], alpha=0.7, \n", | |
" label=r'$K(X, q_{%s} )$' % str(i+1))\n", | |
" ax.legend(bbox_to_anchor=(1.3, 1.05))\n", | |
" ax2.set_ylabel('knot %s' % str(i+1))\n", | |
" ax.set_ylabel('y')\n", | |
" ax.set_xlabel('X')\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Kernel regression is local\n", | |
"As you can see, the x's look like Gaussian's (because they are) around the knot center (the vertical line). The value of $K$ is non-zero only for a small number of data points around the knot center. \n", | |
"\n", | |
"So why do this? \n", | |
"\n", | |
"Well, it allows us to assign a regression coefficient to a small subset of the data points - those that are similar or *local* to the knots. For example, those data far the first knot, i.e. $ |x - q_1|^2 \\gg w$ the value of $K \\simeq 0$. This means, the only terms in the regression equation are those near $q_1$. i.e.: \n", | |
"\n", | |
"$$\n", | |
"\\hat{Y} \\approx \\gamma_1 K(X, q_1) = \\gamma_1 \\exp\\left(-\\frac{||X-q_1||^2}{w}\\right)\n", | |
"$$\n", | |
"\n", | |
"(From now on I'll drop write $K(X, q_1)$ as $K_1(X)$ to save space on the figures.)\n", | |
"\n", | |
"The predicted value of the response variable approaches $\\gamma_1$ as the values of the input variables approach the first knot, $q_1$ from either side. \n", | |
"\n", | |
"For values of $X$ that fall inbetween $q_1$ and $q_2$, the predicted value of the response variable will be a weighted average of predominately $\\gamma_1$ and $\\gamma_2$. The weights will be the values of $K_1(X)$ and $K_2(X)$. \n", | |
"\n", | |
"*So Kernel regression makes predictions at $X$ based on the average of those regression coefficients, $\\gamma$, in the neighbourhood of $X$. *" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Conditioning a kernel regression model\n", | |
"\n", | |
"To find the coefficients let's just use the OLS model and treat each $K_i$ as a different independent variables. This means we conditioning the model just like multivariate linear regression. So $K$ is a $N\\times 5$ matrix, where the $K_{ij}$ element is the value $K_{j}(X_i)$. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"model = sm.OLS(y, K)\n", | |
"result = model.fit()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Let's plot the data and the prediction. To make the prediction curve nice and smooth, we've created a new vector of X values, very tightly spaced. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c22c70630>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"Xnew = np.linspace(x.min(), x.max(), 100)\n", | |
"Knew = gauss_kernel(Xnew, knots, w=1)\n", | |
"y_predict = result.predict(Knew)\n", | |
"\n", | |
"linelabel = ' '.join([r'$ %+4.1f K_{%s}(X)$' % (x,i) for i, x in enumerate(result.params[1:])])\n", | |
"linelabel = 'y = '+' '.join([r'$ %4.1f K_{%s}(X)$' % (x,i) for i, x in enumerate(result.params[:1])]) + linelabel\n", | |
"\n", | |
"plt.scatter(x, y, label='data')\n", | |
"plt.plot(Xnew, y_predict, label='prediction')\n", | |
"plt.plot(Xnew, ytrue(Xnew), label='signal', zorder=0)\n", | |
"plt.xlabel(\"$X$\"); plt.ylabel(\"$y$\")\n", | |
"plt.legend(bbox_to_anchor=(1.05, 1))\n", | |
"_ = plt.suptitle(linelabel, fontsize=14)\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Using more knots comes at a price\n", | |
"\n", | |
"The fit isn't great - it *kind of* gets the shape but misses the amplitude badly. How could we improve the fit? \n", | |
"\n", | |
"Well, in our model we have arbitrarily set three parameters: \n", | |
"1. The number of knots\n", | |
"2. The location of the knots\n", | |
"3. The bandwidth\n", | |
"\n", | |
"One approach to improve our fit would be to use cross validation to select these parameters, but that seems difficult with the location of the knots. \n", | |
"\n", | |
"It makes sense that more knots would increase the flexibility of the basis, so why not just use *the data as the knot points*. \n", | |
"\n", | |
"The regression equation will be then: \n", | |
"\n", | |
"$$\n", | |
"y(X) = \\sum \\gamma_i K(X, q_i = X_i) + \\epsilon\n", | |
"$$\n", | |
"\n", | |
"Observe that there are now as many parameters as data points. This fact is what makes this a [non-parametric](https://en.wikipedia.org/wiki/Nonparametric_statistics) regression method. \n", | |
"\n", | |
"\n", | |
"Let's run the regression in the same way as before. We'll call this new $K$ matrix `Kx` to highlight the fact that the knots are centered at values of $X$. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 47, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(20, 20)" | |
