Saturday, September 25, 2010

Order Matters

Suppose I have an invertible function $f(x)$. In a perfect world, the following holds

$$x=f(f^{-1}(x))=f^{-1}(f(x))$$

To see what happens in a real world, consider the following

$$D=\left(\begin{matrix}1&1 \\\\ 1&0\end{matrix}\right)^{\otimes\ d}$$

$$f(\mathbf{x})=D\exp (\mathbf{x} D)$$

$f(x)$ maps natural parameters $x$ to mean value parameters $\mu$ in an exponential family over $\{0,1\}^d$
Let $d=6, x=<1/2,1/2,1/2,\ldots,1/2,1>$. Using machine arithmetic you get the following

$$\|f^{-1}(f(x))-x\|_{\infty}\approx 2.6\times 10^{-15}$$
and

$$\|f(f^{-1}(x))-x\|_{\infty} \approx 0.21$$

remo said...

THANKS FOR THE INFORMATION...
<a href="http://www.chloros.in/digital-marketing-internship.htmlhttp://www.chloros.in/digital-marketing-internship.html>Digital Marketing Internship Program in Bangalore</a>

draj said...

Excellent machine learning blog,thanks for sharing...
Seo Internship in Bangalore
Smo Internship in Bangalore
Digital Marketing Internship Program in Bangalore

Nursing dissertation writing services said...

I want to always read your blogs. I love them Are you also searching for dissertation writing services? we are the best solution for you. We are best known for delivering Nursing dissertation writing services to students without having to break the bank

Nursing Thesis Writing Services said...

I want to always read your blogs. I love them Are you also searching for Nursing thesis writing services? we are the best solution for you. We are best known for delivering Nursing thesis writing services to students without having to break the bank

nursing writing help said...

Your blogs are great.Are you also searching for Nursing Writing Help? we are the best solution for you. We are best known for delivering nursing writing services to students without having to break the bank.