Sciency stuff

An IPython notebook on the linear perceptron

The jupyter notebook was used as a resource in the MIT class “Deep Learning for Self-Driving Cars”. 🙂

R196, Hilbert's Hotel

Just mirroring a post from the other blog.

Here is an IPython notebook with an implementation of the linear percepton algorithm.

Details will follow in another post and I give a general idea of what it does in the notebook but here is what the picture looks like.

Assuming that you have a set of points and you want to find a line that separates the points into different categories, this algorithm is one way to do this. It picks an initial line and moves it around the space until it finds a good separator of the set. At the end, the result should look like the example below.


You can also fork that notebook on github.

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Sciency stuff

Abstractions in math

Sciency stuff

Academia, Love Me Back


My name is Tiffany Martínez. As a McNair Fellow and student scholar, I’ve presented at national conferences in San Francisco, San Diego, and Miami. I have crafted a critical reflection piece that was published in a peer-reviewed journal managed by the Pell Institute for the Study of Higher Education and Council for Opportunity in Education. I have consistently juggled at least two jobs and maintained the status of a full-time student and Dean’s list recipient since my first year at Suffolk University. I have used this past summer to supervise a teen girls empower program and craft a thirty page intensive research project funded by the federal government. As a first generation college student, first generation U.S. citizen, and aspiring professor I have confronted a number of obstacles in order to earn every accomplishment and award I have accumulated. In the face of struggle, I have persevered and continuously produced…

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At what point does mathematics get hard?

There is a point where math gets hard for anybody and everybody. For some it’s high school, for others college, undergraduate or graduate study, or even research-level math, and there most problems are really hard.

Do not assume that 90’s in all math classes at high school imply that you won’t find any difficulty with college math. You probably still haven’t been taught math in a rigorous way.

You need to have a healthy respect, and know, but not fear, that you will have difficulties with some ideas at first. But as long as you are passionate, it will be fine, and you will do well.



Sciency stuff

Rank of centered data

Consider a {n\times p} matrix {X}. In general, this matrix has rank

\displaystyle \mathrm{rank}(X)\leq \min\{n,p\}.

Now, suppose we wish to column-center the data. We can do this algebraically by using what is known as the centering matrix,

\displaystyle H_n=I_n-\frac{1}{n}\mathbf{O},

where {\mathbf{O}} is the matrix where {\mathbf{O}_{ij}=1} for all {i,j}. Multiplying {H_n} with {X} results to the centering of all the columns.

The vector of ones is the only independent element in its nullspace and so {\mathrm{rank}(H_n)=n-1}. Therefore,

\displaystyle \mathrm{rank}(H_nX)\leq \min\{n-1,n,p\}=\min\{n-1,p\}.

Similarly, for the row-centered matrix {XH_p},

\displaystyle \mathrm{rank}(XH_p)\leq \min\{p-1,n\}.

Sciency stuff

Why am I good at mind calculations but bad at problem solving?


I have this friend who is great at cutting vegetables. You give her whatever you want, she can shred it in seconds. However, when it comes to cooking, she needs to be shown how to combine the vegetables and understand the differences in taste and acidity of each one, etc. Otherwise she can’t progress, she is almost paralyzed by fear. Why doesn’t her great cutting skill translate to great cooking skill?

The answer is that, fundamentally, the two skills are different. Mind calculations take time to do, and you can get better with practice. The same is true of problem solving. However, just because both are parts of mathematics doesn’t mean that practicing one also gives you practice in the other. If you feel weak in problem solving, then the only solution is to practice more in that direction. Try to solve easier problems first, make sure that you understand the theory well, and then work your way up.

As far as I can tell from mine and my students’ work, when you can’t decide what way to go on a problem, most of the time it’s because you are missing some clue from theory.

It would also be helpful to read books on problem solving, like Polya’s “How to solve it”.