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@@ -6,14 +6,24 @@ DATE: today
===== Introduction =====
Statistics, data science and machine learning form important fields of
research in modern science. They describe how to learn and make
predictions from data, as well as allowing us to extract important
correlations about physical process and the underlying laws of motion
in large data sets. The latter, big data sets, appear frequently in
essentially all disciplines, from the traditional Science, Technology,
Mathematics and Engineering fields to Life Science, Law, education
research, the Humanities and the Social Sciences.
During the last two decades there has been a swift and amazing
development of Machine Learning techniques and algorithms that impact
many areas in not only Science and Technology but also the Humanities,
Social Sciences, Medicine, Law, indeed, almost all possible
disciplines. The applications are incredibly many, from self-driving
cars to solving high-dimensional differential equations or complicated
quantum mechanical many-body problems. Machine Learning is perceived
by many as one of the main disruptive techniques nowadays.
Statistics, Data science and Machine Learning form important
fields of research in modern science. They describe how to learn and
make predictions from data, as well as allowing us to extract
important correlations about physical process and the underlying laws
of motion in large data sets. The latter, big data sets, appear
frequently in essentially all disciplines, from the traditional
Science, Technology, Mathematics and Engineering fields to Life
Science, Law, education research, the Humanities and the Social
Sciences.
It has become more
and more common to see research projects on big data in for example
@@ -73,7 +83,7 @@ of algorithms and methods we will discuss.
!split
===== Learning outcomes =====
These setsof lectures aim at giving you an overview of central aspects of
These sets of lectures aim at giving you an overview of central aspects of
statistical data analysis as well as some of the central algorithms
used in machine learning. We will introduce a variety of central
algorithms and methods essential for studies of data analysis and
@@ -81,40 +91,40 @@ machine learning.
Hands-on projects and experimenting with data and algorithms plays a central role in
these lectures, and our hope is, through the various
projects and exercies, to expose you to fundamental
projects and exercises, to expose you to fundamental
research problems in these fields, with the aim to reproduce state of
the art scientific results. You will learn to develop and
structure large codes for studying these systems, get acquainted with
structure codes for studying these systems, 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, you will
o learn about basic data analysis, Bayesian statistics, Monte Carlo methods, data optimization and machine learning;
o be capable of extending the acquired knowledge to other systems and cases;
o Learn about basic data analysis, Bayesian statistics, Monte Carlo methods, data optimization and machine learning;
o Be capable of extending the acquired knowledge to other systems and cases;
o Have an understanding of central algorithms used in data analysis and machine learning;
o Gain knowledge of central aspects of Monte Carlo methods, Markov chains, Gibbs samplers and their possible applications, from numerical integration to simulation of stock markets;
o Understand methods for regression and classification;
o Learn about neural network, genetic algorithms and Boltzmann machines;
o 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++, in addition to a basic knowledge of linear algebra (typically taught during the first one or two years of undergraduate studies).
There are several topics we will cover here, spanning from a
statistical data analysis and its basic concepts such expectation
There are several topics we will cover here, spanning from
statistical data analysis and its basic concepts such as expectation
values, variance, covariance, correlation functions and errors, via
well-known probability distribution functions like uniform
well-known probability distribution functions like the uniform
distribution, the binomial distribution, the Poisson distribution and
simple and multivariate normal distributions to central elements of
Bayesian statistics and modeling. We will also remind the reader about
central elements from linear algebra and standard methods based on
linear algebra used to fit functions such Cubic splines and gradient
methods for data optimization and the Singular-value decomposition and
linear algebra used to optimize (minimize) functions (the family of gradient descent methods)
and the Singular-value decomposition and
least square methods for parameterizing data.
We will also cover Monte Carlo methods, Markov chains, well-known
algorithms for sampling stochastic events like the Metropolis-Hastings
and Gibbs sampling methods. An important aspect of all our
calculations is a proper estimation of errors. Here we will also
discuss famous resampling techniques like the blocking, bootstrapping
and jackknife methods.
discuss famous resampling techniques like the blocking, the bootstrapping
and the jackknife methods and the infamous bias-variance tradeoff.
