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@maxbellec
Created December 15, 2016 15:21
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1> <a href=http://www.datascience-paris-saclay.fr/>Paris Saclay Center for Data Science</a> </h1>\n",
"\n",
"<h2> RAMP on qualitative and quantitative non-invasive monitoring of anti-cancer drugs </h2>\n",
"\n",
"<i>Camille Marini (LTCI/CNRS), Alex Gramfort (LTCI/Télécom ParisTech), Sana Tfaili (Lip(Sys)²/UPSud), Laetitia Le (Lip(Sys)²/UPSud), Mehdi Cherti (LAL/CNRS), Balázs Kégl (LAL/CNRS)</i>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Maxime Bellec report"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Data analysis"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import os\n",
"import glob\n",
"import numpy as np\n",
"from scipy import io\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"data = pd.read_csv('train.csv')\n",
"\n",
"y_df = data[['molecule', 'concentration']]\n",
"X_df = data.drop(['molecule', 'concentration'], axis=1)\n",
"spectra = X_df['spectra'].values \n",
"spectra = np.array([np.array(dd[1:-1].split(',')).astype(float) for dd in spectra]) \n",
"X_df['spectra'] = spectra.tolist()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Target for classification\n",
"molecule = y_df['molecule'].values\n",
"# Target for regression\n",
"concentration = y_df['concentration'].values\n",
"# \"Raw\" features\n",
"X = spectra"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We need to predict molecule type and concentration. Let's see how they vary with the spectrum"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Mean spectrum as a function of the molecule type"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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nfnT4Iy5/4XLMfxnMfxlufvlmbCcnJbRsDFsdF+dMJZeVtdardbQiEgwKtCIi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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x104660410>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.rcParams['figure.figsize'] = (4, 2)\n",
"# Mean Raman spectra for each type of molecule\n",
"for mol in np.unique(molecule):\n",
" plt.plot(np.mean(X[molecule == mol, :], axis=0), label=\"%s\" % mol)\n",
"\n",
"plt.legend(bbox_to_anchor=(1.2, 1),\n",
" bbox_transform=plt.gcf().transFigure);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Dimensionality reduction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have 999 samples and 1800 features : most model\n",
" won't make a lot of sense. Since the raman spetras are similar,\n",
" the intrisic dimension should be smaller. PCA should be able to capture that"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PCA"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn.decomposition import PCA"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"pca = PCA(n_components=20)\n",
"X_reduced = pca.fit_transform(X)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10f6faed0>]"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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uh0/p5GbNGsswnm/F5F//Kswlw4UQv8gVE6fBcddd0KOHpYsvdLp1g0MPhauu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\nFXrGdO1qP+43ZYgCcdxxtg+/cCGMHm3airfeSmzFfP45vPiibfOMGgV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yAAAF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\nKRv+H6K0j+q3AhpaAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f2134d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.subplot(2, 2, 1)\n",
"plt.plot(-pca.components_[0])\n",
"plt.subplot(2, 2, 2)\n",
"plt.plot(-pca.components_[1])\n",
"plt.subplot(2, 2, 3)\n",
"plt.plot(-pca.components_[2])\n",
"plt.subplot(2, 2, 4)\n",
