00 - Tutorial 4 - Machine learning pipelines and systems.ipynb

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   "source": [
    "# Global imports and settings\n",
    "from preamble import *\n",
    "%matplotlib inline\n",
    "plt.rcParams['savefig.dpi'] = 120 # Use 300 for PDF, 100 for slides\n",
    "#InteractiveShell.ast_node_interactivity = \"all\"\n",
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   "source": [
    "# Machine learning pipelines"
   ]
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    "## Preprocessing\n",
    "\n",
    "* Many of the algorithms that we've seen are greatly affected by _how_ you represent the training data\n",
    "* Scaling, numeric/categorical values, missing values, feature selection/construction\n",
    "* We typically need chain together different algorithms\n",
    "    - Many preprocessing steps\n",
    "    - Possibly many models\n",
    "* This is called a _pipeline_ (or _workflow_)"
   ]
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   "source": [
    "Outline:\n",
    "* Examples of which preprocessing steps are best combined with learning algorithm\n",
    "* How to apply preprocessing techniques\n",
    "* How to design and optimize pipelines\n",
    "* Some practical advice"
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    "### Applying data transformations (recap) \n",
    "\n",
    "- First, we `fit` the preprocessor on the __training data__\n",
    "    - This computes the necessary transformation parameters\n",
    "    - For `MinMaxScaler`, these are the min/max values for every feature\n",
    "- Second, we use the fitted preprocessor to `transform` __training data__ and the __test data__\n",
    "    - No information should `leak` from the test data into the training data\n",
    "- You can fit and transform the training together with `fit_transform`"
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   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import MinMaxScaler, StandardScaler\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "\n",
    "cancer = load_breast_cancer()\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data, cancer.target,\n",
    "                                                    random_state=0)\n",
    "scaler = MinMaxScaler()\n",
    "X_train_scaled = scaler.fit_transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)"
   ]
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   "source": [
    "### Other transformation techniques\n",
    "\n",
    "We've covered many other transformation techniques before. These can all be used in pipelines.\n",
    "* `OneHotEncoder`: convert categorical to numeric features\n",
    "* `np.digitize`: discretization (binning) of numeric features\n",
    "* `PolynomialFeatures`: construct all interactions with polynomials up to a given degree\n",
    "* `SelectPercentile`: use ANOVA to select most informative features\n",
    "* `SelectFromModel(RandomForestClassifier())`: model-based feature selection\n",
    "* `RFE`: recursive feature elimination\n",
    "* `VarianceThreshold`: removes low-variance (e.g. constant) features"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "#### Missing value imputation\n",
    "* Many sci-kit learn algorithms cannot handle missing value\n",
    "* `Imputer` replaces specific values\n",
    "    * `missing_values` (default 'NaN') placeholder for the missing value\n",
    "    * `strategy`:\n",
    "        - `mean`, replace using the mean along the axis\n",
    "        - `median`, replace using the median along the axis\n",
    "        - `most_frequent`, replace using the most frequent value\n",
    "* Many more advanced techniques exist, but not yet in scikit-learn\n",
    "    * e.g. low rank approximations (uses matrix factorization)"
   ]
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     "text": [
      "Missing data: [[nan, 2], [6, nan], [7, 6]]\n",
      "Imputed data:\n",
      " [[4.    2.   ]\n",
      " [6.    3.667]\n",
      " [7.    6.   ]]\n"
     ]
    }
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   "source": [
    "from sklearn.preprocessing import Imputer\n",
    "X1_train = [[1, 2], [np.nan, 3], [7, 6]];\n",
    "imp = Imputer(missing_values='NaN', strategy='mean', axis=0)\n",
    "imp.fit(X1_train)\n",
    "X1 = [[np.nan, 2], [6, np.nan], [7, 6]]\n",
    "print(\"Missing data: {}\".format(X1) )                          \n",
    "print(\"Imputed data:\\n {}\".format(imp.transform(X1))  )                         "
   ]
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   "source": [
    "#### Dimensionality reduction techniques \n",
    "- Many techniques\n",
    "    - `decomposition.PCA` (Principal Component Analysis)\n",
    "    - `manifold.MDS` (Multi-Dimensional Scaling)\n",
    "    - `manifold.Isomap`\n",
    "    - `random_projection.GaussianRandomProjection`\n",
    "    - `random_projection.johnson_lindenstrauss_min_dim`\n",
    "    - ...\n",
    "- See coming lectures\n",
    "- Reducing the number of features greatly helps distance-based algorithms (kNN, clustering,...)\n",
    "    - Curse of dimensionality (Bellman's curse): for every new feature, we need exponentially more data\n",
    "- Very useful in their own right \n",
    "- Note: not all dimensionality reduction techniques can be used as a transformer. \n",
    "    - They have a `fit`, but no `transform` method, and can't be applied on test data."
