Applied Data Analysis and Machine Learning¶

Introduction¶

Probability theory and statistical methods play a central role in Science. Nowadays we are surrounded by huge amounts of data. For example, there are more than one trillion web pages; more than one hour of video is uploaded to YouTube every second, amounting to years of content every day; the genomes of 1000s of people, each of which has a length of more than a billion base pairs, have been sequenced by various labs and so on. This deluge of data calls for automated methods of data analysis, which is exactly what machine learning aims at providing.

Learning outcomes¶

This course aims at giving you insights and knowledge about many of the central algorithms used in Data Analysis and Machine Learning. The course is project based and through various numerical projects and weekly exercises you will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. Both supervised and unsupervised methods will be covered. The emphasis is on a frequentist approach with an emphasis on predictions and correaltions. However, we will try, where appropriate, to link our machine learning models with a Bayesian approach as well. You will learn to develop and structure large codes for studying different cases where Machine Learning is applied to, get acquainted with computing facilities and learn to handle large scientific projects. A good scientific and ethical conduct is emphasized throughout the course. More specifically, after this course you will

Learn about basic data analysis, statistical analysis, Bayesian statistics, Monte Carlo sampling, data optimization and machine learning;
Be capable of extending the acquired knowledge to other systems and cases;
Have an understanding of central algorithms used in data analysis and machine learning;
Understand linear methods for regression and classification, from ordinary least squares, via Lasso and Ridge to Logistic regression and Kernel regression;
Learn about neural networks and deep learning methods for supervised and unsupervised learning. Emphasis on feed forward neural networks, convolutional and recurrent neural networks;
Learn about about decision trees, random forests, bagging and boosting methods;
Learn about support vector machines and kernel transformations;
Reduction of data sets and unsupervised learning, from PCA to clustering;
Autoencoders and Reinforcement Learning;
Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++ and/or Fortran (Fortran2003 or later).

Prerequisites and background¶

Basic knowledge in programming and mathematics, with an emphasis on linear algebra. Knowledge of Python or/and C++ as programming languages is strongly recommended and experience with Jupyter notebooks is recommended. Required courses are the equivalents to the University of Oslo mathematics courses MAT1100, MAT1110, MAT1120 and at least one of the corresponding computing and programming courses INF1000/INF1110 or MAT-INF1100/MAT-INF1100L/BIOS1100/KJM-INF1100. Most universities offer nowadays a basic programming course (often compulsory) where Python is the recurring programming language. We recommend also refreshing your knowledge on Statistics and Probability theory. The lecture notes at https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html offer a review of Statistics and Probability theory.

The course has two central parts¶

Statistical analysis and optimization of data
Machine learning

Statistical analysis and optimization of data¶

The following topics will be covered

Basic concepts, expectation values, variance, covariance, correlation functions and errors;
Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;
Central elements of Bayesian statistics and modeling;
Gradient methods for data optimization,
Monte Carlo methods, Markov chains, Gibbs sampling and Metropolis-Hastings sampling;
Estimation of errors and resampling techniques such as the cross-validation, blocking, bootstrapping and jackknife methods;
Principal Component Analysis (PCA) and its mathematical foundation

Machine learning¶

The following topics will be covered:

Linear Regression and Logistic Regression;
Neural networks and deep learning, including convolutional and recurrent neural networks
Decisions trees, Random Forests, Bagging and Boosting
Support vector machines
Bayesian linear and logistic regression
Boltzmann Machines
Unsupervised learning Dimensionality reduction, PCA, k-means and clustering
Autoenconders

Hands-on demonstrations, exercises and projects aim at deepening your understanding of these topics.

Computational aspects play a central role and you are expected to work on numerical examples and projects which illustrate the theory and various algorithms discussed during the lectures. We recommend strongly to form small project groups of 2-3 participants, if possible.

Required Technologies¶

Course participants are expected to have their own laptops/PCs. We use Git as version control software and the usage of providers like GitHub, GitLab or similar are strongly recommended. If you are not familiar with Git as version control software, the following video may be of interest, see https://www.youtube.com/watch?v=RGOj5yH7evk&ab_channel=freeCodeCamp.org

We will make extensive use of Python as programming language and its myriad of available libraries. You will find Jupyter notebooks invaluable in your work. You can run R codes in the Jupyter/IPython notebooks, with the immediate benefit of visualizing your data. You can also use compiled languages like C++, Rust, Julia, Fortran etc if you prefer. The focus in these lectures will be on Python.

If you have Python installed and you feel pretty familiar with installing different packages, we recommend that you install the following Python packages via pip as

pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow

For OSX users we recommend, after having installed Xcode, to install brew. Brew allows for a seamless installation of additional software via for example

brew install python3

For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution, you can use pip as well and simply install Python as

sudo apt-get install python3

Python installers¶

If you don’t want to perform these operations separately and venture into the hassle of exploring how to set up dependencies and paths, we recommend two widely used distrubutions which set up all relevant dependencies for Python, namely

Anaconda:https://docs.anaconda.com/,

which is an open source distribution of the Python and R programming languages for large-scale data processing, predictive analytics, and scientific computing, that aims to simplify package management and deployment. Package versions are managed by the package management system conda.

Enthought canopy:https://www.enthought.com/product/canopy/

is a Python distribution for scientific and analytic computing distribution and analysis environment, available for free and under a commercial license.

Furthermore, Google’s Colab:https://colab.research.google.com/notebooks/welcome.ipynb is a free Jupyter notebook environment that requires no setup and runs entirely in the cloud. Try it out!

Useful Python libraries¶

Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)

NumPy:https://www.numpy.org/ is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays
The pandas:https://pandas.pydata.org/ library provides high-performance, easy-to-use data structures and data analysis tools
Xarray:http://xarray.pydata.org/en/stable/ is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun!
Scipy:https://www.scipy.org/ (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering.
Matplotlib:https://matplotlib.org/ is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.
Autograd:https://github.com/HIPS/autograd can automatically differentiate native Python and Numpy code. It can handle a large subset of Python’s features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives
JAX https://jax.readthedocs.io/en/latest/index.html has now more or less replaced Autograd. JAX is Autograd and XLA, brought together for high-performance numerical computing and machine learning research. It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.
SymPy:https://www.sympy.org/en/index.html is a Python library for symbolic mathematics.
scikit-learn:https://scikit-learn.org/stable/ has simple and efficient tools for machine learning, data mining and data analysis
TensorFlow:https://www.tensorflow.org/ is a Python library for fast numerical computing created and released by Google
Keras:https://keras.io/ is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano
And many more such as pytorch:https://pytorch.org/, Theano:https://pypi.org/project/Theano/ etc

Applied Data Analysis and Machine Learning