"plt.plot(-pca.components_[3])\n",
"plt.rcParams['figure.figsize'] = (8, 5)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"The first component is the average sprectum, the second component captures"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Distribution of the molecules along the 2 principal axis"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x114447c10>"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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yNhhZsgTnm2+43e8nGXjS5yO1YUN63ngjWzdtYv/uHZRjP6OBOsAjBJjCISAz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lep4vLjsCCViNqQ2SQB6RA6ePBgGkbnbB4It1Gaa28k8COlY+loAjIK5Yh6wwfAKFiU3vaex5+j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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1141a00d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"reverse_labels = {'A': 'c', 'B': 'b', 'Q': 'k', 'R': 'r'}\n",
"c = map(lambda x: reverse_labels[x], molecule)\n",
"plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=c)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Distribution of the concentration along the 2 principal axis"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x11582ce10>"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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RUfZ32WrbyPUZZendo3cwTpdSSgWUzvlQV63y5cuTkJjAqV2nuNt0oGtGb7bJ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\nfdmgQX327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LZ7s7m5thraWhDxAzMsDejh6vGH0Q7t27dngjGGjohjTj4brSz1mBSfVCrU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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1156e88d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"reverse_labels = {'A': 'c', 'B': 'b', 'Q': 'k', 'R': 'r'}\n",
"c = map(lambda x: reverse_labels[x], molecule)\n",
"plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=concentration, cmap='spring')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"PCA seems relevant for this task, as only the 2 principal axis\n",
"are enough to have a good first separation of the molecules and concentration"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fourier"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def get_fft(x):\n",
" a = np.fft.rfft(x)\n",
" return np.concatenate([a.real[:70], a.imag[1:70]])\n",
"\n",
"def transform_fft(X):\n",
" return np.apply_along_axis(get_fft, 1, X)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"X_fft = transform_fft(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fourier transform allows to reconstruct the signal with less noise :"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x119ed20d0>]"
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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aVFiIiPgopyCH+M5Vl5quW9e8Rys8EqMTfV5yqpUhUhcVFiIiPsotyK0yDQJu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\nxEIppZRSHvP/uRINxxogk6QAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119bdedd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X[0][np.arange(0, X[0].size + 1, X[0].size / 140)])\n",
"plt.plot(0.07*np.fft.irfft(np.fft.rfft(X[0]), 140))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will see later that a PCA on the Fourier transform performs similarily than a PCA on X in terms of performance,\n",
"but does not fail on the same data, so that keeping both is relevant."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Feature engineering"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I first used only X as a feature, and then tried to add some more. They did not perform very well but could be interesting."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Slope"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see on the mean spectrum for each molecule, the spectrum for the molecule A is small for small frequencies, than highest for big frequencies. So that the slope (linear approximation) of the spectrum will be higher.\n",