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    "### How great is the effect of scaling on (RBF) SVMs?\n",
    "* First, we train the SVM without scaling"
   ]
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     "text": [
      "Test set accuracy: 0.63\n"
     ]
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "svm = SVC()\n",
    "svm.fit(X_train, y_train)\n",
    "print(\"Test set accuracy: {:.2f}\".format(svm.score(X_test, y_test)))"
   ]
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   "source": [
    "* With scaling, we get a much better model"
   ]
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     "text": [
      "Scaled test set accuracy: 0.95\n"
     ]
    }
   ],
   "source": [
    "# preprocessing using 0-1 scaling\n",
    "scaler = MinMaxScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "\n",
    "# learning an SVM on the scaled training data\n",
    "svm.fit(X_train_scaled, y_train)\n",
    "# scoring on the scaled test set\n",
    "print(\"Scaled test set accuracy: {:.2f}\".format(svm.score(X_test_scaled, y_test)))"
   ]
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    "## Hyperparameter Selection with Preprocessing \n",
    "* If we also want to optimize our SVM's hyperparameters, things get more complicated\n",
    "* Indeed, when we `fit` the preprocessor (`MinMaxScaler`), we used _all_ the training data.\n",
    "* The cross-validation splits in GridSearchCV will have training sets preprocessed with information from the test sets (data leakage)"
   ]
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     "text": [
      "Best cross-validation accuracy: 0.98\n",
      "Best set score: 0.97\n",
      "Best parameters:  {'gamma': 1, 'C': 1}\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "# illustration purposes only, don't use this code\n",
    "param_grid = {'C': [0.001, 0.01, 0.1, 1, 10, 100],\n",
    "              'gamma': [0.001, 0.01, 0.1, 1, 10, 100]}\n",
    "grid = GridSearchCV(SVC(), param_grid=param_grid, cv=5)\n",
    "grid.fit(X_train_scaled, y_train)\n",
    "print(\"Best cross-validation accuracy: {:.2f}\".format(grid.best_score_))\n",
    "print(\"Best set score: {:.2f}\".format(grid.score(X_test_scaled, y_test)))\n",
    "print(\"Best parameters: \", grid.best_params_)"
   ]
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    "Visualization of what happens in this code\n",
    "* During cross-validation (grid search) we evaluate hyperparameter settings on a validation set that was preprocessed with information in that validation set\n",
    "* This will lead to overly optimistic results during cross-validation\n",
    "* When we want to use the optimized hyperparameters on the held-out test data, the selected hyperparameters may be suboptimal.\n",
    "* To solve this, we need to _glue_ the preprocessing and learning algorithms together by building a pipeline"
   ]
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gNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAKNjAwIDYwMCA2\nMDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCAzMTggNDAxIDQ2\nMCA4MzggNjM2Cjk1MCA3ODAgMjc1IDM5MCAzOTAgNTAwIDgzOCAzMTggMzYxIDMxOCAzMzcgNjM2\nIDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNgo2MzYgNjM2IDMzNyAzMzcgODM4IDgzOCA4Mzgg\nNTMxIDEwMDAgNjg0IDY4NiA2OTggNzcwIDYzMiA1NzUgNzc1IDc1MiAyOTUKMjk1IDY1NiA1NTcg\nODYzIDc0OCA3ODcgNjAzIDc4NyA2OTUgNjM1IDYxMSA3MzIgNjg0IDk4OSA2ODUgNjExIDY4NSAz\nOTAgMzM3CjM5MCA4MzggNTAwIDUwMCA2MTMgNjM1IDU1MCA2MzUgNjE1IDM1MiA2MzUgNjM0IDI3\nOCAyNzggNTc5IDI3OCA5NzQgNjM0IDYxMgo2MzUgNjM1IDQxMSA1MjEgMzkyIDYzNCA1OTIgODE4\nIDU5MiA1OTIgNTI1IDYzNiAzMzcgNjM2IDgzOCA2MDAgNjM2IDYwMCAzMTgKMzUyIDUxOCAxMDAw\nIDUwMCA1MDAgNTAwIDEzNDIgNjM1IDQwMCAxMDcwIDYwMCA2ODUgNjAwIDYwMCAzMTggMzE4IDUx\nOCA1MTgKNTkwIDUwMCAxMDAwIDUwMCAxMDAwIDUyMSA0MDAgMTAyMyA2MDAgNTI1IDYxMSAzMTgg\nNDAxIDYzNiA2MzYgNjM2IDYzNiAzMzcKNTAwIDUwMCAxMDAwIDQ3MSA2MTIgODM4IDM2MSAxMDAw\nIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDYzNiA2MzYgMzE4IDUwMAo0MDEgNDcxIDYxMiA5Njkg\nOTY5IDk2OSA1MzEgNjg0IDY4NCA2ODQgNjg0IDY4NCA2ODQgOTc0IDY5OCA2MzIgNjMyIDYzMiA2\nMzIKMjk1IDI5NSAyOTUgMjk1IDc3NSA3NDggNzg3IDc4NyA3ODcgNzg3IDc4NyA4MzggNzg3IDcz\nMiA3MzIgNzMyIDczMiA2MTEgNjA1CjYzMCA2MTMgNjEzIDYxMyA2MTMgNjEzIDYxMyA5ODIgNTUw\nIDYxNSA2MTUgNjE1IDYxNSAyNzggMjc4IDI3OCAyNzggNjEyIDYzNAo2MTIgNjEyIDYxMiA2MTIg\nNjEyIDgzOCA2MTIgNjM0IDYzNCA2MzQgNjM0IDU5MiA2MzUgNTkyIF0KZW5kb2JqCjE1IDAgb2Jq\nCjw8IC9sIDE2IDAgUiAvc3BhY2UgMjkgMCBSIC9pIDE3IDAgUiAvZSAxOCAwIFIgL2cgMjAgMCBS\nIC92IDIxIDAgUgovQyAyMiAwIFIgL2MgMjMgMCBSIC9vIDI0IDAgUiAvZiAyNSAwIFIgL2QgMjYg\nMCBSIC9WIDI4IDAgUiAvcyAxOSAwIFIKL1QgMjcgMCBSIC9uIDM0IDAgUiAvUyAzMSAwIFIgL2Eg\nMzIgMCBSIC90IDMzIDAgUiAvcCAzMCAwIFIgL3IgMzUgMCBSID4+CmVuZG9iagozIDAgb2JqCjw8\nIC9GMSAxNCAwIFIgPj4KZW5kb2JqCjQgMCBvYmoKPDwgL0EyIDw8IC9jYSAxIC9UeXBlIC9FeHRH\nU3RhdGUgL0NBIDEgPj4KL0ExIDw8IC9jYSAxIC9UeXBlIC9FeHRHU3RhdGUgL0NBIDAgPj4gPj4K\nZW5kb2JqCjM2IDAgb2JqCjw8IC9NYXRyaXggWyAxIDAgMCAxIDAgNTg0LjEzMjU5MTI4MTcgXSAv\nUGFpbnRUeXBlIDEgL1hTdGVwIDcyIC9MZW5ndGggMTUyCi9SZXNvdXJjZXMgPDwgL1Byb2NzZXRz\nIFsgL1BERiAvVGV4dCAvSW1hZ2VCIC9JbWFnZUMgL0ltYWdlSSBdID4+Ci9UaWxpbmdUeXBlIDEg\nL1BhdHRlcm5UeXBlIDEgL0JCb3ggWyAwIDAgNzIgNzIgXSAvRmlsdGVyIC9GbGF0ZURlY29kZQov\nWVN0ZXAgNzIgL1R5cGUgL1BhdHRlcm4gPj4Kc3RyZWFtCnicJY8xDsMwDAN3vYIfEOA4iuKsXbrn\nD22XeMnS75dUIcKAKetENzTW+bQFqvtT971L9wtv+l8zXxPUNB5LG7joNFDTotPpcnqAojNwpIxl\ngJq2BY5WBt92GtkwQkZC0EzsYmrztP/uyxKuJjspGge9hjmZohHthSd7E43LvQJwe4jHfF4ZFTDE\nZHyvf+gTq7D2sB8lszEcCmVuZHN0cmVhbQplbmRvYmoKMzcgMCBvYmoKPDwgL01hdHJpeCBbIDEg\nMCAwIDEgMCA1ODQuMTMyNTkxMjgxNyBdIC9QYWludFR5cGUgMSAvWFN0ZXAgNzIgL0xlbmd0aCAx\nNjIKL1Jlc291cmNlcyA8PCAvUHJvY3NldHMgWyAvUERGIC9UZXh0IC9JbWFnZUIgL0ltYWdlQyAv\nSW1hZ2VJIF0gPj4KL1RpbGluZ1R5cGUgMSAvUGF0dGVyblR5cGUgMSAvQkJveCBbIDAgMCA3MiA3\nMiBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlCi9ZU3RlcCA3MiAvVHlwZSAvUGF0dGVybiA+PgpzdHJl\nYW0KeJx1jzEOwzAMA3e9gh9wITuK4qxdsvcPbZd4ydLvl3TnwoQBU9aJcjjP4zC/rV739K3Hgv+P\n6z0btiZdT7ys4mNWlgQ1jFf1jpOOgxoWjU6T0wIUnY49ZdQOatga2H0a/NtopKOHjISgmdjE1ORh\nv9mnJYqKrKRobCyzmZ0pGtFl4sleRePwMgNweojHfGVmVMAQk/HL3ENLLMLa3b5HkDfECmVuZHN0\ncmVhbQplbmRvYmoKNSAwIG9iago8PCAvSDIgMzcgMCBSIC9IMSAzNiAwIFIgPj4KZW5kb2JqCjYg\nMCBvYmoKPDwgPj4KZW5kb2JqCjcgMCBvYmoKPDwgPj4KZW5kb2JqCjIgMCBvYmoKPDwgL1R5cGUg\nL1BhZ2VzIC9Db3VudCAxIC9LaWRzIFsgMTAgMCBSIF0gPj4KZW5kb2JqCjM4IDAgb2JqCjw8IC9Q\ncm9kdWNlciAobWF0cGxvdGxpYiBwZGYgYmFja2VuZCkKL0NyZWF0aW9uRGF0ZSAoRDoyMDE3MDMw\nNTIyMjAwNCswMicwMCcpCi9DcmVhdG9yIChtYXRwbG90bGliIDIuMC4wLCBodHRwOi8vbWF0cGxv\ndGxpYi5vcmcpID4+CmVuZG9iagp4cmVmCjAgMzkKMDAwMDAwMDAwMCA2NTUzNSBmIAowMDAwMDAw\nMDE2IDAwMDAwIG4gCjAwMDAwMDk2MTYgMDAwMDAgbiAKMDAwMDAwODU0MCAwMDAwMCBuIAowMDAw\nMDA4NTcyIDAwMDAwIG4gCjAwMDAwMDk1MzEgMDAwMDAgbiAKMDAwMDAwOTU3NCAwMDAwMCBuIAow\nMDAwMDA5NTk1IDAwMDAwIG4gCjAwMDAwMDAwNjUgMDAwMDAgbiAKMDAwMDAwMDM5OCAwMDAwMCBu\nIAowMDAwMDAwMjA4IDAwMDAwIG4gCjAwMDAwMDE1NzcgMDAwMDAgbiAKMDAwMDAwNzI2MSAwMDAw\nMCBuIAowMDAwMDA3MDYxIDAwMDAwIG4gCjAwMDAwMDY2NjYgMDAwMDAgbiAKMDAwMDAwODMxNCAw\nMDAwMCBuIAowMDAwMDAxNTk4IDAwMDAwIG4gCjAwMDAwMDE3MTUgMDAwMDAgbiAKMDAwMDAwMTg1\nNSAwMDAwMCBuIAowMDAwMDAyMTczIDAwMDAwIG4gCjAwMDAwMDI1NzggMDAwMDAgbiAKMDAwMDAw\nMjk4OSAwMDAwMCBuIAowMDAwMDAzMTMzIDAwMDAwIG4gCjAwMDAwMDM0MzggMDAwMDAgbiAKMDAw\nMDAwMzc0MSAwMDAwMCBuIAowMDAwMDA0MDI4IDAwMDAwIG4gCjAwMDAwMDQyMzQgMDAwMDAgbiAK\nMDAwMDAwNDUzNCAwMDAwMCBuIAowMDAwMDA0NjcwIDAwMDAwIG4gCjAwMDAwMDQ4MTIgMDAwMDAg\nbiAKMDAwMDAwNDkwMSAwMDAwMCBuIAowMDAwMDA1MjEwIDAwMDAwIG4gCjAwMDAwMDU2MjEgMDAw\nMDAgbiAKMDAwMDAwNTk5OCAwMDAwMCBuIAowMDAwMDA2MjAyIDAwMDAwIG4gCjAwMDAwMDY0MzYg\nMDAwMDAgbiAKMDAwMDAwODY3MSAwMDAwMCBuIAowMDAwMDA5MDk2IDAwMDAwIG4gCjAwMDAwMDk2\nNzYgMDAwMDAgbiAKdHJhaWxlcgo8PCAvSW5mbyAzOCAwIFIgL1Jvb3QgMSAwIFIgL1NpemUgMzkg\nPj4Kc3RhcnR4cmVmCjk4MjQKJSVFT0YK\n",
