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@adamwlev
Last active January 7, 2020 20:37
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Natural Cubic Splines
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from sklearn.linear_model import LinearRegression\n",
"from sklearn.model_selection import KFold\n",
"import matplotlib.pyplot as plt\n",
"\n",
"class BaseSpline():\n",
" def __init__(self,n_folds=6):\n",
" self.n_folds = n_folds\n",
" \n",
" def score(self,x,y,df,n_iterations=100):\n",
" model = LinearRegression(fit_intercept=False)\n",
" scores = []\n",
" for seed in np.random.randint(0,10000,size=n_iterations):\n",
" cv = KFold(n_splits=self.n_folds,shuffle=True,\n",
" random_state=seed)\n",
" for train,test in cv.split(x,y):\n",
" X_train = self.get_mat(x[train],df,fit=True)\n",
" model.fit(X_train,y[train])\n",
" X_test = self.get_mat(x[test],df,fit=False)\n",
" scores.append(model.score(X_test,y[test]))\n",
" return np.mean(scores)\n",
" \n",
" def fit(self,x,y,dfs=range(2,22)):\n",
" num_unique_x = len(np.unique(x))\n",
" if num_unique_x<min(dfs):\n",
" raise ValueError('x needs to have at least %d unique values' % (min(dfs),))\n",
" if len(x)<self.n_folds:\n",
" raise ValueError('x needs to have length of at least %d' % (self.n_folds,))\n",
" scores = {}\n",
" for df in dfs:\n",
" if df<=num_unique_x:\n",
" scores[df] = self.score(x,y,df)\n",
" print(scores)\n",
" self.scores = scores\n",
" df = max(scores,key=scores.get)\n",
" self.df = df\n",
" print(df)\n",
" X = self.get_mat(x,df,fit=True)\n",
" self.model = LinearRegression(fit_intercept=False)\n",
" self.model.fit(X,y)\n",
" \n",
" def predict(self,x):\n",
" return self.model.predict(self.get_mat(x,self.df,fit=False))\n",
"\n",
"class CubicSpline(BaseSpline):\n",
" def get_mat(self,x,df,fit=True):\n",
" K = df - 4\n",
" if fit:\n",
" self.t = np.percentile(x,np.linspace(0,100,K+2)[1:-1]).tolist()\n",
" X = np.column_stack(([1.0]*len(x),x,x**2,x**3))\n",
" for k in range(K):\n",
" h_x = np.copy(x)\n",
" h_x = (h_x-self.t[k])**3\n",
" h_x[x<=self.t[k]] = 0\n",
" X = np.column_stack((X,h_x))\n",
" return X\n",
"\n",
"class NaturalSpline(BaseSpline):\n",
" def get_mat(self,x,df,fit=True):\n",
" K = df\n",
" if fit:\n",
" self.t = np.percentile(x,np.linspace(0,100,K+2)[1:-1]).tolist()\n",
" X = np.column_stack(([1.0]*len(x),x))\n",
" def d(x,e_k,e_K):\n",
" def pos(x,e):\n",
" x_ = (np.copy(x)-e)**3\n",
" x_[x<=e] = 0.0\n",
" return x_\n",
" return (pos(x,e_k) - pos(x,e_K))/(e_K-e_k)\n",
" for k in range(K-2):\n",
" X = np.column_stack((X,d(x,self.t[k],self.t[-1]) - d(x,self.t[K-2],self.t[-1])))\n",
" return X"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(5)\n",
"x = np.random.normal(1,7,size=30)\n",
"y = np.tanh(x)/np.sinh(x) + np.random.normal(0,.1,size=30)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(x,y);"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"cs = CubicSpline()\n",
"ns = NaturalSpline()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"((30, 5), (30, 5))"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"cs.get_mat(x,df=5,fit=True).shape,ns.get_mat(x,df=5,fit=True).shape"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{2: -2.5494661635808122, 3: -5.315858087791022, 4: -2.5332011506372147, 5: -18.838442383423033, 6: -68.42060099843853, 7: -8.308796918930073, 8: -25.35768012626076, 9: -11.54925472441823, 10: -90.8645276941841, 11: -442.25981173670357, 12: -212.68627225705893, 13: -501.8062485970911, 14: -227.57744230576506, 15: -2998.060434156157, 16: -498.6769778173447, 17: -2329.732519902662, 18: -13019.481421985229, 19: -27416.419624964885, 20: -22674.838986898754, 21: -879226.9881956927}\n",
