{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Using TensorFlow backend.\n" ] }, { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import os\n", "import warnings\n", "import time\n", "import copy\n", "\n", "import numpy as np\n", "import pandas as pd\n", "\n", "from sklearn.metrics import mean_squared_error, explained_variance_score, r2_score\n", "from sklearn.model_selection import train_test_split, KFold\n", "from sklearn.linear_model import LinearRegression, Lasso, lasso_path, lars_path, LassoLarsIC\n", "from sklearn.neural_network import MLPRegressor\n", "\n", "os.environ['TF_CPP_MIN_LOG_LEVEL'] = '3' #Hide messy TensorFlow warnings\n", "warnings.filterwarnings(\"ignore\") #Hide messy Numpy warnings\n", "\n", "import keras\n", "from keras.layers.core import Dense, Activation, Dropout\n", "from keras.layers import Input\n", "from keras.models import Model\n", "\n", "from keras.layers.recurrent import LSTM, GRU\n", "from keras.regularizers import l1\n", "from keras.models import Sequential\n", "from keras.models import load_model\n", "\n", "#plotly charts\n", "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n", "from plotly.graph_objs import *\n", "import plotly.figure_factory as ff\n", "init_notebook_mode(connected=True)\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# splines chart\n", "# R code\n", "\"\"\"\n", "testdata <- data.frame(seq(from=1, to = 1000))\n", "testdata['x'] <- seq(from=0, to = 3*pi, length.out=1000)\n", "testdata['y'] <- -cos(testdata$x) + testdata$x/(3*pi) + rnorm(1000)*0.25\n", "nrows <- 300\n", "indexes <- sample(nrow(testdata), nrows)\n", "indexes <- indexes[order(indexes)]\n", "testdata <- testdata[indexes, ]\n", "plot(testdata$x, testdata$y, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=2)\n", "testdata$fit2 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit2, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=3)\n", "testdata$fit3 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit3, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=4)\n", "testdata$fit4 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit4, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=5)\n", "testdata$fit5 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit5, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=6)\n", "testdata$fit6 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit6, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=20)\n", "testdata$fit20 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit20, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=40)\n", "testdata$fit40 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit40, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=80)\n", "testdata$fit80 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit80, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=160)\n", "testdata$fit160 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit160, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,df=240)\n", "testdata$fit240 <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fit240, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "fit <- smooth.spline(testdata$x,testdata$y,cv=TRUE)\n", "testdata$fitcv <- predict(fit, newdata=testdata$x)[2]$y\n", "plot(testdata$x, testdata$fitcv, main=\"Scatterplot\", xlab=\"x\", ylab=\"y\", pch=1)\n", "\n", "write.csv(testdata, \"splines.csv\")\n", "print(fit)\n", "\"\"\"\n", "splines = pd.read_csv('splines.csv')\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "data": [ { "marker": { "line": { "color": "rgba(128, 128, 192, .75)", "width": 2 }, "size": 3 }, "mode": "markers", "name": "Raw data", "type": "scatter", "x": [ 0.0566052730376539, 0.12264475824825, 0.264157940842385, 0.29246057736121195, 