Understanding Convolutions

from: https://colah.github.io/posts/2014-07-Understanding-Convolutions/

neural networks, convolutional neural networks, convolution, math, probability

In a previous post, we built up an understanding of convolutional neural networks, without referring to any significant mathematics. To go further, however, we need to understand convolutions.

If we just wanted to understand convolutional neural networks, it might suffice to roughly understand convolutions. But the aim of this series is to bring us to the frontier of convolutional neural networks and explore new options.

https://www.autonlab.org/_media/tutorials/vcdim08.pdf

Machine f can shatter a set of points x1 , x2 .. Xr if and only if… For every possible training set of the form (x1 ,y1 ) , (x2 ,y2 ) ,… (xr ,yr ) …There exists some value of a that gets zero training error.

Given machine f, the VC-dimension h is The maximum number of points that can be arranged so that f shatter them

For 2-d inputs, what’s VC-dim of f(x,w,b) = sign(w.x+b)? Well, can we find four points that f can shatter? Can always draw six lines between pairs of four points.

How can I call an external command (as if I’d typed it at the Unix shell or Windows command prompt) from within a Python script?

A CASE expression returns a value from the THEN portion of the clause. You could use it thusly:

Note that you need to do something with the returned value, e.g. compare it to 1. Your statement attempted to return the value of an assignment or test for equality, neither of which make sense in the context of a CASE/THEN clause. (If BOOLEAN was a datatype then the test for equality would make sense.)

http://stackoverflow.com/questions/10256848/can-i-use-case-statement-in-a-join-condition

Darts, Dice, and Coins: Sampling from a Discrete Distribution

Earlier this year, I asked a question on Stack Overflow about a data structure for loaded dice. Specifically, I was interested in answering this question:

“You are given an n-sided die where side i has probability pi of being rolled. What is the most efficient data structure for simulating rolls of the die?”

This data structure could be used for many purposes. For starters, you could use it to simulate rolls of a fair, six-sided die by assigning probability 1616 to each of the sides of the die,

The Alias Method

The previous technique has excellent best-case behavior, generating a random roll using a single fair die roll and coin flip. On expectation, its worst-case behavior is much worse, though, potentially requiring a linear number of die rolls and coin flips. The reason for this is that, unlike the previous techniques, the algorithm may “miss” and have to repeatedly iterate until it decides on a decision. Graphically, this is because it works by throwing darts at a target that may contain a large amount of empty space not assigned to any outcome. If there were a way to eliminate all of that empty space such that every piece of the target was covered by a rectangle corresponding to some side of the loaded die,