From 46fae93569f1a0b9256f69a232ef1f3e298306c8 Mon Sep 17 00:00:00 2001 From: Klaus Reygers Date: Fri, 10 Mar 2023 14:19:06 +0100 Subject: [PATCH] initial set of slides corresponding to 2022 version --- slides/.gitignore | 1 + slides/Makefile | 10 + slides/README.md | 2 + slides/copy_slides.sh | 6 + slides/decision_trees.md | 347 +++++ ...asics_galton_linear_regression_iminuit.pdf | Bin 0 -> 14629 bytes .../03_ml_basics_log_regr_heart_disease.pdf | Bin 0 -> 11449 bytes .../03_ml_basics_logistic_regression.pdf | Bin 0 -> 13081 bytes slides/figures/L1vsL2.pdf | Bin 0 -> 20766 bytes slides/figures/activation_functions.png | Bin 0 -> 254718 bytes slides/figures/adversarial_attack.png | Bin 0 -> 2417255 bytes slides/figures/ai_history.png | Bin 0 -> 394752 bytes slides/figures/ai_ml_dl.pdf | Bin 0 -> 216631 bytes slides/figures/ann.png | Bin 0 -> 190304 bytes slides/figures/anomaly_detection.png | Bin 0 -> 125756 bytes slides/figures/autoencoder_example.pdf | Bin 0 -> 104287 bytes 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files of all newly edited .md files + +SRCS := $(wildcard *.md) +PDF := $(SRCS:%.md=%.pdf) + +OPT := --pdf-engine=xelatex --variable mainfont="Helvetica" --variable sansfont="Helvetica" -t beamer -s -fmarkdown-implicit_figures --template=template.beamer --highlight-style=kate +all: ${PDF} + +%.pdf: %.md + pandoc $(OPT) --output=$@ $< diff --git a/slides/README.md b/slides/README.md new file mode 100644 index 0000000..c22dd99 --- /dev/null +++ b/slides/README.md @@ -0,0 +1,2 @@ +Pandoc slides example following style of [Stefan Wunsch's CERN IML workhsop presenation](https://github.com/stwunsch/iml_keras_workshop) on [keras](https://keras.io/) (see slides folder) + diff --git a/slides/copy_slides.sh b/slides/copy_slides.sh new file mode 100755 index 0000000..89a426e --- /dev/null +++ b/slides/copy_slides.sh @@ -0,0 +1,6 @@ +# slides (do chgrp machlearn later) +# scp CIPpoolAccess.PDF reygers@rho0:public_html/lectures/2021/ml/transparencies/ +# scp 03_ml_basics.pdf reygers@rho0:public_html/lectures/2021/ml/transparencies/ +# scp 04_decision_trees.pdf reygers@rho0:public_html/lectures/2021/ml/transparencies/ +scp 05_neural_networks.pdf reygers@rho0:public_html/lectures/2021/ml/transparencies/ + diff --git a/slides/decision_trees.md b/slides/decision_trees.md new file mode 100644 index 0000000..06817cd --- /dev/null +++ b/slides/decision_trees.md @@ -0,0 +1,347 @@ +--- +title: | + | Introduction to Data Analysis and Machine Learning in Physics: + | 4. Decisions Trees + +author: "Martino Borsato, Jörg Marks, Klaus Reygers" +date: "Studierendentage, 11-14 April 2022" +--- +## Exercises + +* Exercise 1: Compare different decision tree classifiers + * [`04_decision_trees_ex_1_compare_tree_classifiers.ipynb`](https://nbviewer.jupyter.org/urls/www.physi.uni-heidelberg.de/~reygers/lectures/2022/ml/exercises/04_decision_trees_ex_1_compare_tree_classifiers.ipynb) +* Exercise 2: Apply XGBoost classifier to MAGIC data set + * [`04_decision_trees_ex_2_magic_xgboost_and_random_forest.ipynb`](https://nbviewer.jupyter.org/urls/www.physi.uni-heidelberg.de/~reygers/lectures/2022/ml/exercises/04_decision_trees_ex_2_magic_xgboost_and_random_forest.ipynb) +* Exercise 3: Feature importance +* Exercise 4: Interpret a classifier with SHAP values + +## Decision trees + +\begin{figure} +\centering +\includegraphics[width=0.85\textwidth]{figures/mini_boone_decisions_tree.png} +\end{figure} + +\begin{center} +Leaf nodes classify events as either signal or background +\end{center} + +## Decision trees: Rectangular volumes in feature