0.311329001707097, 0.32076321388003903, 0.339631638225924, 0.386802699090635, 0.41510533560946206, 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" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "data = splines.values\n", "\n", "x = data[:,2]\n", "y = data[:,3] \n", "fit2 = data[:,4]\n", "fit3 = data[:,5]\n", "fit4 = data[:,6]\n", "fit5 = data[:,7]\n", "fit6 = data[:,8]\n", "fit20 = data[:,9]\n", "fit40 = data[:,10]\n", "fit80 = data[:,11]\n", "fit160 = data[:,12]\n", "fit240 = data[:,13]\n", "fitcv = data[:,14]\n", "\n", "plotdata = []\n", "plotdata.append(Scatter(x=x,\n", " y=y,\n", " name='Raw data',\n", " mode = 'markers',\n", " marker = dict(\n", " size = 3,\n", " line = dict(\n", " width = 2,\n", " color = 'rgba(128, 128, 192, .75)',\n", " )\n", " )\n", " )\n", " )\n", "plotdata.append(Scatter(x=x,\n", " y=fit2,\n", " name='Linear (high bias / low variance)',\n", " mode = 'line',\n", " line = dict(\n", " color = ('orange'),\n", " width = 2) \n", " ))\n", "plotdata.append(Scatter(x=x,\n", " y=fit4,\n", " name='Underfit (high bias / low variance)',\n", " mode = 'line',\n", " line = dict(\n", " width = 2,\n", " color= ('blue'), \n", " ) \n", " ))\n", "plotdata.append(Scatter(x=x,\n", " y=fitcv,\n", " name='Lowest CV error',\n", " mode = 'line',\n", " line = dict(\n", " color = ('green'),\n", " width = 5)\n", ") )\n", "plotdata.append(Scatter(x=x,\n", " y=fit240,\n", " name='Overfit (high variance / low bias)',\n", " mode = 'line',\n", " line = dict(\n", " width = 2,\n", " color= ('rgb(192,0,0)')) \n", " \n", " ))\n", "\n", "layout = Layout(\n", " yaxis=dict(\n", " autorange=True))\n", "\n", "\n", "fig = Figure(data=plotdata, layout=layout)\n", "\n", "iplot(fig) # png to save notebook w/static image " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# create a data set, sin wave plus trend plus random noise\n", "nobs = 2000\n", "x = np.linspace(0, 3*np.pi, num=nobs)\n", "y = -np.cos(x) + x/(3*np.pi) + np.random.normal(0, 0.25, nobs)\n", "\n", "x2 = np.linspace(0, 15*np.pi, num=nobs)\n", "y1 = -np.sin(x2) + x2/(3*np.pi) + np.random.normal(0, 0.25, nobs)\n", "y2 = -np.cos(x2) + x2/(3*np.pi) + np.random.normal(0, 0.25, nobs)\n", "\n", "# sample 20% to make it more sparse\n", "#arr = np.arange(nobs)\n", "#np.random.shuffle(arr)\n", "#x = arr[:200]\n", "#y = y[x]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "data": [ { "mode": "markers", "type": "scatter", "x": [ 0, 0.004714746353561471, 0.009429492707122941, 0.014144239060684412, 0.018858985414245882, 0.023573731767807353, 0.028288478121368824, 0.033003224474930294, 0.037717970828491765, 0.042432717182053235, 0.047147463535614706, 0.051862209889176177, 0.05657695624273765, 0.06129170259629912, 0.06600644894986059, 0.07072119530342205, 0.07543594165698353, 0.08015068801054501, 0.08486543436410647, 0.08958018071766793, 0.09429492707122941, 0.09900967342479089, 0.10372441977835235, 0.10843916613191382, 0.1131539124854753, 0.11786865883903677, 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pass some 2d n x 1 arrays, x, y, z\n", " \n", " # 1st array is independent vars\n", " # reshape to 1 dimensional array\n", " x = args[0].reshape(-1)\n", " \n", " # following are dependent vars plotted on y axis\n", " data = []\n", " for i in range(1, len(args)):\n", " data.append(Scatter(x=x,\n", " y=args[i].reshape(-1),\n", " mode = 'markers'))\n", "\n", " layout = Layout(\n", " yaxis=dict(\n", " autorange=True))\n", " \n", " fig = Figure(data=data, layout=layout)\n", " \n", " return iplot(fig) # png to save notebook w/static image \n", " \n", "mychart(x,y)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "data": [ { "mode": "markers", "type": "scatter", "x": [ 0, 0.02357373176780735, 0.0471474635356147, 0.07072119530342205, 0.0942949270712294, 0.11786865883903674, 0.1414423906068441, 0.16501612237465144, 0.1885898541424588, 0.21216358591026616, 0.2357373176780735, 0.25931104944588085, 0.2828847812136882, 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272 | \n", "889 | \n", "889 | \n", "8.377580 | \n", "1.070650 | \n", "0.899835 | \n", "0.997383 | \n", "1.102828 | \n", "1.182170 | \n", "1.236144 | \n", "1.339964 | \n", "1.329076 | \n", "1.247071 | \n", "1.206912 | \n", "1.206912 | \n", "1.320577 | \n", "