"\n",
"I computed two kinds of slope. Because classical least squares approximation is influenced a lot by the concentration\n",
"of the molecule, I also computed the least absolute error slope, that is not influenced by large outliers."
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn.linear_model import RANSACRegressor, LinearRegression\n",
"r = RANSACRegressor(LinearRegression())\n",
"def get_l1_slope(array):\n",
" \"\"\"\n",
" We use a linear regression with least absolute loss to be resistent\n",
" to the high peak\n",
" \"\"\"\n",
" n_features = 1200\n",
" return r.fit(np.arange(1200).reshape((1200, 1)), array[:1200]).estimator_.coef_[0]\n",
"\n",
"\n",
"def get_l2_slope(x):\n",
" \"\"\"\n",
" l2 slope is an easy computation\n",
" \"\"\"\n",
" n = x.shape[0]\n",
" return np.dot(range(n), x) / n - (n - 1) /2. * x.mean()"
]
},
{
"cell_type": "code",
"execution_count": 228,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"if False:\n",
" l1_slope = np.apply_along_axis(get_l1_slope, 1, X)\n",
" l2_slope = np.apply_along_axis(get_l2_slope, 1, X)\n",
"\n",
" # influence on the molecule type and concentration\n",
"\n",
" slopes = pd.DataFrame([l1_slope, l2_slope, molecule, concentration]).T\n",
" slopes.columns = 'l1', 'l2', 'molecule', 'concentration'\n",
" slopes.l1 = 1e5*slopes.l1.astype(np.float64)\n",
" slopes.l2 = slopes.l2.astype(np.float64)\n",
" df = slopes.groupby('molecule')['l1', 'l2'].agg('mean')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>l1</th>\n",
" <th>l2</th>\n",
" </tr>\n",
" <tr>\n",
" <th>molecule</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>A</th>\n",
" <td>1.693955</td>\n",
" <td>6.478152</td>\n",
" </tr>\n",
" <tr>\n",
" <th>B</th>\n",
" <td>0.781880</td>\n",
" <td>3.661328</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Q</th>\n",
" <td>1.476900</td>\n",
" <td>5.517031</td>\n",
" </tr>\n",
" <tr>\n",
" <th>R</th>\n",
" <td>1.268023</td>\n",
" <td>4.916396</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The average slope is indeed much smaller for molecule B than for the others, and relatively different for each molecule. Keeping both as features is a bad idea for most models because they are strongly correlated, making the optimisation slow, so I only kept the l2 slope (faster to compute). There is still information in keeping both though, as shown by following plots (top: concentration, bottom: molecule)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src='https://dl.dropboxusercontent.com/s/dp4z7jje959l0d8/Capture%20d%27%C3%A9cran%202016-12-15%2015.28.53.png?dl=0' width='500px'>\n",
"<img src='https://dl.dropboxusercontent.com/s/veeh74msk8vd3rq/Capture%20d%27%C3%A9cran%202016-12-15%2015.29.06.png?dl=0' width='500px'>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Models"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Failed idea: predict a model as a linear combination of the others"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The idea is that the same molecule in different solutions and concentration have similar spectrum. What's more, we could imagine that the spectrum is an approximation of a linear combination of the spectrum of the soluté and that of the molecule. So that\n",
"\n",
"$$Spectrum(molecule \\space M1, soluté \\space S1, concentration \\space C1) = \\\\ K(concentration) \\space Spectrum(soluté \\space S1) + \\\\ K'(concentration) \\space Spectum(molecule \\space M1, concentration \\space C2)$$\n",
