diff --git a/is/ubA/ExerciseSheet10.ipynb b/is/ubA/ExerciseSheet10.ipynb index 1e8c218..8c1f9d0 100644 --- a/is/ubA/ExerciseSheet10.ipynb +++ b/is/ubA/ExerciseSheet10.ipynb @@ -102,7 +102,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -124,7 +124,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -158,7 +158,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -167,147 +167,146 @@ "name": "stdout", "output_type": "stream", "text": [ - "Number of components covering 0.95 of variance: 138\n" + "Number of components covering 0.95 of variance: 139\n" ] }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEACAYAAABcXmojAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", - "AAALEgAACxIB0t1+/AAAHNBJREFUeJzt3X2UXXV97/H3JyEJgQRjQBPyAIkSbkmiVrFEb6tEqxBy\n", - 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@@ -371,7 +370,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "{'kernel': 'linear', 'C': 0.9}\n", + "{'kernel': 'linear', 'C': 0.1}\n", "Fitting the classifier to the training set\n" ] } @@ -387,7 +386,7 @@ "Yld= y_train\n", "#print(np.shape(y_train))\n", "\n", - "parameters ={'kernel':('linear', 'rbf'), 'C':[0.9,1,1.1]}\n", + "parameters ={'kernel':('linear', 'rbf'), 'C':[0.1,1,10]}\n", "clf = GridSearchCV(SVC(), parameters,refit=True,n_jobs=4)\n", "clf.fit(Xld,Yld)\n", "print(clf.best_params_)\n", @@ -410,7 +409,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -420,26 +419,26 @@ "output_type": "stream", "text": [ "Predicting people's names on the test set\n", - "done in 0.124s\n", + "done in 0.106s\n", " precision recall f1-score support\n", "\n", - " Ariel Sharon 0.26 0.90 0.40 20\n", - " Colin Powell 1.00 0.20 0.33 56\n", - " Donald Rumsfeld 0.36 0.55 0.44 22\n", - " George W Bush 0.98 0.34 0.51 137\n", - "Gerhard Schroeder 0.59 0.42 0.49 24\n", - " Hugo Chavez 1.00 0.14 0.24 22\n", - " Tony Blair 0.28 0.95 0.43 41\n", + " Ariel Sharon 0.44 0.50 0.47 16\n", + " Colin Powell 0.85 0.55 0.67 60\n", + " Donald Rumsfeld 0.40 0.70 0.51 27\n", + " George W Bush 1.00 0.04 0.07 139\n", + "Gerhard Schroeder 0.62 0.33 0.43 30\n", + " Hugo Chavez 0.00 0.00 0.00 18\n", + " Tony Blair 0.16 0.97 0.27 32\n", "\n", - " avg / total 0.78 0.43 0.44 322\n", + " avg / total 0.72 0.33 0.29 322\n", "\n", - "[[18 0 1 0 0 0 1]\n", - " [23 11 2 0 0 0 20]\n", - " [10 0 12 0 0 0 0]\n", - " [13 0 16 47 2 0 59]\n", - " [ 4 0 1 0 10 0 9]\n", - " [ 1 0 0 1 5 3 12]\n", - " [ 1 0 1 0 0 0 39]]\n" + "[[ 8 0 3 0 0 0 5]\n", + " [ 4 33 4 0 0 0 19]\n", + " [ 1 2 19 0 0 0 5]\n", + " [ 4 3 20 5 2 1 104]\n", + " [ 1 0 1 0 10 0 18]\n", + " [ 0 1 0 0 3 0 14]\n", + " [ 0 0 0 0 1 0 31]]\n" ] } ], @@ -458,7 +457,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": { "collapsed": false }, 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diff --git a/mr/ub7/mr7.pdf b/mr/ub7/mr7.pdf index 8ee3d23..cc00e4f 100644 --- a/mr/ub7/mr7.pdf +++ b/mr/ub7/mr7.pdf Binary files differ diff --git a/mr/ub7/mr7.tex b/mr/ub7/mr7.tex index 2aea176..ccdba3c 100644 --- a/mr/ub7/mr7.tex +++ b/mr/ub7/mr7.tex @@ -87,32 +87,35 @@ \item $\frac{p(m_i|z_{1,\dots,t})}{1-p(m_i|z_{1,\dots,t})}=\frac{p(m_i|z_t)}{1-p(m_i|z_t)}\frac{p(m_i|z_{1,\dots,t-1})}{1-p(m_i|z_{1,\dots,t-1})}\frac{1-p(m_i)}{p(m_i)}$\\ $\Leftrightarrow\frac{A}{1-A}=\underbrace{\frac{B}{1-B}\frac{C}{1-C}\frac{1-D}{D}}_F$\\ $\Leftrightarrow A=(1-A)F$\\ - $\Leftrightarrow A=\left(1+\frac{1}{F}\right)^{-1}=\left(1+\frac{1-B}{B}\frac{1-C}{C}\frac{D}{1-D}\right)^{-1}=\left(1+\frac{1-p(m_i|z_t)}{p(m_i|z_t)}\frac{1-p(m_i|z_{1,\dots,t-1})}{p(m_i|z_{1,\dots,t-1})}\frac{p(m_i)}{1-p(m_i)}\right)^{-1}\\ + $\Leftrightarrow