273 | \n", "897 | \n", "897 | \n", "8.453054 | \n", "1.666208 | \n", "0.908379 | \n", "1.024105 | \n", "1.153949 | \n", "1.245697 | \n", "1.302093 | \n", "1.423501 | \n", "1.510355 | \n", "1.728304 | \n", "1.809082 | \n", "1.809082 | \n", "1.385514 | \n", "
274 | \n", "902 | \n", "902 | \n", "8.500225 | \n", "2.164331 | \n", "0.913720 | \n", "1.040920 | \n", "1.186119 | \n", "1.285510 | \n", "1.343161 | \n", "1.471858 | \n", "1.587764 | \n", "1.832285 | \n", "1.896199 | \n", "1.896199 | \n", "1.425103 | \n", "
275 | \n", "910 | \n", "910 | \n", "8.575699 | \n", "1.598121 | \n", "0.922266 | \n", "1.067986 | \n", "1.237899 | \n", "1.349337 | \n", "1.408590 | \n", "1.540403 | \n", "1.640360 | \n", "1.720218 | \n", "1.699297 | \n", "1.699297 | \n", "1.486653 | \n", "
276 | \n", "912 | \n", "912 | \n", "8.594567 | \n", "1.674038 | \n", "0.924403 | \n", "1.074781 | \n", "1.250897 | \n", "1.365312 | \n", "1.424890 | \n", "1.555704 | \n", "1.641260 | \n", "1.671724 | \n", "1.646877 | \n", "1.646877 | \n", "1.501679 | \n", "
277 | \n", "914 | \n", "914 | \n", "8.613436 | \n", "1.414879 | \n", "0.926539 | \n", "1.081586 | \n", "1.263914 | \n", "1.381293 | \n", "1.441165 | \n", "1.570257 | \n", "1.638037 | \n", "1.625459 | \n", "1.610072 | \n", "1.610072 | \n", "1.516558 | \n", "
278 | \n", "916 | \n", "916 | \n", "8.632304 | \n", "1.742757 | \n", "0.928676 | \n", "1.088402 | \n", "1.276950 | \n", "1.397280 | \n", "1.457418 | \n", "1.584188 | \n", "1.632486 | \n", "1.585905 | \n", "1.584810 | \n", "1.584810 | \n", "1.531294 | \n", "
279 | \n", "926 | \n", "926 | \n", "8.726646 | \n", "1.570245 | \n", "0.939362 | \n", "1.122621 | \n", "1.342384 | \n", "1.477277 | \n", "1.538342 | \n", "1.648121 | \n", "1.609439 | \n", "1.527509 | \n", "1.535119 | \n", "1.535119 | \n", "1.603040 | \n", "
280 | \n", "928 | \n", "928 | \n", "8.745515 | \n", "1.643629 | \n", "0.941499 | \n", "1.129490 | \n", "1.355517 | \n", "1.493288 | \n", "1.554462 | \n", "1.660238 | \n", "1.609349 | \n", "1.537043 | \n", "1.539531 | \n", "1.539531 | \n", "1.617032 | \n", "
281 | \n", "932 | \n", "932 | \n", "8.783252 | \n", "1.318655 | \n", "0.945774 | \n", "1.143251 | \n", "1.381823 | \n", "1.525316 | \n", "1.586643 | \n", "1.684328 | \n", "1.617467 | \n", "1.568683 | \n", "1.562898 | \n", "1.562898 | \n", "1.644693 | \n", "
282 | \n", "933 | \n", "933 | \n", "8.792686 | \n", "1.618969 | \n", "0.946843 | \n", "1.146695 | \n", "1.388408 | \n", "1.533324 | \n", "1.594676 | \n", "1.690366 | \n", "1.621550 | \n", "1.578440 | \n", "1.571771 | \n", "1.571771 | \n", "1.651545 | \n", "
283 | \n", "950 | \n", "950 | \n", "8.953067 | \n", "2.012024 | \n", "0.965012 | \n", "1.205484 | \n", "1.500747 | \n", "1.669515 | \n", "1.730547 | \n", "1.791749 | \n", "1.773085 | \n", "1.792390 | \n", "1.810661 | \n", "1.810661 | \n", "1.764372 | \n", "
284 | \n", "960 | \n", "960 | \n", "9.047409 | \n", "1.624429 | \n", "0.975702 | \n", "1.240220 | \n", "1.567092 | \n", "1.749627 | \n", "1.809931 | \n", "1.845555 | \n", "1.864767 | \n", "1.904327 | \n", "1.900205 | \n", "1.900205 | \n", "1.827779 | \n", "
285 | \n", "961 | \n", "961 | \n", "9.056844 | \n", "1.996643 | \n", "0.976771 | \n", "1.243698 | \n", "1.573734 | \n", "1.757636 | \n", "1.817850 | \n", "1.850507 | \n", "1.871202 | \n", "1.912575 | \n", "1.902017 | \n", "1.902017 | \n", "1.834010 | \n", "