"\n",
"Even though we do not have access to $Spectrum(soluté \\space S1)$, in that case we would have\n",
"\n",
"$$Spectrum(molecule \\space M1, soluté \\space S1, concentration \\space C1) = \\\\ K(concentration) \\space Spectum(molecule \\space M1, concentration \\space C2) + \\\\ K'(concentration) \\space Spectum(molecule \\space M1, concentration \\space C2)$$\n",
"\n",
"\n",
"So we predict a spectrum as a linear combination of the other sprectrum. Since there are many other spectrum,\n",
"we will use a Lasso penalization in order to have very few other spectrum in that linear combination.\n",
"\n",
"Once we have that combination, we predict the molecule to be the most frequent found amongst the spectrum having non-null coefficients, and the concentration to be the weighted average of the corresponding spectrum."
]
},
{
"cell_type": "code",
"execution_count": 178,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# both train and test data\n",
"full_df = X_df.join(y_df)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### <span style='color:gray'>Warning: code in next cell takes ~30min to run, so I print the result but the code does not actually run</span>"
]
},
{
"cell_type": "code",
"execution_count": 229,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mare score for linear combination predictor: 0.56504819375707427\n",
"confusion matrix for linear combination predictor: \n",
"[[243 0 0 0]\n",
" [154 91 0 14]\n",
" [233 4 0 0]\n",
" [217 22 0 21]]\n",
"0/1 loss for molecule prediction: 0.35535535535535534\n"
]
}
],
"source": [
"from sklearn.linear_model import Lasso\n",
"pred_molecule = pd.Series(np.zeros(999))\n",
"pred_concentration = pd.Series(np.zeros(999))\n",
"similar_molecules = pd.Series(np.zeros(999))\n",
"\n",
"n_samples = X.shape[0]\n",
"\n",
"# change 0 to 999 for the cell to actually run\n",
"for ix in range(0):\n",
" print(ix)\n",
" # have every spectrum but the one we are currently predicting\n",
" mask = np.arange(n_samples) != ix\n",
" X_minus_ix = X[mask, :]\n",
" \n",
" # linear lasso to predict current spectrum as sparse linear combination\n",
" # of the others\n",
" reg = Lasso(alpha=1e-5)\n",
" reg.fit(X_minus_ix.T, X[ix])\n",
" \n",
" # keeping only non-null indices\n",
" non_null_indices = reg.coef_ != 0\n",
" non_null_coefs = reg.coef_[non_null_indices]\n",
" \n",
" corr_df = full_df[mask][non_null_indices]\n",
" # the predicted concentration is a weighted average of the coefficients of\n",
" # the linear combination\n",
" pred_concentration[ix] = np.dot(corr_df.concentration.values, non_null_coefs)\\\n",
" / non_null_coefs.sum()\n",
" # the predicted molecule is the most frequent molecule \n",
" pred_molecule[ix] = corr_df.molecule.value_counts().idxmax()\n",
" similar_molecules[ix] = non_null_coefs.size\n",
"\n",
"if False:\n",
" res = pd.DataFrame([molecule, pred_molecule, concentration, pred_concentration, similar_molecules]).T\n",
" res.columns = 'molecule', 'predicted_molecule', 'concentration', 'predicted_concentration', 'n_molecules'\n",
" # the mare scare\n",
" np.mean(np.abs((res.predicted_concentration - res.concentration)) / res.concentration)\n",
" # the confusion matrix\n",
" from sklearn.metrics import confusion_matrix\n",
" confusion_matrix(res.molecule, res.predicted_molecule)\n",
" # 0/1 loss\n",
" (res.molecule == res.predicted_molecule).mean()\n",
"\n",
"print(\"Mare score for linear combination predictor: 0.56504819375707427\")\n",
"print(\"confusion matrix for linear combination predictor: \\n{}\".format(np.array([[243, 0, 0, 0], [154, 91, 0, 14],[233, 4, 0, 0],[217, 22, 0, 21]])))\n",
