updating p3

doc/src/Projects/2021/Project3/Project3.do.txt

@@ -10,10 +10,10 @@ DATE: today
 For project 3, you can propose own data sets that relate to your research interests or just use existing data sets from say
 o "Kaggle":"https://www.kaggle.com/datasets" 
 o The "University of California at Irvine (UCI) with its  machine learning repository":"https://archive.ics.uci.edu/ml/index.php".
-
+o Or other sources.
 
 The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:
-o Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among _linear regression (including Ridge and Lasso)_, _Logistic Regression_, _Neural Networks_, _Convolution Neural Networks_, _Recurrent Neural Networks_, _Support Vector Machines_ and _Decision Trees, Random Forests_, _Bagging and Boosting_. You could for example explore  all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into _convolutional neural networks_ or _recurrent neural networks_, or extensions of neural networkds, feel free to do so. 
+o Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among _linear regression (including Ridge and Lasso)_, _Logistic Regression_, _Neural Networks_, _Convolution Neural Networks_, _Recurrent Neural Networks_, _Adversarial Neural Networks_, _Support Vector Machines_ and _Decision Trees, Random Forests, Bagging and Boosting_. You could for example explore  all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into _convolutional neural networks_ or _recurrent neural networks_, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attendtion to supervised learning. The methods we have explored as _Principal Component Analysis_ and _k-means Clustering_.
 
 For Boosting, feel also free to write your own codes.
 
@@ -27,11 +27,14 @@ o If possible, you should link the data sets with exisiting research and analyse
 
 o A critical assessment of the methods with ditto perspectives and recommendations is also something you need to include.
 
-All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc.. 
+All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..
 
-We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.. 
+We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.
 
-This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides "from week 43":"https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43.html" and/or the textbook by "Yadav et al":"https://www.springer.com/gp/book/9789401798150".
+This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides "from week 43":"https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week42.html" and/or the textbook by "Yadav et al":"https://www.springer.com/gp/book/9789401798150".
+
+
+_Note_: Project 3 has an additional exercise which can give you an additional score of 30 (thirty) points. These are added to the total score from all projects. See below for the additional exercise. 
 
 =====  The basic structure of your project =====
 
@@ -168,6 +171,32 @@ eigenvalues. Compare with the solution from numerical diagonalization with stand
 Finally, present a critical assessment of the methods you have studied and discuss the potential for the solving differential equations and eigenvalue problems with machine learning methods. 
 
 
+===== Additonal (optional) exercise, adding 30 more points to final score =====
+
+This exercise can be done independently of the other tasks. Here you
+can also choose the data set you want to use. Furthermore, you can use
+your codes from projects 1 and 2 as well as the codes here or simply use
+libraries like _Scikit-Learn_, _Tensorflow_ or similar.
+
+Your task is to perform an analysis of the bias-variance tradeoff
+using at least three of the main sets  algorithms we have discussed in this
+course. We will limit ourselves to a regression problem (fitting). You
+are free to choose between bootstrap for resampling (recommended) or
+cross-validation in order to get the best possible estimates. The
+methods you could study are Linear Regression (OLS, Ridge and Lasso),
+deep learning (feed forward neural networks and/or recurrent neural
+networks), Ensemble methods (decision trees, bagging, random forests
+and boosting) and support vector machines.
+
+Study the bias-variance tradeoff for at least three of these sets of
+algorithms for a data set of your choice as function of the complexity
+of your model.  Comment and discuss the results. Discuss the pros and
+cons of the various methods. Are there some methods which provide both
+low variance and low bias?
+
+
+
+
 ===== Introduction to numerical projects =====
 
 Here follows a brief recipe and recommendation on how to write a report for each