      "image/png": 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VwmMAAAAAACqExwAAAAAAVAiPAQAAAACoEB4DAAAAAFAhPAYAAAAAoEJ4DAAAAABAhfAY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\ndttuu+1S2xRFkW2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qhMcAAAAAAFR0bO8CAGBVVBTF7Ul2aO86oJG/lGV5THsXAQAArD2E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\n8up0z8WT++1XJ3n7lNXn/Zy11lZX1UPSzVf9xCS/ku6DgI8leUNr7St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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1110cc9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_improper_processing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Using Pipelines in Grid-searches\n",
    "* We can use the pipeline as a single estimator in `cross_val_score` or `GridSearchCV`\n",
    "* To define a grid, refer to the hyperparameters of the steps\n",
    "    * Step `svm`, parameter `C` becomes `svm__C`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "param_grid = {'svm__C': [0.001, 0.01, 0.1, 1, 10, 100],\n",
    "              'svm__gamma': [0.001, 0.01, 0.1, 1, 10, 100]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best cross-validation accuracy: 0.98\n",
      "Test set score: 0.97\n",
      "Best parameters: {'svm__C': 1, 'svm__gamma': 1}\n"
     ]
    }
   ],
   "source": [
    "from sklearn import pipeline\n",
    "\n",
    "pipe = pipeline.Pipeline([(\"scaler\", MinMaxScaler()), (\"svm\", SVC(C=100))])\n",
    "grid = GridSearchCV(pipe, param_grid=param_grid, cv=5)\n",
    "grid.fit(X_train, y_train)\n",
    "print(\"Best cross-validation accuracy: {:.2f}\".format(grid.best_score_))\n",
    "print(\"Test set score: {:.2f}\".format(grid.score(X_test, y_test)))\n",
    "print(\"Best parameters: {}\".format(grid.best_params_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Now, the preprocessors are refit with only the training data in each cross-validation split."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "application/pdf": 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5ubWw/e0hT+apJDh1nmytYyzyT5f0l27jdvSr/770iy3yDrvzxNh6kmOWGQ+d9ozTtj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a9be0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_proper_processing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* When we request the best estimator of the grid search, we'll get the best pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best estimator:\n",
      "Pipeline(memory=None,\n",
      "     steps=[('scaler', MinMaxScaler(copy=True, feature_range=(0, 1))), ('svm', SVC(C=1, cache_size=200, class_weight=None, coef0=0.0,\n",
      "  decision_function_shape='ovr', degree=3, gamma=1, kernel='rbf',\n",
      "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
      "  tol=0.001, verbose=False))])\n"
     ]
    }
   ],
   "source": [
    "print(\"Best estimator:\\n{}\".format(grid.best_estimator_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* And we can drill down to individual components and their properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVM step:\n",
      "SVC(C=1, cache_size=200, class_weight=None, coef0=0.0,\n",
      "  decision_function_shape='ovr', degree=3, gamma=1, kernel='rbf',\n",
      "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
      "  tol=0.001, verbose=False)\n"
     ]
    }
   ],
   "source": [
    "# Get the SVM\n",
    "print(\"SVM step:\\n{}\".format(\n",
    "      grid.best_estimator_.named_steps[\"svm\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVM support vector coefficients:\n",
      "[[-1.    -1.    -1.    -1.    -1.    -1.    -1.    -1.    -0.822 -0.609\n",
      "  -0.93  -1.    -0.665 -1.    -0.793 -1.    -1.    -1.    -1.    -1.\n",
      "  -1.    -0.63  -1.    -1.    -1.    -0.166 -0.575 -1.    -0.119 -1.\n",
      "  -0.38  -1.    -0.55  -0.048 -0.606 -1.    -0.071 -1.    -0.126 -0.106\n",
      "  -0.285 -1.    -1.    -1.    -0.46   1.     0.932  1.     1.     0.901\n",
