ubuntu 鏡像網站掛掉怎麼辦

sudo apt-get update 時看到
Err http://tw.archive.ubuntu.com raring Release.gpg Something wicked happened resolving 'tw.archive.ubuntu.com:http' (-11 - System error)

這代表我系統用的軟件包鏡像伺服器不在線上，我也不能用 sudo apt-get install 安裝軟體了

於是只好去打開 /etc/apt/sources.list 把 http://tw.archive.ubuntu.com 換成別的伺服器
注意不同伺服器的速度！台灣最快的是 NCHC的，這也是朋友建議我用的伺服器。

Does it really make sense ...

to use Gaussian distributions everywhere?

Wix Could Be Better

Wix is really crappy in so many ways. The really problem is that in their rush to make things easy and user-friendly, they apparently forgot everything they knew about programming and making repetitive tasks easy to manage. Strange really. For example there's no way to insert items into a list at arbitrary positions. Instead, every new item is added to the top. This can be a real problem when the lists get long ... Another issue is that their no way to generate more of an existing element in a "smart" way. Overall, I think choosing to use Wix was a bad idea. I'm locked in, I can't make edits as easily as I'd like, and there are ads. Oh yeah, THERE'S NO WAY TO EDIT THE SOURCE. No methods of last resort. That said, maybe they'll make improvements in this regard in the future. I hope so because I really want to avoid having to deal with the nitty-gritty of front-end website design and Wix is nothing if not committed to that goal.

WTF Is Marginal Likelihood

As if "likelihood" wasn't confusing enough now we have "marginal likelihood" (or "integrated likelihood") WTF It's also sometimes called "model evidence" or "evidence". Why?

wikipedia's definition is $$ p(\mathbb{X}|\alpha) = \int_\theta p(\mathbb{X}|\theta) \, p(\theta|\alpha)\ \operatorname{d}\!\theta $$

Isn't this just the bottom of Bayes' formula? So it's the probability of the observations? But why call it these strange names?

Wait that's not quite right. You can't actually know the probability of an observation. You need the assumption of what generated the observations.

So it's the probability of the observations under the chosen model. But this is still too simple because you don't actually have this probability either. A model has parameters ... how can you know the probability of these observations without a parametrized model?

So it's expressed as the marginalization of the likelihood since the likelihood can be calculated directly. No we have the probability of the observations under this model is the probability of these observations under this model with some parameters theta (likelihood) times the prior probability of theta integrated over all possible parameters theta. And since this number is how probable whatever model you chose is, it's also called the evidence of this model.

Matrix Inversion Lemma

This equation is used everywhere.


Matrix Inversion Lemma: $$\mathbf{(A^{-1} + B^{-1})^{-1} = A - A(A+B)^{-1} A = B-B(A+B)^{-1}B}$$
I saw this and went WTF? But let's not panic. Let's take this in the one dimensional case and see if it holds.
Working backwards ... $$ \begin{align*} a-a(a+b)^{-1} a &= a-\frac{a^2}{a+b} \\ &= \frac{a(a+b)}{a+b} - \frac{a^2}{a+b} \\ &= \frac{a^2 + ab}{a+b} - \frac{a^2}{a+b} \\ &= \frac{ab}{a+b} \end{align*} $$
Oh hey that's not too bad. The last equation is easily recognizable as $$\frac{1}{\frac{1}{a} + \frac{1}{b}}$$ which when written as $$(a^{-1} + b^{-1})^{-1}$$ is our original equation as expected.
OK so just repeat it with matrices! $$ \begin{align*} \mathbf{(A^{-1} + B^{-1})^{-1}} &= \mathbf{ (A^{-1} (BB^{-1}) + (A^{-1}A)B^{-1})^{-1} } \\ &= \mathbf{(A^{-1} (A+B) B^{-1})^{-1}} \\ &= \mathbf{ (B (A+B)^{-1} A ) } \\ &= \mathbf{ ((A+B - A) (A+B)^{-1} A ) } \\ &= \mathbf{(A+B)(A+B)^{-1}A - A (A+B)^{-1}A} \\ &= \mathbf{A - A(A+B)^{-1}A} \end{align*} $$ Note: This is also known as the Woodbury matrix identity.