] | |
}, | |
"execution_count": 47, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"bw = 2\n", | |
"Kx = gauss_kernel(x, knots=x, w=bw)\n", | |
"Kx.shape" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"So now `Kx` is an $N\\times N$ instead of $N\\times 5$ matrix. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 48, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"model = sm.OLS(y, Kx)\n", | |
"result = model.fit()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 49, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c24bef0b8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"Xnew = np.linspace(x.min(), x.max(), 100)\n", | |
"Knew = gauss_kernel(Xnew, x, w=bw) \n", | |
"y_predict = result.predict(Knew)\n", | |
"\n", | |
"plt.scatter(x, y, label='data')\n", | |
"plt.plot(Xnew, y_predict, label='prediction')\n", | |
"plt.xlabel(\"$X$\"); plt.ylabel(\"$y$\")\n", | |
"_ = plt.legend()\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Let's disect this. \n", | |
"\n", | |
"**The good**: the regression line goes through the data! But that's only to be expected - we have as many parameters ($\\gamma$s) as data points. \n", | |
"\n", | |
"**The bad** We've totally [overfit](https://en.wikipedia.org/wiki/Overfitting) our model. At the moment it just looks like we could have linearly interpolated and done as good a job. \n", | |
"\n", | |
"Nevertheless it does seem like the fit is better compared to 5 knots so let's investigate the model a bit more carefully. What can the fitted values of $\\gamma_i$ reveal?\n", | |
"\n", | |
"Let's look at the summary of the fit. \n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 50, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": [ | |
"<table class=\"simpletable\">\n", | |
"<caption>OLS Regression Results</caption>\n", | |
"<tr>\n", | |
" <th>Dep. Variable:</th> <td>y</td> <th> R-squared: </th> <td> 1.000</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 0.000</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Date:</th> <td>Mon, 27 Aug 2018</td> <th> Prob (F-statistic):</th> <td> nan</td> \n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Time:</th> <td>16:25:10</td> <th> Log-Likelihood: </th> <td> 454.46</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>No. Observations:</th> <td> 20</td> <th> AIC: </th> <td> -868.9</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Df Residuals:</th> <td> 0</td> <th> BIC: </th> <td> -849.0</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Df Model:</th> <td> 19</td> <th> </th> <td> </td> \n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n", | |
"</tr>\n", | |
"</table>\n", | |
"<table class=\"simpletable\">\n", | |
"<tr>\n", | |
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[0.025</th> <th>0.975]</th> \n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x1</th> <td> 1255.3516</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x2</th> <td>-5673.7457</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x3</th> <td> 1.441e+04</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x4</th> <td>-2.722e+04</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x5</th> <td> 4.267e+04</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x6</th> <td>-5.875e+04</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x7</th> <td> 7.35e+04</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x8</th> <td>-8.535e+04</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x9</th> <td> 9.324e+04</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x10</th> <td> -9.66e+04</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x11</th> <td> 9.527e+04</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x12</th> <td>-8.945e+04</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x13</th> <td> 7.968e+04</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x14</th> <td>-6.685e+04</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x15</th> <td> 5.216e+04</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x16</th> <td>-3.708e+04</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x17</th> <td> 2.324e+04</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x18</th> <td>-1.213e+04</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x19</th> <td> 4721.1359</td> <td> inf</td> <td> 0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>x20</th> <td>-1036.8394</td> <td> inf</td> <td> -0</td> <td> nan</td> <td> nan</td> <td> nan</td>\n", | |