space + +\begin{figure} +\centering +\includegraphics[width=0.75\textwidth]{figures/decision_trees_feature_space.png} +\end{figure} + +* Easy to interpret and visualize: Space of feature vectors split up into rectangular volumes (attributed to either signal or background) +* How to build a decision tree in an optimal way? + +## Finding optimal cuts + +Separation btw. signal and background is often measured with the Gini index (or Gini impurity): + +$$ G = p (1-p) $$ + +Here $p$ is the purity: +$$ p = \frac{\sum_\mathrm{signal} w_i}{\sum_\mathrm{signal} w_i + \sum_\mathrm{background} w_i}, \quad w_i = \text{weight of event}\; i$$ + +\vfill +\textcolor{gray}{Usefulness of weights will become apparent soon.} + +\vfill +Improvement in signal/background separation after splitting a set A into two sets B and C: +$$ \Delta = W_A G_A - W_B G_B - W_C G_C \quad \text{where} \quad W_X = \sum_{X} w_i $$ + +## Gini impurity and other purity measures +\begin{figure} +\centering +\includegraphics[width=0.7\textwidth]{figures/signal_purity.png} +\end{figure} + + +## Decision tree pruning + +::: columns +:::: {.column width=50%} + +When to stop growing a tree? + +* When all nodes are essentially pure? +* Well, that's overfitting! + +\vspace{3ex} + +Pruning + +* Cut back fully grown tree to avoid overtraining, i.e., replace nodes and subtrees by leaves + +:::: +:::: {.column width=50%} +\begin{figure} +\centering +\includegraphics[width=0.85\textwidth]{figures/tree_pruning_slides.png} +\end{figure} +:::: +::: + +## Single decision trees: Pros and cons + +\textcolor{green}{Pros:} + +* Requires little data preparation (unlike neural networks) +* Can use continuous and categorical inputs + +\vfill + +\textcolor{red}{Cons:} + +* Danger of overfitting training data +* Sensitive to fluctuations in the training data +* Hard to find global optimum +* When to stop splitting? + +## Ensemble methods: Combine weak learners + +::: columns +:::: {.column width=70%} +* Bootstrap Aggregating (Bagging) + * Sample training data (with replacement) and train a separate model on each of the derived training sets + * Classify example with majority vote, or compute average output from each tree as model output + +:::: +:::: {.column width=30%} +$$ y(\vec x) = \frac{1}{N_\mathrm{trees}} \sum_{i=1}^{N_{trees}} y_i(\vec x) $$ +:::: +::: +\vfill +::: columns +:::: {.column width=70%} +* Boosting + * Train $N$ models in sequence, giving more weight to examples not correctly classified by previous model + * Take weighted average to classify examples + +:::: +:::: {.column width=30%} +$$ y(\vec x) = \frac{\sum_{i=1}^{N_\mathrm{trees}} \alpha_i y_i(\vec x)}{\sum_{i=1}^{N_\mathrm{trees}} \alpha_i} $$ +:::: +::: + +## Random forests + +* "One of the most widely used and versatile algorithms in data science and machine learning" +\tiny \textcolor{gray}{arXiv:1803.08823v3} \normalsize +\vfill +* Use bagging to select random example subset +\vfill +* Train a tree, but only use random subset of features at each split + * this reduces the correlation between different trees + * makes the decision more robust to missing data + +## Boosted decision trees: Idea + +\begin{figure} +\centering +\includegraphics[width=0.75\textwidth]{figures/bdt.png} +\end{figure} + +## AdaBoost (short for Adaptive Boosting) + +Initial training sample + +\begin{center} +\begin{tabular}{l l} +$\vec x_1, ..., \vec x_n$: & multivariate event data \\ +$y_1, ..., y_n$: & true class labels, $+1$ or $-1$ \\ +$w_1^{(1)}, ..., w_n^{(1)}$ & event weights +\end{tabular} +\end{center} + +with equal weights normalized as + +$$ \sum_{i=1}^n w_i^{(1)} = 1 $$ + +Train first classifier $f_1$: + +\begin{center} +\begin{tabular}{l l} +$f_1(\vec x_i) > 0$ & classify as signal \\ +$f_1(\vec x_i) < 0$ & classify as background +\end{tabular} +\end{center} + +## AdaBoost: Updating events weights + +Define training sample $k+1$ from training sample $k$ by updating weights: + +$$ w_i^{(k+1)} = w_i^{(k)} \frac{e^{- \alpha_k f_k(\vec x_i) y_i/2}}{Z_k} $$ + +\footnotesize +\textcolor{gray}{$$ i = \text{event index}, \quad Z_k:\; \text{normalization factor so that } \sum_{i=1}^n w_i^{(k)} = 1$$} +\normalsize + +Weight is increased if event was misclassified by the previous classifier + +$\to$ "Next classifier should pay more attention to misclassified events" + + +\vfill +At each step the classifier $f_k$ minimizes error rate: + +$$ \varepsilon_k = \sum_{i=1}^n w_i^{(k)} I(y_i f_k( \vec x_i) \le 0), +\quad I(X) = 1 \; \text{if} \; X \; \text{is true, 0 otherwise} $$ + +## AdaBoost: Assigning the classifier score + +Assign score to each classifier according to its error rate: +$$ \alpha_k = \ln \frac{1 - \varepsilon_k}{\varepsilon_k} $$ + +\vfill + +Combined classifier (weighted average): +$$ f(\vec x) = \sum_{k=1}^K \alpha_k f_k(\vec x) $$ + + + +## Gradient boosting + +Basic idea: + +* Train a first decision tree +* Then train a second one on the residual errors made by the first tree +* And so on + +\vfill + +In slightly more detail: + +* \color{gray} Consider labeled training data: $\{\vec x_i, y_i\}$ +* Model prediction at iteration $m$: $F_m(\vec x_i)$ +* New model: $F_{m+1}(\vec x) = F_m(\vec x) + h_m(\vec x)$ +* Find $h_m(\vec x)$ by fitting it to +$\{(\vec x_1, y_1 - F_m(\vec x_1)), \; (\vec x_2, y_2 - F_m(\vec x_2)), \; ... \; (\vec x_n, y_n - F_m(\vec x_n)) \}$ + +\color{black} + +## Example 1: Predict critical temperature for superconductivty (Regression with XGBoost) (1) +\small +[\textcolor{gray}{04\_decision\_trees\_critical\_temp\_regression.ipynb}](https://nbviewer.jupyter.org/urls/www.physi.uni-heidelberg.de/~reygers/lectures/2022/ml/examples/04_decision_trees_critical_temp_regression.ipynb) +\normalsize + +\vfill + +Superconductivty data set: + +Predict the critical temperature based on 81 material features. +\footnotesize +[\textcolor{gray}{https://archive.ics.uci.edu/ml/datasets/Superconductivty+Data}](https://archive.ics.uci.edu/ml/datasets/Superconductivty+Data) +\normalsize + +\vfill + +From the abstract: + + +We estimate a statistical model to predict the superconducting critical temperature based on the features extracted from the superconductor’s chemical formula. The statistical model gives reasonable out-of-sample predictions: ±9.5 K based on root-mean-squared-error. Features extracted based on thermal conductivity, atomic radius, valence, electron affinity, and atomic mass contribute the most to the model’s predictive accuracy. + +\vfill + +\tiny +[\textcolor{gray}{https://doi.org/10.1016/j.commatsci.2018.07.052}](https://doi.org/10.1016/j.commatsci.2018.07.052) +\normalsize + + +## Example 1: Predict critical temperature for superconductivty (Regression with XGBoost) (2) + +::: columns +:::: {.column width=60%} +\footnotesize +```python +import xgboost as xgb + +XGBreg = xgb.sklearn.XGBRegressor() + +XGBreg.fit(X_train, y_train) + +y_pred = XGBreg.predict(X_test) + +from sklearn.metrics import mean_squared_error +rms = np.sqrt(mean_squared_error(y_test, y_pred)) +print(f"root mean square error {rms:.2f}") +``` + +\textcolor{gray}{This gives:} + +`root mean square error 9.68` +:::: +:::: {.column