A=\left(1+\frac{1}{F}\right)^{-1}=\left(1+\frac{1-B}{B}\frac{1-C}{C}\frac{D}{1-D}\right)^{-1}=\left(1+\frac{1-p(m_i|z_t)}{p(m_i|z_t)}\frac{1-p(m_i|z_{1,\dots,t-1})}{p(m_i|z_{1,\dots,t-1})}\frac{p(m_i)}{1-p(m_i)}\right)^{-1}\\ $ - \item $\left(1+\frac{1-p(m_i|z_t)}{p(m_i|z_t)}\frac{1-a}{a}\cdot b \right)^{-1}$\\ 3 Add/Sub, 5 Div/Mult - \item $o(m_i|z_{t,\dots,1})=\frac{p(m_i|z_t)}{1-p(m_i|z_t)}\frac{p(m_i|z_{1,\dots,t-1})}{1-p(m_i|z_{1,\dots,t-1})}\frac{1-p(m_i)}{p(m_i)}=\frac{p(m_i|z_t)}{1-p(m_i|z_t)}\frac{a}{1-a}b$\\ - 2 Add/Sub, 4 Div/Mult\\ + \item $\left(1+\frac{1-p(m_i|z_t)}{p(m_i|z_t)}\frac{1-a}{a}\cdot b \right)^{-1}$\textcolor{red}{$=\left(1+\frac{1-a}{a}\cdot \begin{cases} + b\frac{1-p(m_i|z_t=1)}{p(m_i|z_t=1)} & z_t=1\\ + b\frac{1-p(m_i|z_t=0)}{p(m_i|z_t=0)} & z_t=0\\ + \end{cases}\right)^{-1}$\\ 2 Add/Sub, 3 Div/Mult} + \item \textcolor{red}{(see above)} $o(m_i|z_{t,\dots,1})=\frac{p(m_i|z_t)}{1-p(m_i|z_t)}\frac{p(m_i|z_{1,\dots,t-1})}{1-p(m_i|z_{1,\dots,t-1})}\frac{1-p(m_i)}{p(m_i)}=\frac{p(m_i|z_t)}{1-p(m_i|z_t)}\frac{a}{1-a}b$\\ + \textcolor{red}{0 Add/Sub, 1 Div/Mult}\\ $ log(o(m_i|z_{t,\dots,1}))= log(p(m_i|z_t))-log(1-p(m_i|z_t))+log(a)-log(1-a)+c $\\ - 6 Add/Sub, 4 logs \\ - + \textcolor{red}{1 Add/Sub}\\ + \item grids are evaluated clockwise \\ $ p(m_1|z_{1,\dots,5})=0.9942$\\ $ p(m_2|z_{1,\dots,5})=0.9660$\\ $ p(m_3|z_{1,\dots,5})=0.1164$\\ $ p(m_4|z_{1,\dots,5})=0.8258$\\ - + $ o(m_1|z_{1,\dots,5})=170.6667$\\ $ o(m_2|z_{1,\dots,5})=28.4444 $\\ $ o(m_3|z_{1,\dots,5})=0.1317$\\ $ o(m_4|z_{1,\dots,5})=4.7407$\\ - + $ lo(m_1|z_{1,\dots,5})=5.1397$\\ $ lo(m_2|z_{1,\dots,5})=3.3480 $\\ $ lo(m_3|z_{1,\dots,5})=-2.0273 $\\ $ lo(m_4|z_{1,\dots,5})=1.5562$\\ - - + + Rechenweg Matlab siehe Abbildung \ref{fig:1dMatlab}: \begin{figure} \centering @@ -154,19 +157,19 @@ [.g b b b w ] w [.g b w b b ] - b - ] + b + ] [.g w w w b ] ] - } - \item + } + \item %Die meisten nötigen Änderungen am Baum verursacht eine Änderung in einem zusammenhängenden Quadrat, also beispielsweise links oben in der Ecke. Eine Änderung dort bewirkt vier neue Knoten und einen geänderten.\\ % Die wenigsten nötigen ergeben sich, wenn ein ohnehin einzelnes Gridfeld geändert wird. Dabei darf jedoch der Baum nicht kleiner werden. Dies ist beispielsweise der Fall bei dem Feld links unten.\\ - Grid cells with as many operations as possible to have their values changed are those belonging to a leaf node with the lowest depth and holding the value occupied or free. One example in this qtree is the quadrad in the upper left corner. Changing the value of one grid cell of this quadrad results in 4 new nodes and the change of the value of their parent node to grey. + Grid cells with as many operations as possible to have their values changed are those belonging to a leaf node with the lowest depth and holding the value occupied or free. One example in this qtree is the quadrad in the upper left corner. Changing the value of one grid cell of this quadrad results in 4 new nodes and the change of the value of their parent node to grey. \\Grid cells with as few operations as possible to have their value changed are all leaf nodes with the highest depth. Here only the color value of the nodes has to be changed. E.g the black cell in the lower left corner. \item $256^2=\left(2^8\right)^2=4^8$\\ $\Rightarrow$ maxdepth: 8 \\ According to the definition of the depths of a general tree it has to be 9 - + % $\Rightarrow$ maxnodes: $\sum\limits_{i=0}^9\frac{4^9-1}{4-1}=87381$ $\Rightarrow$ maxnodes: $\sum\limits_{i=0}^8 4^{i}=\frac{4^9-1}{4-1}=87381$ \end{enumerate}