"</tr>\n", | |
"</table>\n", | |
"<table class=\"simpletable\">\n", | |
"<tr>\n", | |
" <th>Omnibus:</th> <td> 5.083</td> <th> Durbin-Watson: </th> <td> 0.471</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Prob(Omnibus):</th> <td> 0.079</td> <th> Jarque-Bera (JB): </th> <td> 1.915</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Skew:</th> <td> 0.372</td> <th> Prob(JB): </th> <td> 0.384</td>\n", | |
"</tr>\n", | |
"<tr>\n", | |
" <th>Kurtosis:</th> <td> 1.679</td> <th> Cond. No. </th> <td>3.70e+06</td>\n", | |
"</tr>\n", | |
"</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 1.54e-12. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular." | |
], | |
"text/plain": [ | |
"<class 'statsmodels.iolib.summary.Summary'>\n", | |
"\"\"\"\n", | |
" OLS Regression Results \n", | |
"==============================================================================\n", | |
"Dep. Variable: y R-squared: 1.000\n", | |
"Model: OLS Adj. R-squared: nan\n", | |
"Method: Least Squares F-statistic: 0.000\n", | |
"Date: Mon, 27 Aug 2018 Prob (F-statistic): nan\n", | |
"Time: 16:25:10 Log-Likelihood: 454.46\n", | |
"No. Observations: 20 AIC: -868.9\n", | |
"Df Residuals: 0 BIC: -849.0\n", | |
"Df Model: 19 \n", | |
"Covariance Type: nonrobust \n", | |
"==============================================================================\n", | |
" coef std err t P>|t| [0.025 0.975]\n", | |
"------------------------------------------------------------------------------\n", | |
"x1 1255.3516 inf 0 nan nan nan\n", | |
"x2 -5673.7457 inf -0 nan nan nan\n", | |
"x3 1.441e+04 inf 0 nan nan nan\n", | |
"x4 -2.722e+04 inf -0 nan nan nan\n", | |
"x5 4.267e+04 inf 0 nan nan nan\n", | |
"x6 -5.875e+04 inf -0 nan nan nan\n", | |
"x7 7.35e+04 inf 0 nan nan nan\n", | |
"x8 -8.535e+04 inf -0 nan nan nan\n", | |
"x9 9.324e+04 inf 0 nan nan nan\n", | |
"x10 -9.66e+04 inf -0 nan nan nan\n", | |
"x11 9.527e+04 inf 0 nan nan nan\n", | |
"x12 -8.945e+04 inf -0 nan nan nan\n", | |
"x13 7.968e+04 inf 0 nan nan nan\n", | |
"x14 -6.685e+04 inf -0 nan nan nan\n", | |
"x15 5.216e+04 inf 0 nan nan nan\n", | |
"x16 -3.708e+04 inf -0 nan nan nan\n", | |
"x17 2.324e+04 inf 0 nan nan nan\n", | |
"x18 -1.213e+04 inf -0 nan nan nan\n", | |
"x19 4721.1359 inf 0 nan nan nan\n", | |
"x20 -1036.8394 inf -0 nan nan nan\n", | |
"==============================================================================\n", | |
"Omnibus: 5.083 Durbin-Watson: 0.471\n", | |
"Prob(Omnibus): 0.079 Jarque-Bera (JB): 1.915\n", | |
"Skew: 0.372 Prob(JB): 0.384\n", | |
"Kurtosis: 1.679 Cond. No. 3.70e+06\n", | |
"==============================================================================\n", | |
"\n", | |
"Warnings:\n", | |
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", | |
"[2] The smallest eigenvalue is 1.54e-12. This might indicate that there are\n", | |
"strong multicollinearity problems or that the design matrix is singular.\n", | |
"\"\"\"" | |
] | |
}, | |
"execution_count": 50, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"result.summary()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Oh dear. The $\\gamma$s are huge and their standard errors are infinite. We also have a warning about *strong [multicollinearity](https://en.wikipedia.org/wiki/Multicollinearity)*. That is indeed our problem - let's just look at two of the $K_i$ plotted against each other. \n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 51, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c24bdd7b8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"i, j = 4, 5\n", | |
"plt.scatter(Kx[:,i], Kx[:,j])\n", | |
"plt.xlabel(r'$K_{% d}(X)$' % i); _ = plt.ylabel(r'$K_{% d}(X)$' % j)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We can even drop in to see what [condition](https://en.wikipedia.org/wiki/Condition_number) our matrix is in: \n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 52, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"3704592.808511907" | |
] | |
}, | |
"execution_count": 52, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"np.linalg.cond(Kx)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"So clearly we have a problem. Let's try to figure out what the $\\gamma$s *should* be and see if we can fix it. \n", | |
"\n", | |
