It is the distribution of the average of n binomial distributions (taking on values x±1)†, which according to the CLT converges to a Gaussian as n→∞.
[†] x is where it is centered.
52 karma · joined April 1, 2011
[†] x is where it is centered.
Another way to see the FT is as the basis where the convolution operators are diagonal - this is used in image processing, where computing the FFT of a filter + entry-wise multiplication can be much faster than running the convolution at each pixel of the input image.
1) a convex problem which means a unique solution and a lot of already existing technology can be used
2) the "kernel trick" which enables us to learn in complicated spaces without computing the transformations
3) can be trained online, which makes them great for huge datasets (here the point 2) might not apply - but there exist ways - if someone's interested I can point out some papers)
There is an ongoing craze about deep belief networks developed by Hinton et al. (who is teaching this course) who came up with an algorithm that can train them reasonably well (there exist local optima and such, so it's far from ideal). Some of the reasons they're popular
1) they seem to be winning algorithm for many competitions / datasets, ranging from classification in computer vision to speech recognition and if I'm not mistaken even parsing. They are for example used in the newer Androids.
2) DBNs can be used in an unsupervised mode to _automatically_ learn different representations (features) of the data, which can be then used in subsequent stages of the classification pipeline. This makes them very interesting because while labelled data might be hard to get by, we have a lot of unlabelled datasets thanks to the Internet. As what they can do - see the work by Andrew Ng when they automatically learned a cat detector.
3) DBS are "similar" to biological neural networks, so one might think they have the necessary richness for many interesting AI applications.
1) a convex problem which means a unique solution and a lot of already existing technology can be used
2) the "kernel trick" which enables us to learn in complicated spaces without computing the transformations
3) can be trained online, which makes them great for huge datasets (here the point 2) might not apply - but there exist ways - if someone's interested I can point out some papers)
1) They seem to be winning algorithm for many competitions / datasets, ranging from classification in computer vision to speech recognition and if I'm not mistaken even parsing. They are for example used in the newer Androids.
2) They can be used in an unsupervised mode to _automatically_ learn different representations (features) of the data, which can be then used in subsequent stages of the classification pipeline. This makes them very interesting because while labelled data might be hard to get by, we have a lot of unlaballed datasets thanks to the Internet. As what they can do - see the work by Andrew Ng when they automatically learned a cat detector.
3) They're "similar" to biological neural networks, so one might think they have the necessary richness for many interesting AI applications.* Looks nicer.
* You can't modify the panels. I always had some shortcuts there, now I have to go through the menu.
* You can't even change the default icon theme using the customization app. You have to get gnome-tweak-tool (IIRC).
* ALT+F2 doesn't do anything by default. I guess the key bindings are changed/some are disabled by default.
* It tried to install the new ATI drivers, then miserably failed. Trying to fix it, I purged the old drivers, but it still didn't work. This only caused it to freeze at boot time, so I had to the recovery console to fix it.
* Bottom line: never ever upgrade from an old version. Always do a clean install (or pick up a different distro/OS).
* Note: I'm using Gnome (now not so) classic.