width=40%} +\vspace{6ex} +![](figures/critical_temperature.pdf) +:::: +::: + +## Exercise 1: Compare different decision tree classifiers + +\small +[\textcolor{gray}{04\_decision\_trees\_ex\_1\_compare\_tree\_classifiers.ipynb}](https://nbviewer.jupyter.org/urls/www.physi.uni-heidelberg.de/~reygers/lectures/2022/ml/exercises/04_decision_trees_ex_1_compare_tree_classifiers.ipynb) + +\vspace{5ex} + +Compare scikit-learns's `AdaBoostClassifier`, `RandomForestClassifier`, and `GradientBoostingClassifier` by plotting their ROC curves for the heart disease data set. \newline + +\vspace{2ex} + +Is there a classifier that clearly performs best? + + +## Exercise 2: Apply XGBoost classifier to MAGIC data set + +\small +[\textcolor{gray}{04\_decision\_trees\_ex\_2\_magic\_xgboost\_and\_random\_forest.ipynb}](https://nbviewer.jupyter.org/urls/www.physi.uni-heidelberg.de/~reygers/lectures/2022/ml/exercises/04_decision_trees_ex_2_magic_xgboost_and_random_forest.ipynb) +\normalsize + +\footnotesize +```python +# train XGBoost boosted decision tree +import xgboost as xgb +XGBclassifier = xgb.sklearn.XGBClassifier(nthread=-1, seed=1, n_estimators=1000) +``` +\normalsize + +\small +a) Plot predicted probabilities for the test sample for signal and background events (\texttt{plt.hist}) +b) Which is the most important feature for discriminating signal and background according to XGBoost? \ +Hint: use plot_impartance from XGBoost (see [XGBoost plotting API](https://xgboost.readthedocs.io/en/latest/python/python_api.html)). Do you get the same answer for all three performance measures provided by XGBoost (“weight”, “gain”, or “cover”)? +c) Visualize one decision tree from the ensemble (let's say tree number 10). For this you need the the graphviz package (`pip3 install graphviz`) +d) Compare the performance of XGBoost with the [**random forest classifier**](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) from [**scikit learn**](https://scikit-learn.org/stable/index.html). Plot signal and background efficiency for both classifiers in one plot. Which classifier performs better? +\normalsize + + +## Exercise 3: Feature importance + +\small +[\textcolor{gray}{04\_decision\_trees\_ex\_3\_magic\_feature\_importance.ipynb}](https://nbviewer.jupyter.org/urls/www.physi.uni-heidelberg.de/~reygers/lectures/2022/ml/exercises/04_decision_trees_ex_3_magic_feature_importance.ipynb) +\normalsize + +\vspace{3ex} + +Evaluate the importance of each of the $n$ features in the training of the XGBoost classifier for the MAGIC data set by dropping one of the features. This gives $n$ different classifiers. Compare the performance of these classifiers using the AUC score. + + +## Exercise 4: Interpret a classifier with SHAP values + +SHAP (SHapley Additive exPlanations) are a means to explain the output of any machine learning model. [Shapeley values](https://en.wikipedia.org/wiki/Shapley_value) are a concept that is used in cooperative game theory. They are named after Lloyd Shapley who won the Nobel Prize in Economics in 2012. + +\vfill + +Use the Python library [`SHAP`](https://shap.readthedocs.io/en/latest/index.html) to quantify the feature importance. + +a) Study the documentation at [https://shap.readthedocs.io/en/latest/tabular_examples.html](https://shap.readthedocs.io/en/latest/tabular_examples.html) + +b) Create a summary plot of the feature importance in the MAGIC data set with `shap.summary_plot` for the XGBoost classifier of exercise 2. What are the three most important features? + +c) Do the same for the superconductivity data set? 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