"4\n",
"{2: -2.0338926372117223, 3: -1.5532831354961645, 4: -2.779838009708909, 5: 0.5310598686713996, 6: 0.4782433144968428, 7: 0.5816667583847588, 8: 0.6240702966275542, 9: 0.606179719964663, 10: 0.5323893468781664, 11: 0.4694324877720262, 12: 0.48532303175452757, 13: 0.4188684211623156, 14: 0.46164172182797747, 15: 0.10135864445412826, 16: -1.5260937106621033, 17: -0.604333880684091, 18: -1.8812692428376898, 19: -10.309852776493702, 20: -17.731071502617148, 21: -105.13234387453763}\n",
"8\n"
]
}
],
"source": [
"cs.fit(x,y)\n",
"ns.fit(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1224x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,1,figsize=(17,8))\n",
"plt.scatter(x,y,label='observed values')\n",
"xs = np.linspace(x.min()-1,x.max()+1,7000)\n",
"plt.plot(xs,cs.predict(xs),c='red',label='cubic spline')\n",
"plt.plot(xs,ns.predict(xs),c='orange',label='natural spline')\n",
"plt.plot(xs,np.tanh(xs)/np.sinh(xs),c='green',label='ground truth')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(5)\n",
"x = np.random.normal(1,7,size=50)\n",
"y = np.sin(np.cos(x)) + np.random.normal(0,.1,size=50)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(x,y);"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{2: -0.4944051507505113, 3: -0.4756625333453782, 4: -0.5603567704225803, 5: -0.876763983436781, 6: -3.885388293493577, 7: -3.134576883577292, 8: -20.10089637646953, 9: -39.11213820609111, 10: -37.64106177142625, 11: -52.15313678827539, 12: -46.20332217705293, 13: -62.89125823926214, 14: -61.79982413100071, 15: -88.50648426650491, 16: -165.63933385933368, 17: -86.9631608346647, 18: -120.25007845406229, 19: -145.58061859013364, 20: -266.08409804250607, 21: -176.86173516135355}\n",
"3\n",
"{2: -0.30549974669541363, 3: -0.4926319283499621, 4: -0.23214613867052405, 5: -0.31362341725459475, 6: 0.020474660707806104, 7: -0.09942662225583808, 8: -0.13459425773095898, 9: -0.15737394888269865, 10: 0.12530616075757356, 11: 0.1463342434000706, 12: 0.261433668183509, 13: 0.26349768037973037, 14: 0.22488329044372135, 15: 0.12696441941215372, 16: 0.061757432455086775, 17: 0.295469579240914, 18: 0.13904987936904664, 19: 0.18210086120676242, 20: 0.31146100508088453, 21: 0.2619276599466959}\n",
"20\n"
]
}
],
"source": [
"cs.fit(x,y)\n",
"ns.fit(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1224x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,1,figsize=(17,8))\n",
"plt.scatter(x,y,label='observed values')\n",
"xs = np.linspace(x.min()-1,x.max()+1,7000)\n",
"plt.plot(xs,cs.predict(xs),c='red',label='cubic spline')\n",
"plt.plot(xs,ns.predict(xs),c='orange',label='natural spline')\n",
"plt.plot(xs,np.sin(np.cos(xs)),c='green',label='ground truth')\n",
"plt.legend();"
]
},
{
"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": "3.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@adamwlev
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adamwlev commented Jan 7, 2020

Python implementation of Natural Cubic Splines from Elements of Statistical Learning (HTF).

Natural Cubic Splines have the restriction of being linear at the edges and therefore are better at extrapolation. This implementation uses internal Cross Validation during a fit to find the best number of degrees of freedom. Natural Cubic Splines do better than Cubic Splines especially when the number of observations is small and/or there is a significant amount of noise in the observed data.

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