"print(\"0/1 loss for molecule prediction: 0.35535535535535534\".format())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The results are interesting (mare of 0.56, not very good but not stupid) for the concentration, but very bad for the predicted molecule (though still above random). For some reason, the predicted molecule is almost only A and B.\n",
"\n",
"This model is intersting in that it has no hyperparameters, but **does not have a good prediction, we can drop it**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## More traditional models and parameter selection"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I used scikit-learn's implementations and Random Forests and SVM, as well as xgboost's regression trees.\n",
"\n",
"The model selection is done using a grid search with cross validation.\n",
"For each model, I tried using both the PCA on the spectrum and the PCA of the Fourier transform of the spectrum, they both had interesting results."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Parameter selection using grid search and cross validation\n",
"\n",
"We'll have a look at one example since it's similar for others"
]
},
{
"cell_type": "code",
"execution_count": 199,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn.model_selection import GridSearchCV\n",
"from sklearn.ensemble import RandomForestClassifier\n",
"from sklearn.svm import SVC"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At the beginning, the grid search should only contain a few (2-3) different values for each parameter, as we'll do\n",
"n_parameter_1 * n_parameter_2 * n_fold trainings. They should cover a large range, that can be refined (a bit, to avoid overfitting) after around best values"
]
},
{
"cell_type": "code",
"execution_count": 243,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"best params: {'max_features': 5, 'n_estimators': 1000}\n"
]
}
],
"source": [
"if False:\n",
" param_grid = [{'n_estimators': [20, 100, 1000], 'max_features': [5, 10, 20]}]\n",
"\n",
" # for classification, the default scoring value is the one of the problem (0/1 loss)\n",
" # for regression, we would passe scoring=mare_loss\n",
" grid_search = GridSearchCV(RandomForestClassifier(), param_grid)\n",
"\n",
" grid_search.fit(X_reduced, molecule)\n",
"\n",
" print(grid_search.best_params_)\n",
" pd.DataFrame(grid_search.cv_results_)\n",
"print(\"best params: {}\".format({'max_features': 5, 'n_estimators': 1000}))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>mean_fit_time</th>\n",
" <th>mean_score_time</th>\n",
" <th>mean_test_score</th>\n",
" <th>mean_train_score</th>\n",
" <th>param_max_features</th>\n",
" <th>param_n_estimators</th>\n",
" <th>params</th>\n",
" <th>rank_test_score</th>\n",
" <th>split0_test_score</th>\n",
" <th>split0_train_score</th>\n",
" <th>split1_test_score</th>\n",
" <th>split1_train_score</th>\n",
" <th>split2_test_score</th>\n",
" <th>split2_train_score</th>\n",
" <th>std_fit_time</th>\n",
" <th>std_score_time</th>\n",
" <th>std_test_score</th>\n",
" <th>std_train_score</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.147008</td>\n",
" <td>0.023465</td>\n",
" <td>0.912913</td>\n",
" <td>1.000000</td>\n",
" <td>5</td>\n",
" <td>20</td>\n",
" <td>{u'max_features': 5, u'n_estimators': 20}</td>\n",
" <td>4</td>\n",
" <td>0.931138</td>\n",
" <td>1.000000</td>\n",
" <td>0.894895</td>\n",
" <td>1.000000</td>\n",
" <td>0.912651</td>\n",
" <td>1.000000</td>\n",
" <td>0.026022</td>\n",
" <td>0.008019</td>\n",
" <td>0.014808</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.666344</td>\n",
" <td>0.083507</td>\n",
" <td>0.922923</td>\n",
" <td>1.000000</td>\n",