286 | \n", "962 | \n", "962 | \n", "9.066278 | \n", "1.777070 | \n", "0.977840 | \n", "1.247176 | \n", "1.580376 | \n", "1.765645 | \n", "1.825766 | \n", "1.855370 | \n", "1.876986 | \n", "1.919627 | \n", "1.903155 | \n", "1.903155 | \n", "1.840221 | \n", "
287 | \n", "965 | \n", "965 | \n", "9.094581 | \n", "1.932855 | \n", "0.981047 | \n", "1.257615 | \n", "1.600309 | \n", "1.789670 | \n", "1.849495 | \n", "1.869428 | \n", "1.890573 | \n", "1.928173 | \n", "1.912138 | \n", "1.912138 | \n", "1.858747 | \n", "
288 | \n", "967 | \n", "967 | \n", "9.113449 | \n", "2.122920 | \n", "0.983185 | \n", "1.264578 | \n", "1.613602 | \n", "1.805684 | \n", "1.865300 | \n", "1.878369 | \n", "1.896750 | \n", "1.919566 | \n", "1.929082 | \n", "1.929082 | \n", "1.871011 | \n", "
289 | \n", "971 | \n", "971 | \n", "9.151186 | \n", "1.849789 | \n", "0.987461 | \n", "1.278507 | \n", "1.640196 | \n", "1.837708 | \n", "1.896880 | \n", "1.895414 | \n", "1.905165 | \n", "1.883622 | \n", "1.952431 | \n", "1.952431 | \n", "1.895362 | \n", "
290 | \n", "973 | \n", "973 | \n", "9.170054 | \n", "2.085739 | \n", "0.989599 | \n", "1.285474 | \n", "1.653497 | \n", "1.853718 | \n", "1.912656 | \n", "1.903625 | \n", "1.908997 | \n", "1.867122 | \n", "1.934527 | \n", "1.934527 | \n", "1.907461 | \n", "
291 | \n", "978 | \n", "978 | \n", "9.217225 | \n", "1.845186 | \n", "0.994944 | \n", "1.302898 | \n", "1.686757 | \n", "1.893738 | \n", "1.952067 | \n", "1.923569 | \n", "1.921577 | \n", "1.858799 | \n", "1.789746 | \n", "1.789746 | \n", "1.937531 | \n", "
292 | \n", "980 | \n", "980 | \n", "9.236094 | \n", "1.432716 | \n", "0.997082 | \n", "1.309869 | \n", "1.700063 | \n", "1.909744 | \n", "1.967820 | \n", "1.931353 | \n", "1.927733 | \n", "1.868867 | \n", "1.738972 | \n", "1.738972 | \n", "1.949500 | \n", "
293 | \n", "986 | \n", "986 | \n", "9.292699 | \n", "2.110915 | \n", "1.003496 | \n", "1.330786 | \n", "1.739989 | \n", "1.957758 | \n", "2.015055 | \n", "1.954210 | \n", "1.948939 | \n", "1.941426 | \n", "1.871168 | \n", "1.871168 | \n", "1.985259 | \n", "
294 | \n", "988 | \n", "988 | \n", "9.311567 | \n", "2.150585 | \n", "1.005634 | \n", "1.337760 | \n", "1.753298 | \n", "1.973761 | \n", "2.030794 | \n", "1.961701 | \n", "1.956536 | \n", "1.976895 | \n", "2.053107 | \n", "2.053107 | \n", "1.997144 | \n", "
295 | \n", "990 | \n", "990 | \n", "9.330436 | \n", "1.970253 | \n", "1.007772 | \n", "1.344733 | \n", "1.766609 | \n", "1.989764 | \n", "2.046531 | \n", "1.969119 | \n", "1.963709 | \n", "2.006993 | \n", "2.207295 | \n", "2.207295 | \n", "2.009016 | \n", "
296 | \n", "993 | \n", "993 | \n", "9.358738 | \n", "2.289554 | \n", "1.010979 | \n", "1.355194 | \n", "1.786574 | \n", "2.013768 | \n", "2.070134 | \n", "1.980067 | \n", "1.972180 | \n", "2.016287 | \n", "2.120013 | \n", "2.120013 | \n", "2.026805 | \n", "
297 | \n", "994 | \n", "994 | \n", "9.368173 | \n", "1.766312 | \n", "1.012048 | \n", "1.358681 | \n", "1.793230 | \n", "2.021769 | \n", "2.078001 | \n", "1.983659 | \n", "1.974087 | \n", "2.004609 | \n", "1.957363 | \n", "1.957363 | \n", "2.032730 | \n", "
298 | \n", "995 | \n", "995 | \n", "9.377607 | \n", "1.850753 | \n", "1.013117 | \n", "1.362168 | \n", "1.799885 | \n", "2.029770 | \n", "2.085867 | \n", "1.987228 | \n", "1.975583 | \n", "1.986822 | \n", "1.770286 | \n", "1.770286 | \n", "2.038654 | \n", "
299 | \n", "999 | \n", "999 | \n", "9.415344 | \n", "1.948860 | \n", "1.017394 | \n", "1.376116 | \n", "1.826506 | \n", "2.061773 | \n", "2.117333 | \n", "2.001399 | \n", "1.979900 | \n", "1.906551 | \n", "1.950956 | \n", "1.950956 | \n", "2.062340 | \n", "
300 rows × 15 columns
\n", "