      "   1.     0.911  1.     1.     1.     0.653  1.     1.     0.953  0.577\n",
      "   1.     1.     1.     1.     1.     0.659  1.     1.     0.757  1.\n",
      "   1.     1.     1.     1.     1.     1.     0.096  0.274  0.329  1.\n",
      "   1.     1.     0.491  1.     0.41 ]]\n"
     ]
    }
   ],
   "source": [
    "# Get the SVM dual coefficients (support vector weights)\n",
    "print(\"SVM support vector coefficients:\\n{}\".format(\n",
    "      grid.best_estimator_.named_steps[\"svm\"].dual_coef_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Information leakage \n",
    "\n",
    "* See 'Elements of statistical learning' for a great example of data leakage\n",
    "* Consider a synthetic regression task with 100 samples and 10,000 features with data and labels independently sampled from a Gaussian distribution\n",
    "    * Hence, there should be no relation between the data `X` and target `y`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rnd = np.random.RandomState(seed=0)\n",
    "X = rnd.normal(size=(100, 10000))\n",
    "y = rnd.normal(size=(100,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* First, we select the 5% most informative features with `SelectPercentile`, and then evaluate a `Ridge` regressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_selected.shape: (100, 500)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.feature_selection import SelectPercentile, f_regression\n",
    "\n",
    "select = SelectPercentile(score_func=f_regression, percentile=5).fit(X, y)\n",
    "X_selected = select.transform(X)\n",
    "print(\"X_selected.shape: {}\".format(X_selected.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross-validation accuracy (cv only on ridge): 0.91\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.linear_model import Ridge\n",
    "print(\"Cross-validation accuracy (cv only on ridge): {:.2f}\".format(\n",
    "      np.mean(cross_val_score(Ridge(), X_selected, y, cv=5))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* The $R^{2}$ performance is 0.91 (a very good model). This can't be right given that our data is random.\n",
    "* Our feature selection picked out some of the random features which (by chance) correlated with the random target.\n",
    "* Because we selected the features _outside_ of the cross-validation, it could find features that are correlated on the samples in the test folds.\n",
    "* Hence, information leaked from the test set into the training set (through the selection of features)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Now, let's do a proper cross-validation using a pipeline:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross-validation accuracy (pipeline): -0.25\n"
     ]
    }
   ],
   "source": [
    "pipe = pipeline.Pipeline([(\"select\", SelectPercentile(score_func=f_regression,\n",
    "                                             percentile=5)),\n",
    "                 (\"ridge\", Ridge())])\n",
    "print(\"Cross-validation accuracy (pipeline): {:.2f}\".format(\n",
    "      np.mean(cross_val_score(pipe, X, y, cv=5))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* We get a negative $R^2$ score (a very poor model), as expected.\n",
    "* The feature selection now happens _inside_ the cross-validation loop, using only the training folds.\n",
    "* It will still find features that correlate with the labels in the training data, but not with those in the test data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Grid-searching preprocessing steps and model parameters\n",
    "* We can use grid search to optimize the hyperparameters of our preprocessing steps and learning algorithms at the same time\n",
    "* Consider the following pipeline:\n",
    "    - `StandardScaler`, without hyperparameters\n",
    "    - `PolynomialFeatures`, with the max. _degree_ of polynomials\n",