" <td>5</td>\n",
" <td>100</td>\n",
" <td>{u'max_features': 5, u'n_estimators': 100}</td>\n",
" <td>2</td>\n",
" <td>0.946108</td>\n",
" <td>1.000000</td>\n",
" <td>0.903904</td>\n",
" <td>1.000000</td>\n",
" <td>0.918675</td>\n",
" <td>1.000000</td>\n",
" <td>0.058890</td>\n",
" <td>0.011265</td>\n",
" <td>0.017501</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>6.358472</td>\n",
" <td>0.816569</td>\n",
" <td>0.924925</td>\n",
" <td>1.000000</td>\n",
" <td>5</td>\n",
" <td>1000</td>\n",
" <td>{u'max_features': 5, u'n_estimators': 1000}</td>\n",
" <td>1</td>\n",
" <td>0.946108</td>\n",
" <td>1.000000</td>\n",
" <td>0.909910</td>\n",
" <td>1.000000</td>\n",
" <td>0.918675</td>\n",
" <td>1.000000</td>\n",
" <td>0.370262</td>\n",
" <td>0.052399</td>\n",
" <td>0.015432</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.171352</td>\n",
" <td>0.017605</td>\n",
" <td>0.902903</td>\n",
" <td>0.998998</td>\n",
" <td>10</td>\n",
" <td>20</td>\n",
" <td>{u'max_features': 10, u'n_estimators': 20}</td>\n",
" <td>6</td>\n",
" <td>0.940120</td>\n",
" <td>0.998496</td>\n",
" <td>0.864865</td>\n",
" <td>0.998498</td>\n",
" <td>0.903614</td>\n",
" <td>1.000000</td>\n",
" <td>0.007739</td>\n",
" <td>0.001743</td>\n",
" <td>0.030750</td>\n",
" <td>0.000708</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.795902</td>\n",
" <td>0.085024</td>\n",
" <td>0.906907</td>\n",
" <td>1.000000</td>\n",
" <td>10</td>\n",
" <td>100</td>\n",
" <td>{u'max_features': 10, u'n_estimators': 100}</td>\n",
" <td>5</td>\n",
" <td>0.928144</td>\n",
" <td>1.000000</td>\n",
" <td>0.888889</td>\n",
" <td>1.000000</td>\n",
" <td>0.903614</td>\n",
" <td>1.000000</td>\n",
" <td>0.017887</td>\n",
" <td>0.008550</td>\n",
" <td>0.016205</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>8.654545</td>\n",
" <td>0.874869</td>\n",
" <td>0.915916</td>\n",
" <td>1.000000</td>\n",
" <td>10</td>\n",
" <td>1000</td>\n",
" <td>{u'max_features': 10, u'n_estimators': 1000}</td>\n",
" <td>3</td>\n",
" <td>0.928144</td>\n",
" <td>1.000000</td>\n",
" <td>0.891892</td>\n",
" <td>1.000000</td>\n",
" <td>0.927711</td>\n",
" <td>1.000000</td>\n",
" <td>0.260688</td>\n",
" <td>0.008321</td>\n",
" <td>0.016988</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>0.213665</td>\n",
" <td>0.017699</td>\n",
" <td>0.885886</td>\n",
" <td>0.999500</td>\n",
" <td>20</td>\n",
" <td>20</td>\n",
" <td>{u'max_features': 20, u'n_estimators': 20}</td>\n",
" <td>9</td>\n",
" <td>0.889222</td>\n",
" <td>1.000000</td>\n",
" <td>0.870871</td>\n",
" <td>1.000000</td>\n",
" <td>0.897590</td>\n",
" <td>0.998501</td>\n",
" <td>0.014222</td>\n",
" <td>0.002851</td>\n",
" <td>0.011153</td>\n",
" <td>0.000707</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>1.204252</td>\n",
" <td>0.099529</td>\n",
" <td>0.887888</td>\n",
" <td>1.000000</td>\n",
" <td>20</td>\n",
" <td>100</td>\n",
" <td>{u'max_features': 20, u'n_estimators': 100}</td>\n",
" <td>8</td>\n",
" <td>0.898204</td>\n",
" <td>1.000000</td>\n",
" <td>0.876877</td>\n",
" <td>1.000000</td>\n",
" <td>0.888554</td>\n",
" <td>1.000000</td>\n",
" <td>0.030286</td>\n",
" <td>0.021612</td>\n",
" <td>0.008726</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>10.848640</td>\n",
" <td>1.180378</td>\n",
" <td>0.888889</td>\n",
" <td>1.000000</td>\n",
" <td>20</td>\n",
" <td>1000</td>\n",
" <td>{u'max_features': 20, u'n_estimators': 1000}</td>\n",
" <td>7</td>\n",
" <td>0.892216</td>\n",
" <td>1.000000</td>\n",
" <td>0.879880</td>\n",
" <td>1.000000</td>\n",
" <td>0.894578</td>\n",
" <td>1.000000</td>\n",
" <td>0.383802</td>\n",
" <td>0.461439</td>\n",