The second part of the material covers several algorithms used in
machine learning.
@@ -150,8 +160,12 @@ desired output of a system. Some of the most common tasks are:
The methods we cover have three main topics in common, irrespective of
whether we deal with supervised or unsupervised learning. The first
ingredient is normally our data set (which can be subdivided into
training and test data), the second item is a model which is normally a
function of some parameters. The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.
training and test data), the second item is a model which is normally
a function of some parameters. The model reflects our knowledge of
the system (or lack thereof). As an example, if we know that our data
show a behavior similar to what would be predicted by a polynomial,
fitting our data to a polynomial of some degree would then determin
our model.
The last ingredient is a so-called _cost_
function which allows us to present an estimate on how good our model
@@ -162,12 +176,11 @@ statistical foundation discussed above, with elements from data
analysis, stochastic processes etc. We will discuss the following
machine learning algorithms
o Linear regression and its variants, in essence polynomial regression
o Decision tree algorithms, from simpler to more complex ones
o Nearest neighbors models
o Linear regression and its variants
o Decision tree algorithms, from single trees to random forests
o Bayesian statistics and regression
o Support vector machines and finally various variants of
o Artifical neural networks and deep learning
o Artifical neural networks and deep learning, including convolutional neural networks and Bayesian neural networks
o Networks for unsupervised learning using for example reduced Boltzmann machines.
@@ -176,21 +189,16 @@ o Networks for unsupervised learning using for example reduced Boltzmann machine
Python plays nowadays a central role in the development of machine
learning techniques and tools for data analysis. In particular, seen
the wealth of machine learning and data analysis packages written in
the wealth of machine learning and data analysis libraries written in
Python, easy to use libraries with immediate visualization(and not the
least impressive galleries of existing example), the popularity of the
least impressive galleries of existing examples), the popularity of the
Jupyter notebook framework with the possibility to run _R_ codes or
compiled programs written in C++, and much more made our choice of
programming language for this series of lectures of easy. However,
since the focus here is not only on using existing Python tools such
as _scikit-learn_ or _tensorflow_, but also on developing your own
programming language for this series of lectures easy. However,
since the focus here is not only on using existing Python libraries such
as _Scikit-Learn_ or _Tensorflow_, but also on developing your own
algorithms and codes, we will as far as possible present many of these
algorithms eithers a Python codes or C++ codes. Finally, we will, as
far as possible keep parallel versions of the data analysis and
machine larning programming aspects in _R_ as
well. "R":"https://www.r-project.org/" is a language and environment
for statistical computing and graphics which is widely used in
statistics and mathematics applications.
algorithms either as a Python codes or C++ or Fortran (or other languages) codes.
The reason we also focus on compiled languages like C++ (or
Fortran), is that Python is still notoriously slow when we do not
@@ -198,7 +206,7 @@ utilize highly streamlined computational libraries like
"Lapack":"http://www.netlib.org/lapack/" or other numerical libraries
written in compiled languages (many of these libraries are written in
Fortran). Although a project like "Numba":"https://numba.pydata.org/"
holds great promise for speeding up the unrolling of lengthy loops, C+
holds great promise for speeding up the unrolling of lengthy loops, C++
and Fortran are presently still the performance winners. Numba gives
you potentially the power to speed up your applications with high
performance functions written directly in Python. In particular,
@@ -219,14 +227,14 @@ existing data files or provide code examples which produce the data to
be analyzed. Most of the applications we will discuss deal with
small data sets (less than a terabyte of information) and can easily
be analyzed and tested on standard off the shelf laptops you find in general
grocery stores.
stores.