    "    - `Ridge` regression, with L2 regularization parameter _alpha_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "boston = load_boston()\n",
    "X_train, X_test, y_train, y_test = train_test_split(boston.data, boston.target,\n",
    "                                                    random_state=0)\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "pipe = pipeline.make_pipeline(\n",
    "    StandardScaler(),\n",
    "    PolynomialFeatures(),\n",
    "    Ridge())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* We don't know the optimal polynomial degree or alpha value, so we use a grid search (or random search) to find the optimal values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=5, error_score='raise',\n",
       "       estimator=Pipeline(memory=None,\n",
       "     steps=[('standardscaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomialfeatures', PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)), ('ridge', Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001))]),\n",
       "       fit_params=None, iid=True, n_jobs=1,\n",
       "       param_grid={'ridge__alpha': [0.001, 0.01, 0.1, 1, 10, 100], 'polynomialfeatures__degree': [1, 2, 3]},\n",
       "       pre_dispatch='2*n_jobs', refit=True, return_train_score='warn',\n",
       "       scoring=None, verbose=0)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "param_grid = {'polynomialfeatures__degree': [1, 2, 3],\n",
    "              'ridge__alpha': [0.001, 0.01, 0.1, 1, 10, 100]}\n",
    "# Note: I had to use n_jobs=1. (n_jobs=-1 stalls on my machine)\n",
    "grid = GridSearchCV(pipe, param_grid=param_grid, cv=5, n_jobs=1)\n",
    "grid.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Visualing the $R^2$ results as a heatmap:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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h7yggV9SshaF0YogNlgApvqsNiZio2aCHhJWSqh3S8Yyk8FvBXYlhUFtb2wR4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\nJSVFT0YK\n",
      "image/png": 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k5s/o/gXHL6lG9yVJkqTynKKzUqkR/PUZezvdDQu1I0mSJHUR9dGk/mAoNYL/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\nSZIaxAJfkiRJahALfEmSJKlB/gX7IAUs/CRyiwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118ccba90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(grid.cv_results_['mean_test_score'].reshape(3, -1),\n",
    "            vmin=0, cmap=\"viridis\")\n",
    "plt.xlabel(\"ridge__alpha\")\n",
    "plt.ylabel(\"polynomialfeatures__degree\")\n",
    "plt.xticks(range(len(param_grid['ridge__alpha'])), param_grid['ridge__alpha'])\n",
    "plt.yticks(range(len(param_grid['polynomialfeatures__degree'])),\n",
    "           param_grid['polynomialfeatures__degree'])\n",
    "\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Here, degree-2 polynomials help (but degree-3 ones don't), and tuning the alpha parameter helps as well.\n",
    "* Not using the polynomial features leads to suboptimal results (see the results for degree 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best parameters: {'ridge__alpha': 10, 'polynomialfeatures__degree': 2}\n",
      "Test-set score: 0.77\n"
     ]
    }
   ],
   "source": [
    "print(\"Best parameters: {}\".format(grid.best_params_))\n",
    "print(\"Test-set score: {:.2f}\".format(grid.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Algorithm selection\n",
    "* It is also possible to use a grid search to consider various alternative algorithms for a specific step, and tune the pipelines as well\n",
    "    - StandardScaler or MinMaxScaler?\n",
    "    - RandomForest or SVM?\n",
    "* Note that the search space quickly becomes huge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* As an example, let's consider a pipeline that explores:\n",
    "    - StandardScaler + SVM, varying `gamma` and `C`\n",