" <td>0.006443</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Chosen models"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After choosing parameters with cross validation for each, I kept the following models for classification:"
]
},
{
"cell_type": "code",
"execution_count": 211,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from xgboost import XGBClassifier"
]
},
{
"cell_type": "code",
"execution_count": 215,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"rfc = RandomForestClassifier(n_estimators=300, max_features=5)\n",
"rfc_fft = RandomForestClassifier(n_estimators=300, max_features=5)\n",
"svc = SVC(C=1e7, kernel='rbf', probability=True)\n",
"svc_fft = SVC(C=1e7, kernel='rbf', probability=True)\n",
"bst = XGBClassifier(max_depth=6, learning_rate=0.1, n_estimators=500,\n",
" objective='multi:softprob', subsample=0.2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model aggregation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are different possible aggreation:\n",
"- chose the most likely (multiply the probabilities)\n",
"- chose the argmax of the probabilities\n",
"- keep only the best\n",
"- chose the most voted\n",
"- custom\n",
"\n",
"I tried all different aggregations, evaluating them on many folds. The best aggregations were most voted and most likely, giving very similar results.\n",
"\n",
"The next cell shows how I did it, but does not run (takes a long time)"
]
},
{
"cell_type": "code",
"execution_count": 221,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result:\n"
]
},
{
"data": {
"text/plain": [
"bst 0.9160\n",
"bst_fft 0.9180\n",
"most_common 0.9320\n",
"new 0.9055\n",
"rfc 0.9155\n",
"rfc_fft 0.9175\n",
"svc 0.8460\n",
"svc_fft 0.8780\n",
"svc_or_else 0.9235\n",
"tot 0.9375\n",
"dtype: float64"
]
},
"execution_count": 221,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# change to other than 0 for code to run\n",
"for i in range(0):\n",
" skf = ShuffleSplit(n_splits=2, test_size=0.2)\n",
"\n",
" train_is, test_is = next(skf.split(y_df))\n",
"\n",
" X_train_df = X_df.iloc[train_is].copy()\n",
" y_train_df = y_df.iloc[train_is].copy()\n",
" X_test_df = X_df.iloc[test_is].copy()\n",
" y_test_df = y_df.iloc[test_is].copy()\n",
" y_train_clf = y_train_df['molecule'].values\n",
" y_train_reg = y_train_df['concentration'].values\n",
" y_test_clf = y_test_df['molecule'].values\n",
" y_test_reg = y_test_df['concentration'].values\n",
"\n",
" fe_clf = feature_extractor_clf.FeatureExtractorClf()\n",
" fe_clf.fit(X_train_df, y_train_df)\n",
" X_train_array_clf = fe_clf.transform(X_train_df)\n",
" X_test_array_clf = fe_clf.transform(X_test_df)\n",
"\n",
" X, X_fft = X_train_array_clf\n",
"\n",
" rfc = RandomForestClassifier(n_estimators=300, max_features=5)\n",
" rfc_fft = RandomForestClassifier(n_estimators=300, max_features=5)\n",
" svc = SVC(C=1e7, kernel='rbf', probability=True)\n",
" svc_fft = SVC(C=1e7, kernel='rbf', probability=True)\n",
" boost_params = {\n",
" 'max_depth': 6,\n",
" 'eta': 1,\n",
" 'gamma': 0,\n",
" 'lambda': 0,\n",
" 'silent':1,\n",
" 'objective':'multi:softprob',\n",
" 'n_thread': 4,\n",
" 'num_class': 4,\n",
" 'eval_metric': 'mlogloss'\n",
" }\n",
"\n",
" y_train_clf.shape\n",
"\n",
" rfc.fit(X, y_train_clf)\n",
" rfc_fft.fit(X_fft, y_train_clf)\n",
" svc.fit(X, y_train_clf)\n",
" svc_fft.fit(X_fft, y_train_clf)\n",
" dtrain = xgb.DMatrix(X, label=float_labels(y_train_clf))\n",
" dtrain_fft = xgb.DMatrix(X_fft, label=float_labels(y_train_clf))\n",
" bst = xgb.train(boost_params, dtrain, num_boost_round=50)\n",
" bst_fft = xgb.train(boost_params, dtrain_fft, num_boost_round=50)\n",
"\n",
" X_test, X_test_fft = X_test_array_clf\n",
"\n",
" rfc_prob = rfc.predict_proba(X_test)\n",
