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Finding sparse solutions to linear systems
Dec 9, 2015 in math machinelearning optimization
This post is a part 2 of a 3 part series: Part I, Part II, Part III
We often have fewer measurements than unknowns, which happens all the time in genomics and medical imaging. For example, we might be collecting 8,000 gene measurements in 300 patients and we’d like to determine which ones are most important in determining cancer.
This means that we typically have an underdetermined system because we’re collecting more measurement than unknowns. This is an unfavorable situation – there are infinitely may solutions to this problem. However, in the case of breast cancer, biological intuition might tell us that most of the 8,000 genes aren’t important and have zero important in cancer expression.
How do we enforce that most of the variables are 0? This post will try and give intuition for the problem formulation and dig into the algorithm to solve the posed problem. I’ll use a realworld cancer dataset^{1} to predict which genes are important for cancer expression. It should be noted that we’re more concerned with the type of solution we obtain rather than how well it performs.

This data set is detailed in the section titled Predicting Breast Cancer ↩


Stepping from Matlab to Python
Sep 1, 2015 in python
It’s not a big leap; it’s one small step. There’s only a little to pick up and there’s not a huge difference in use or functionality. The difference is so small you can switch and just google any conversion issues you have: they’re so small you’ll have no trouble finding the appropriate functions/syntax.
There is a wrapper package in Python with the aim of providing a Matlablike interface that is well suited for numerical linear algebra. This package is called pylab and wraps NumPy, SciPy and matplotlib. When I use pylab, this is how similar my Python and Matlab code is:
Python even has a matrix multiplication operator! Python 3.5 introduces the matrix multiplication operator
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detailed in PEP 465. Python is remarkably well suited for developing numerical algorithms – what else does Python offer?

Computer color is only kinda broken
Apr 23, 2015 in images imagecompression dsp

Common mathematical misconceptions
Jul 31, 2014 in math
When I heard course names for higher mathematical classes during high school and even part of college, it seemed as if they were teaching something simple that I learned back in middle school. I knew that couldn’t be the case, and three years of college have taught me otherwise.
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Fourier transforms and optical lenses
The Fourier transform and it’s closely related cousin the discrete time Fourier transform (computed by the FFT) is a powerful mathematical concept. It breaks an input signal down into it’s frequency components. The best example is lifted from Wikipedia.
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