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).

Thus, a really efficient Bayesian regression algorithm.

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.

> 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.

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?

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.

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