diff --git a/is/UB3/ExerciseSheet3final.ipynb b/is/UB3/ExerciseSheet3final.ipynb index 4480cec..eb11ca5 100644 --- a/is/UB3/ExerciseSheet3final.ipynb +++ b/is/UB3/ExerciseSheet3final.ipynb @@ -87,7 +87,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 13, "metadata": { "collapsed": false }, @@ -103,7 +103,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 14, "metadata": { "collapsed": false, "scrolled": false @@ -124,7 +124,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 15, "metadata": { "collapsed": false }, @@ -147,7 +147,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 16, "metadata": { "collapsed": false, "scrolled": false @@ -156,144 +156,122 @@ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 7, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ - 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"A = a.T.dot(a)\n", - "\n", - "B,rank = linalg.pinv(A,return_rank=True)\n", - "#print rank\n", - "#print B\n", - "#print np.allclose(A,A.dot(B.dot(A)))" - ] - }, - { - "cell_type": "code", - "execution_count": 14, + "execution_count": 21, "metadata": { "collapsed": false }, @@ -630,264 +549,323 @@ { "data": { "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEKCAYAAAAGvn7fAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XecFPX9x/HXmyYI2I2goKCCxgoGwYBlwN5jjF2KvYu9\n", - "/wRiL7EmauydxITYEhtGxt5Qwd5QoiIiNkREpXx+f3znYO9u727vdvdmd+/zfDz2cbc7OzOf3b37\n", - "7Hc+853vV2aGc865ytEq7QCcc84Vlid255yrMJ7YnXOuwnhid865CuOJ3TnnKownduecqzCe2N0i\n", - "kk6XdEPacTjn8uOJvQgkTZX0s6Tlazz+mqSFklZN7neTNE7STEnfSXpD0vBkWY/kubNr3PaoY5+x\n", - "pIPyidvMLjCzQ/LZRkY8Jyev53tJH0k6KWPZipLGSpqWvO5nJPWvZ1vHS5qSbGuGpFskdc5YPlDS\n", - "S8nyyZIGZSyLsryPQzOW35p8VlXLvpekZNlmWd7/hZJ2S5YvIeny5HV8I+kvktrk+P5Ufb55/w8m\n", - "r+GcBp4zVdKPGa/jkYxlZ9R4jT9KWiBpuSzbyfmzk3Rz8hpXz3hsKUl3Jn/zM5PfMz/LhZJ+yIjl\n", - 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plt.title(\"MSE train: %f test %f\" % (MSE(X.dot(w),y),MSE(Xt.dot(w),yt)))\n", - " plt.plot(xt,yt)\n", - " plt.plot(x,y)\n", - "# was ist mit fehler kurven gemeint?" + " plt.plot(x,X.dot(w),'g',label='regression training')\n", + " plt.plot(xt,Xt.dot(w),'b',label='regression test')\n", + " plt.title(\"MSE train: %f MSE test: %f\" % (MSE(X.dot(w),y),MSE(Xt.dot(w),yt)))\n", + " plt.plot(xt,yt,'b*',label='data test')\n", + " plt.plot(x,y,'go',label='data trainig')\n", + " plt.ylabel('Output y') \n", + " plt.xlabel('Input x') \n", + " plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#####Conclusion:\n", + "We get suitable solutions for n from 5 to 7 for the test regression. For higher values we get overfitting. For lower ones underfitting. The MSE of the test regression is always higher than the one of the training regression. That's evident because the regression function is fitted to the values of the training data and so doesn't provide an optimal fitting for the test data.\n" ] }, { @@ -923,7 +911,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 22, "metadata": { "collapsed": false }, @@ -932,255 +920,327 @@ "name": "stdout", "output_type": "stream", "text": [ - "1.75123654094\n", - "0.781528050024\n", - "11.0428184273\n" + "Minimum MSE: 0.6275\n" ] }, { "data": { "image/png": [ - "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEKCAYAAAAGvn7fAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xd4VNXWx/HvCoSODWmiAtarSBPFipwICNgQFUVF7AXx\n", - "qtjbfYe5VsDeexfLtV0pClzlIDYQBUERxQKCIkhTiggk6/1jnySTMEkmmZrJ+jxPniQzZ87Zw6O/\n", - "7Nln77VFVTHGGJM9ctLdAGOMMYllwW6MMVnGgt0YY7KMBbsxxmQZC3ZjjMkyFuzGGJNlLNiNMSbL\n", - "WLCbpBKRBSLyt4g0KfX4TBEpEJGdg993FJHXReR3EVktInNE5IzguTbBsWtKfQ0o45onicjHIrJO\n", - "RCZHef4xEZknIvmF1yin/XVF5CkR+UNElojIsDKOGxy08ZyIx84QkRnBaxeJyAgRqRXx/I4iMkZE\n", - 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% MSE(X.dot(w),y))\n", + " \n", " \n", " w = wRidge(X,y,10.0)\n", - " plt.plot(xt,Xt.dot(w))\n", - " plt.title(\"MSE %f\" % MSE(X.dot(w),y))\n", - " print(MSE(X.dot(w),y))\n", + " plt.plot(xt,Xt.dot(w),label='$\\lambda$ = 10.0'+\" MSE: %f\" % MSE(X.dot(w),y))\n", + " \n", + " \n", " \n", - " plt.plot(xt,yt)\n", - " #plt.plot(x,y)\n", - "plot(1)" + " plt.plot(xt,yt,'b*',label='data test')\n", + " plt.plot(x,y,'go',label='data trainig')\n", + " plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n", + "plot()\n", + "print(\"Minimum MSE: 0.6275\")" ] }, {