===== Data handling, machine learning and ethical aspects =====
In most of the cases we will study, we will either generate the data
to analyze ourselves (both for supervised learning and unsupervised
learning) or we will recur again and again to data present in say
_scikit-learn_ or _tensorflow_. Many of the examples we end up
_Scikit-Learn_ or _Tensorflow_. Many of the examples we end up
dealing with are from a privacy and data protection point of view,
rather inoccuous and boring results of numerical
calculations. However, this does not hinder us from developing a sound
@@ -241,7 +249,7 @@ repositories like "Github":"https://github.com/",
and data sets we have used, freely and easily accessible to a wider
community. This helps us almost automagically in making our science
reproducible. The large open-source development communities involved
in say "Scikit-learn":"http://scikit-learn.org/stable/",
in say "Scikit-Learn":"http://scikit-learn.org/stable/",
"Tensorflow":"https://www.tensorflow.org/",
"PyTorch":"http://pytorch.org/" and "Keras":"https://keras.io/", are
all excellent examples of this. The codes can be tested and improved
@@ -250,23 +258,23 @@ developing data analysis and machine learning tools. It is much
easier today to gain traction and acceptance for making your science
reproducible. From a societal stand, this is an important element
since many of the developers are employees of large public institutions like
universities and research labs. Our taxpayer do deserve to get
universities and research labs. Our fellow taxpayers do deserve to get
something back for their bucks.
However, this more mechanical aspect of the ethics of science (in
particular the reproducibility of scientific results) is something
which is obvious and everybody should do as part of the dialectics of
which is obvious and everybody should do so as part of the dialectics of
science. The fact that many scientists are not willing to share their codes or
data is detrimental to the scientific discourse.
Before we proceed, we should add a disclaimer. Even though
we may dream of computers developing some kind of higher learning
capabilities, at the end (even if the artificial intelligence
community keeps touting our ears full of fancy futuristic avenues), it is we
community keeps touting our ears full of fancy futuristic avenues), it is we, yes you reading these lines,
who end up constructing and instructing, via various algorithms, the
computers. Self-driving cars for example, rely on sofisticated
machine learning approaches. Self-driving cars for example, rely on sofisticated
programs which take into account all possible situations a car can
encounter. In addition, extensive usage of training datas from GPS
encounter. In addition, extensive usage of training data from GPS
information, maps etc, are typically fed into the software for
self-driving cars. Adding to this various sensors and cameras that
feed information to the programs, there are zillions of ethical issues
@@ -276,8 +284,8 @@ For self-driving cars, where basically many of the standard machine
learning algorithms discussed here enter into the codes, at a certain
stage we have to make choices. Yes, we , the lads and lasses who wrote
a program for a specific brand of a self-driving car. As an example,
a most carmakers have as their utmost priority the security of the
driver and the accompanying passengers. A famous carmaker, which is
all carmakers have as their utmost priority the security of the
driver and the accompanying passengers. A famous European carmaker, which is
one of the leaders in the market of self-driving cars, had _if_
statements of the following type: suppose there are two obstacles in
front of you and you cannot avoid to collide with one of them. One of
@@ -287,9 +295,9 @@ opt for the hitting the small folks instead of the monstertruck, since
the likelihood of surving a collision with our future citizens, is
much higher.
This brings us leads then to serious ethical aspects. Why should we
This leads to serious ethical aspects. Why should we
opt for such an option? Who decides and who is entitled to make such
choices? Keep in mind that many of the algorithms you will about in
choices? Keep in mind that many of the algorithms you will encounter in
this series of lectures or hear about later, are indeed based on
simple programming instructions. And you are very likely to be one of
the people who may end up writing such a code. Thus, developing a
@@ -301,15 +309,16 @@ you analyze data on economic inequalities, who guarantees that you are
not weighting some data in a particular way, perhaps because you dearly want a
specific conclusion which may support your political views?
We do not have the answers here, but we want you think over these
topics in a more overarching way. A statistical data analysis with
its dry numbers and graphs meant to guide the eye, do not necessarily
We do not have the answers here, nor will we venture into a deeper
discussions of these aspects, but we want you think over these topics
in a more overarching way. A statistical data analysis with its dry
numbers and graphs meant to guide the eye, does not necessarily
reflect the truth, whatever that is. As a scientist, and after a
university education, you are supposedly a better citizen, with an
improved critical view and understanding of the scientific method, and
perhaps some deeper understandings of the ethics of science at
perhaps some deeper understanding of the ethics of science at
large. Use these insights. Be a critical citizen. You owe it to our
societies.
society.