"We've already said the value of $K_i(X)$ gives the weight of $\\gamma_i$ in the sum predicting $y$:\n", | |
"\n", | |
"$$\n", | |
"\\hat{y}(X) = \\sum \\gamma_i K(X, q_i = X_i)\n", | |
"$$\n", | |
"\n", | |
"If the weights all summed to one at any particular $X$ then it would make sense to have $\\gamma_i = y_i$ because then our prediction would be a weighted average of the nearby values of our response which seems reasonable. Well, we can do this simply dividing each $K_i(X)$ by the sum of all kernels at $X$:\n", | |
"$$\n", | |
"\\hat{y}(X_i) = \\sum_j y_j \\frac{K(X_i, q_j = X_j)}{\\sum_k K(X_i, q_k = X_k)}\n", | |
"$$\n", | |
"\n", | |
"Or in matrix notation: \n", | |
"\n", | |
"$$\n", | |
"\\hat{y}(X) = W\\cdot y\n", | |
"$$\n", | |
"\n", | |
"where\n", | |
"\n", | |
"$$\n", | |
"W_{ij} = \\frac{K(X_i, q_j = X_j)}{\\sum_k K(X_i, q_k = X_l)}\n", | |
"$$\n", | |
"\n", | |
"\n", | |
"Now we can abandon OLS regression all together and just use this analytic expression to make predictions. Let's do this now, using the same bandwidth as before. The knot points are the values of $X_i$ and our coefficients $\\gamma_i$ are the response $y_i$. We'll create a dense grid on $X$ to get a nice smooth prediction as we've done before. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 65, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def kregression(x, y, knots, bw=2):\n", | |
" # Get kernel\n", | |
" Kx = gauss_kernel(x, knots=knots, w=bw)\n", | |
" Kx_norm = Kx/Kx.sum(axis=1)[:, np.newaxis]\n", | |
"\n", | |
" # Prediction\n", | |
" y_predict = np.dot(Kx_norm, y)\n", | |
" return y_predict" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 67, | |
"metadata": { | |
"scrolled": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c24a4c898>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"Xnew = np.linspace(x.min(), x.max(), 100)\n", | |
"y_predict = kregression(x=Xnew, y=y, knots=x, bw=1)\n", | |
"\n", | |
"plt.plot(Xnew, y_predict, label='prediction')\n", | |
"plt.scatter(x, y, label='data')\n", | |
"plt.xlabel(\"$X$\"); plt.ylabel(\"$y$\")\n", | |
"_ = plt.legend(bbox_to_anchor=(1.05, 1))\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Great! Now we're getting somewhere. In fact, we have arrived exactly at [Nadaraya–Watson kernel regression](https://en.wikipedia.org/wiki/Kernel_regression). So we have rid oursevelves of:\n", | |
"* OLS regression and the regression parameters,\n", | |
"* the need to decide how many knots,\n", | |
"* and where to place them. \n", | |
"\n", | |
"All we have to tackle now is the bandwidth parameter. " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## The bandwidth controls the smoothness\n", | |
"Let's see what happens when we change the bandwith by an arbitrary factor of 10 each way. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 68, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c24bee898>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"bandwidths = [0.1, 1, 10]\n", | |
"Xnew = np.linspace(x.min(), x.max(), 100)\n", | |
"\n", | |
"fig, axes = plt.subplots(len(bandwidths), figsize=(5,10), sharex=True)\n", | |
"\n", | |
"for i, bw in enumerate(bandwidths): \n", | |
" ax = axes[i]\n", | |
" \n", | |
"\n", | |
" y_predict = kregression(x=Xnew, y=y, knots=x, bw=bw)\n", | |
"\n", | |
" # plot\n", | |
" ax.scatter(x, y, label='data')\n", | |
" ax.plot(Xnew, y_predict, label='prediction')\n", | |
" ax.set_ylabel(\"$y$\")\n", | |
" ax.set_title('bandwidth = {}'.format(bw))\n", | |
" ax.legend(bbox_to_anchor=(1.05, 1))\n", | |
"\n", | |
"ax.set_xlabel(\"$X$\"); \n", | |
"plt.tight_layout()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"So if the bandwidth is too small then we overfit to our data, if it's too large then we don't reproduce the patter - the [bias-variance tradeoff](https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff).\n", | |
"\n", | |
"Why is this? First, let's remember that the value of the predicted response, $\\hat{y}$ at any arbitrary point $X=x'$ is the weighted average of ALL the $y_i$. The weights (given by the values of the all the kernels at $x'$) measure the similarity of $x_i$ to $x'$. The more similar $x_i$ is to $x'$ the more heavily the value of $y_i$ weighs in the prediction. \n", | |
"\n", | |
"As you can see below, as the bandwidth increases the range of $X$ over which the kernel is non-zero increases. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 70, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c25311470>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"for bw in bandwidths: \n", | |
