kshitijl

In the event of liquidation, shareholders are on the list of those owed a portion of the proceeds. In fact they are last on the list, after creditors (those who have loaned the company money directly), bondholders (bonds are a form of debt), and holders of preferred stock.

That right is the ultimate determinant of the value of a no-dividend no-vote stock: fractional ownership of the right to proceeds in the event of liquidation, after those above have had theirs.

As a higher-risk asset, it produces greater returns, since otherwise there is an arbitrage: buy bonds issued by the same company instead. This arbitrage lasts until the bond becomes "expensive", and therefore produces worse returns (since its payout is independent of its price).

Can't you always lower the brightness in software, at the OS/driver level? Unless you're saying that this compresses the dynamic range of brightnesses too much, to the point where you can't distinguish shades that you need to be able to for your work.

The studied circumspection in his responses to questions about Trump amused me. But I noticed that he said "the kind of leadership those voters wanted" (emphasis mine).

This is what New York still feels like to me, 4 years after moving here. Don't own a car, hope I never have to.

For people familiar with Gaussian Processes, it may help to think of Kalman filters as a special case of GPs where you can construct the inverse of the covariance matrix directly, and this inverse has a tridiagonal structure.

Thus, a really efficient Bayesian regression algorithm.

The whole point is that it enables spam, broadly interpreted to include unsolicited mail of all kinds.

I am also very interested in knowing what to do when the dimension of the input space can vary.

For example, suppose that I'm interested in learning 4-body gravitational motion using 3-body training data ie. predict total energy of a system given mutual distances.

Notwithstanding the fact that this is trivial to compute directly, how do I set this up as a GP? Are there general strategies for this? What do I look up on google scholar, or what application field of ML most deals with this?

Thanks a lot for your help.

Ahh thanks, this line

> Notice that both the polynomial and kernel methods have less than N terms which are nonzero, but [...]

starts to answer my worry a little bit. It really is not the case that there are N true degrees of freedom, we just nominally started out with that many and then gave up certain ones of them.

What I would love to have is a quantitative analysis of the "number of free parameters" in my model after I have fit it, so that I can compare it to (say) a 50-parameter polynomial model that is equally good at reproducing the training set.

With N parameters for N data points I have far, far too many degrees of freedom and have grossly overfit my training set. The only way to guarantee good generalization outside one's training set is to have a lot of data compared to the number of degrees of freedom in the model.

To avoid this, we use bias/prior/regularization which reduces the effective number of degrees of freedom. For example, fitting a quadratic polynomial to some data, we have 3 degrees of freedom including the constant term. If I add a regularization term \lambda*||a|| where a is the vector of coefficients, I can alleviate overfitting. We can determine an optimal value for \lambda using validation or cross-validation. For \lambda=0, we have 3 parameters. As \lambda->infinity, we force the answer closer and closer to the constant 0 polynomial ie. no degrees of freedom.

In other words, regularization avoids overfitting by reducing the dimension of the model.

I am not worried about the amount of data I have to carry around; rather, it was a way of thinking about the dimension of parameter-space.

Don't big alarm bells go off in your head when you hear N parameters for N data points?

I am familiar with basic regression theory and numerical optimization; I have a qualitative understanding of VC bound. Given this background:

What is the number of parameters in a GP model?

A parametric regression/classification model has some number of parameters, and having estimated them I only need to carry them around. If a model has more parameters, it is less parsimonious and less desirable than a model with fewer parameters that achieves the same error.

If I add regularization/bias/prior to a model, it reduces the dimension of parameter-space.

In a GP model I need to hold on to my entire training set. But clearly the number of parameters I'm fitting is much smaller. So how do I quantify that?

To be clear, I'm not talking about the hyperparameters of the covariance function.

Did you read the Wikipedia article you link to? This has everything to do with memoizing the result of running compilation programs (function) on input files (arguments).

The "trick" here is using strace to figure out the complete set of inputs to the (assumed to be) idempotent compilation steps.

A long time ago I worked on the modified ejabberd servers that provide this service. A shame indeed.