    "    - None + RandomForest, varying `max_features`\n",
    "* We instantiate a general pipeline, and define everything else in the grid\n",
    "    - We need to define a list of 2 grids because of dependencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "pipe = pipeline.Pipeline([('preprocessing', StandardScaler()), ('classifier', SVC())])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "param_grid = [\n",
    "    {'classifier': [SVC()], 'preprocessing': [StandardScaler(), None],\n",
    "     'classifier__gamma': [0.001, 0.01, 0.1, 1, 10, 100],\n",
    "     'classifier__C': [0.001, 0.01, 0.1, 1, 10, 100]},\n",
    "    {'classifier': [RandomForestClassifier(n_estimators=100)],\n",
    "     'preprocessing': [None], 'classifier__max_features': [1, 2, 3]}]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The Scaling+SVM pipeline wins!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best params:\n",
      "{'preprocessing': StandardScaler(copy=True, with_mean=True, with_std=True), 'classifier__C': 10, 'classifier': SVC(C=10, cache_size=200, class_weight=None, coef0=0.0,\n",
      "  decision_function_shape='ovr', degree=3, gamma=0.01, kernel='rbf',\n",
      "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
      "  tol=0.001, verbose=False), 'classifier__gamma': 0.01}\n",
      "\n",
      "Best cross-validation score: 0.99\n",
      "Test-set score: 0.98\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    cancer.data, cancer.target, random_state=0)\n",
    "\n",
    "grid = GridSearchCV(pipe, param_grid, cv=5)\n",
    "grid.fit(X_train, y_train)\n",
    "\n",
    "print(\"Best params:\\n{}\\n\".format(grid.best_params_))\n",
    "print(\"Best cross-validation score: {:.2f}\".format(grid.best_score_))\n",
    "print(\"Test-set score: {:.2f}\".format(grid.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Algorithm selection: the road ahead\n",
    "_Automating_ the construction of machine learning pipelines is a hot topic of research, with different possible solutions:\n",
    "\n",
    "* Model-based optimization: search large algorithm+hyperparameter spaces more effectively (limited to the learning step)\n",
    "    - E.g. `Auto-SKLearn` and `Hyperopt-SKLearn`\n",
    "* Multi-armed bandits and Racing: train algorithms first on a small sample, train the best 50% on a larger sample, continue until full dataset\n",
    "* Genetic programming: very good at exploring large spaces\n",
    "    - E.g. `sklearn-deap` or `TPOT` (builds pipelines as well)\n",
    "* Meta-learning: build _meta-models_ to predict which algorithms/hyperparameter ranges are most useful on new datasets\n",
    "    - Requires large amounts of observations on previous datasets, as well as measureable dataset properties (meta-features) -> OpenML\n",
    "* Combinations of the above\n",
    "    - Especially meta-learning with all others\n",
    "    - Contact me if interested :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Approaching machine learning problems\n",
    "\n",
    "* Just running your favourite algorithm on every new problem is usually not a great way to start\n",
    "* Consider the problem at large\n",
    "    - Do you want exploratory analysis or (black box) modelling?\n",
    "    - How to define and measure success? Are there costs involved?\n",
    "    - Do you have the right data? How can you make it better?\n",
    "* Build prototypes early-on to evaluate the above.\n",
    "* Analyse your model's mistakes\n",
    "    - Should you collect more, or additional data?\n",
    "    - Should the task be reformulated?\n",
    "    - Often a higher payoff than endless grid searching\n",
    "* Technical debt\n",
    "    - Very complex machine learning prototypes are hard/impossible to put into practice\n",
    "    - There is a creation-maintenance trade-off\n",