" plt.plot(Xnew, gauss_kernel(Xnew, knots=x, w=bw).T[10], label='bw {}'.format(bw))\n", | |
"plt.xlabel(\"$X$\"); plt.ylabel(\"$K_{10}(x)$\")\n", | |
"_ = plt.legend()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"So let's plot ALL the kernels and zoom in on the region around $X = \\pi/2$ (the first top of the curve) for the low bandwidth first. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 71, | |
"metadata": { | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c2553a240>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"Xnew = np.linspace(x.min(), x.max(), 100)\n", | |
"\n", | |
"bw = bandwidths[0]\n", | |
"\n", | |
"y_predict = kregression(x=Xnew, y=y, knots=x, bw=bw)\n", | |
"\n", | |
"#plot\n", | |
"plt.plot(Xnew, y_predict, label='prediction')\n", | |
"for i in range(len(x)):\n", | |
" plt.plot(Xnew, gauss_kernel(Xnew, knots=x, w=bw).T[i], alpha=0.5)\n", | |
"plt.scatter(x, y, label='Data')\n", | |
"plt.scatter(Xnew[13], y_predict[13], marker='x', color='k', zorder=2+len(x))\n", | |
"plt.xlim(np.pi/2-1, np.pi/2+1)\n", | |
"plt.title('Bandwidth = {}'.format(bw))\n", | |
"_ = plt.legend()\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Take the point marked with a black 'x'. The kernels significantly greater than zero at that point are from the neighbouring two data points. Essentially the predicted value is an interpolation of just the two neighbouring $y$ values.\n", | |
"\n", | |
"Now let's look at the high bandwidth case. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 72, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1c255eb588>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"Xnew = np.linspace(x.min(), x.max(), 100)\n", | |
"\n", | |
"bw = bandwidths[-1]\n", | |
"y_predict = kregression(x=Xnew, y=y, knots=x, bw=bw)\n", | |
"\n", | |
"plt.scatter(Xnew[13], y_predict[13], marker='x', color='k', zorder=2+len(x))\n", | |
"plt.plot(Xnew, y_predict, label='prediction')\n", | |
"for i in range(len(x)):\n", | |
" plt.plot(Xnew, gauss_kernel(Xnew, knots=x, w=bw).T[i], alpha=0.5)\n", | |
"plt.scatter(x, y, label='Data')\n", | |
"plt.xlim(np.pi/2-1, np.pi/2+1)\n", | |
"plt.title('Bandwidth = {}'.format(bw))\n", | |
"_ = plt.legend()\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Here we can clearly see that many more of the kernel values are non-zero at the point marked 'x'. This means the prediction takes into account many more $\\gamma$'s, albeit those further away from 'x' are weighted less. The change in $\\hat{y}$ as we traverse the $X$ axis will therefor be slower. \n", | |
"\n", | |
"So clearly the bandwidth has an essential role to play in Kernel regression. How should be select it? A single parameter like this is really ammenable to selection through [cross-validation][1], but we won't pursue that here. \n", | |
"[1]:https://en.wikipedia.org/wiki/Cross-validation_(statistics)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Summary\n", | |
"\n", | |
"We've seen that in order to regress non-linear data we can add polynomial terms to simple linear regression. Essentially we are creating new input variables ($X^2$ etc.) to create flexibility in our regressions. We can take this further and replace the polynomial terms with functions of $X$ called *kernels*. These kernels measure the similarity of the input variables to arbitrary points (knots) in the input variable space. This technique works by taking weighted averages of regression coefficients. The closer a data point is to a knot, the more the predicted value resembles the regression coefficient at that knot. With a few knots we get an OK fit to highly non-linear data. \n", | |
"\n", | |
"However if we make the knots equal to the data points themselves, our ordinary least squares regression technique breaks down because of multi-collinearity. Instead we replace the regression coefficients with the values of the observed response variable ($y$). A prediction at $x'$ is now a weighted average of $y_i$'s whose corresponsding $X_i$ values are similar to $x'$. The bias-variance tradeoff is controlled by the bandwidth of the kernel which can be chosen by cross-validation. " | |
] | |
}, | |
{ | |
"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": "3.5.4" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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