" rfc_pred = labels[np.argmax(rfc_prob, axis=1)]\n",
"\n",
" rfc_fft_prob = rfc_fft.predict_proba(X_test_fft)\n",
" rfc_fft_pred = labels[np.argmax(rfc_fft_prob, axis=1)]\n",
"\n",
" svc_prob = svc.predict_proba(X_test)\n",
" svc_pred = labels[np.argmax(svc_prob, axis=1)]\n",
"\n",
" svc_fft_prob = svc_fft.predict_proba(X_test_fft)\n",
" svc_fft_pred = labels[np.argmax(svc_fft_prob, axis=1)]\n",
"\n",
" bst_prob = bst.predict(xgb.DMatrix(X_test))\n",
" bst_pred = labels[np.argmax(bst_prob, axis=1)]\n",
"\n",
" bst_fft_prob = bst_fft.predict(xgb.DMatrix(X_test_fft))\n",
" bst_fft_pred = labels[np.argmax(bst_fft_prob, axis=1)]\n",
"\n",
" tot_prob = rfc_prob * rfc_fft_prob * svc_prob * svc_fft_prob * bst_prob * bst_fft_prob\n",
" tot_pred = labels[np.argmax(tot_prob, axis=1)]\n",
"\n",
" res = pd.DataFrame([rfc_pred, svc_pred, rfc_fft_pred, svc_fft_pred, bst_pred, bst_fft_pred, tot_pred, y_test_clf]).T\n",
"\n",
" res.columns = 'rfc', 'svc', 'rfc_fft', 'svc_fft', 'bst', 'bst_fft', 'tot', 'true'\n",
"\n",
" def get_res(row):\n",
" counts = row.value_counts()\n",
" if counts.max() >= 4:\n",
" return counts.argmax()\n",
" else:\n",
" return row['svc']\n",
"\n",
" res['most_common'] = res.iloc[:, :6].apply(lambda row: row.value_counts().argmax(), axis=1)\n",
"\n",
" res['new'] = res.iloc[:, :5].apply(get_res, axis=1)\n",
"\n",
" probs = np.dstack([rfc_prob,\n",
" rfc_fft_prob,\n",
" svc_prob,\n",
" svc_fft_prob,\n",
" bst_prob,\n",
" bst_fft_prob])\n",
"\n",
" res['svc_or_else'] = ''\n",
"\n",
" res.loc[svc_prob.max(axis=1) > 0.5, 'svc_or_else'] = svc_pred[svc_prob.max(axis=1) > 0.5]\n",
"\n",
" res.loc[svc_prob.max(axis=1) <= 0.67, 'svc_or_else'] = res.loc[svc_prob.max(axis=1) <= 0.67, 'tot']\n",
"\n",
" columns = [u'rfc', u'svc', u'rfc_fft', u'svc_fft', u'bst', u'bst_fft', u'tot', \n",
" u'most_common', u'new', u'svc_or_else']\n",
"\n",
" for column in columns:\n",
" big_res[column].append(accuracy_score(res.true, res[column]))\n",
" print(\"done 1 more\", i)\n",
" \n",
"print(\"result:\")\n",
"pd.Series({u'bst': 0.91600000000000004,\n",
" u'bst_fft': 0.91799999999999993,\n",
" u'most_common': 0.93200000000000005,\n",
" u'new': 0.90549999999999997,\n",
" u'rfc': 0.91549999999999998,\n",
" u'rfc_fft': 0.91750000000000009,\n",
" u'svc': 0.84599999999999986,\n",
" u'svc_fft': 0.87800000000000011,\n",
" u'svc_or_else': 0.9235000000000001,\n",
" u'tot': 0.9375})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Regression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using the same method, I tried different models, but didn't get very good results.\n",
"\n",
"At one point I accidentally got much better, result, because **as a result of a typo, I wrote SVC instead of SVR, actually doing classification instead of regression**!\n",
"\n",
"It actually works since there are not many different possible values for the concentration. I then tried two methods\n",
"- other classifiers. They did not perform as well.\n",
"- correcting the regressor predictions to the closest possible values (amongst seen values). That lead to better results but not as good as classification."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below is a plot of the relative absolute error as a function of the true concentration:\n",
"\n",
"<img src='https://dl.dropboxusercontent.com/s/fpf5lxeu4y7ilja/Capture%20d%27%C3%A9cran%202016-12-15%2015.39.23.png?dl=0' width='500px'/>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The error is especially big when the concentration is small, so that we need to focus on small concentration to get better results."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
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