    "    - See 'Machine Learning: The High Interest Credit Card of Technical Debt'"
   ]
  },
  {
   "cell_type": "markdown",
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    "### Concept drift\n",
    "* Data is often a stream, and model building is often part of a feedback cycle\n",
    "    - Collect new data, cleaning, build models, analyse\n",
    "    - Continually check that your model is still working\n",
    "* Concept drift: sudden or gradual changes in the phenomenon that you want to model\n",
    "    - External: market/weather evolutions, human behavior\n",
    "    - Feedback: your predictions (and actions) may change future data\n",
    "        - E.g. movie recommendations, new drugs, treatments, ...\n",
    "* Different ways to tackle this:\n",
    "    - Repeated retraining (but often not sure when)\n",
    "    - Stream mining algorithms (learn on fast streaming data)\n",
    "    - Change detection techniques (retrain when model starts failing)\n",
    "    - Meta-learning (switch algorithms depending on data properties)"
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    "### Real world evaluations\n",
    "* Accuracy is seldomly the right measure. Usually, costs are involved.\n",
    "* Don't just evaluate your predictions themselves, also evaluate how the outcome improves _after_ you take actions based on them\n",
    "* Beware of non-representative samples. You often don't have the data you really need.\n",
    "* Adversarial situations (e.g. spam filtering) can subvert your predictions\n",
    "* Data leakage: the signal your model found was just an artifact of your data\n",
    "    - See 'Why Should I Trust You?' by Marco Ribeiro et al.\n",
    "* A/B testing to evaluate algorithms in the wild\n",
    "    - More advanced: bandit algorithms"
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    "### Further reading (Theory)\n",
    "* The Elements of Statistical Learning (Hastie, Tibshirani, Friedman)\n",
    "* Deep Learning (Goodfellow, Bengio, Courville) - see later\n",
    "* Gaussian Processes for Machine Learning (Rasmussen, Williams)\n",
    "* Machine Learning: An Algorithmic Perspective (Marsland)\n",
    "* Pattern Recognition and Machine Learning (Bishop)\n",
    "* Machine Learning: A Probabilistic Perspective (Murphy)\n",
    "* Foundations of Data Science (Blum, Hopcroft, Kannan)"
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    "### Other packages\n",
    "* Deep learning: `TensorFlow`, `Torch`, `Caffe`,...\n",
    "    - `Keras`, `Lasagne` provide simpler interfaces\n",
    "* R libraries often provide a richer variation of techniques\n",
    "    - Powerful statistical analysis and visualization tools\n",
    "    - mlr (Machine Learning in R)\n",
    "* `vowpal wabbit` (vw): C++ library for large datasets and streaming data\n",
    "* MOA (Massive Online Analysis): Java library for streaming data\n",
    "* MLLib: Scala library on top of Spark, for large distributed systems\n",
    "* PyMC/Stan: Probabilistic programming, allows to model how likely each data point is correct. Simple, elegant way to build models."
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    "## Summary"
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    "* Pipelines allow us to encapsulate multiple steps into a single estimator\n",
    "    - Has `fit`, `transform`, and `predict` methods\n",
    "* Avoids data leakage, hence crucial for proper evaluation\n",
    "* Choosing the right combination of feature extraction, preprocessing, and models is somewhat of an art.\n",
    "* Pipelines + Grid/Random Search help, but search space is huge\n",
    "    - Smarter techniques are being researched\n",
    "* Real world applications require careful thought, prototyping, and tireless evaluation.   "
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