PCA from Scratch
Principal Component Analysis (PCA) is a technique for linear data
visualization and general dimensionality reduction. The technique
is based on decomposition into eigenvectors and eigenvalues.
Eigenvectors and eigenvalues can be explained and exemplified with
reasonable ease. Yet, to calculate them from a matrix can be quite
Sample Bias Derivation
Statistics over a population are well defined but when all the data
we have is a collected sample of the population we need to account
for issues with the collection of the sample. The simplest
correction is to subtract one from the number of data points when
calculating the statistics. That "minus one" seem quite arbitrary
at first but there is a lot more theory behind that value than it
Least Squares Derivation
Least Squares is quite and old technique, likely the eighteen
century or even as early as Newton, but still is the basis for most
regressions. The derivation of the technique in a few dimensions
can be done by hand and then extrapolated into further
MOOC Confidence Analysis - Sustainable Energy Access
Statistical Analysis of MOOC Data. We take data from a MOOC
(Massive Online Open Courses) platform and build statistics on
participants of the course. Notably statistics on the attendance
of the course and the confidence of participants in applying the
knowledge in the material.
MOOC Confidence Analysis - SEA on a different MOOC platform
Given a new dataset one should be able to write only the parts that
fit the data model and the analysis part should just work on the
new dataset - perhaps with minimal tweaks. This is an example of
such new dataset analysis, which builds the same data model using
data collected from a different MOOC platform.
Entropy is a measure of information. When faced with a prediction,
e.g. in machine learning, one uses known information to make a
prediction. In linear problems such predictive information can be
well represented by entropy. In non-linear problems on the other
hand different entropic forms are needed.
Non-extensive Entropy is better suited to describe learning systems
than plain Entropy. Notably because plain entropy is a special
case of non-extensive entropy. Parallels can be drawn between
problem linearity and entropic forms.