

Differential Equations in Data Science - jmilinovich
http://blog.urx.com/post/79290681131/differential-equations-in-data-science?utm_source=blog&utm_medium=hn&utm_campaign=differentialsindatascience

======
jamessb
Several things about this just seem odd:

\- the second example given of an ODE is Black-Scholes (which is a PDE)

\- ODE's are said to be missing from the "top 10 data science algorithms", but
the actual title of the linked paper is "Top 10 algorithms in _data mining_ ".
Clearly, ODEs are not data mining algorithms and would not belong on such a
list.

\- it repeatedly refers to the "derivate of a function", instead of
"derivative of a function"

\- it introduces the matrix exponential without giving a definition or link to
wikipedia (it's important to at least mention in passing that it is _not_
formed by taking the exponential of each matrix element)

\- it says that "They're common constructs used in physics (Newton's law is a
second-order ODE), chemistry and biology where it's often easier to measure
the derivate of a function (e.g., velocity) than the function itself (e.g.,
position)". I'd have said that differential equations are ubiquitous in
science and engineering because they can be used to describe how quantities
change over (continuous) time.

etc.

~~~
jisaacso
Good catches. One point,

"because they can be used to describe how quantities change over (continuous)
time"

I would argue that time series problems are common throughout data science.
Uber's prediction of arrival time, Kaggle flight time prediction, etc.

------
cwal37
I recently finished my masters in environmental science, which was diffeq
heavy, and got a position working with energy data and doing some economic
modeling and operations research. I was a bit surprised that the project I
came into doesn't seem to use any diffeq in its broad pieces, although it's
possible I just haven't come across it yet.

We're doing most of our analysis in python with the scipy stack, so maybe I'll
try a couple ODE-based projections this afternoon.

~~~
jisaacso
That's awesome to hear! Keep me posted as you work through some projects. I'm
curious to hear how ODEs can help in environmental science.

~~~
cwal37
Differential equations basically _are_ environmental science. I happen to work
more in econometrics now, but things like population/ecology,
environmental/pollution/waste engineering, and environmental chemistry
research are chock full of papers and projects driven by differential
equations.

------
alook
It's exciting to see under-appreciated math techniques in use for modern-day
data science!

~~~
trhway
ODE is an "under-appreciated math technique"? Where? In math or in "modern-day
data science"?

~~~
jisaacso
I would say it's under-appreciated in modern data science. It's well
appreciated in applied mathematics.

