I just had to build the QuickFIX C++ client library on Solaris, and here are a few notes that might be useful when doing the same:
* Make sure you have
/usr/ccs/bin in your PATH (so that
ar can be found);
* If you are using gmake, you may need to
export MAKE=gmake before you run
* If building static libs as well as .so files, run
Once the libraries are built, you can compile and link using:
$ g++ -I /usr/local/include/quickfix/include/ main.cpp libquickfix.a -o main -lxml2
This will statically compile against quickfix and dynamically link against libxml2.
Probably one of the nicest explanations of the bias/variance tradeoff is the one I found in the book Introduction to Information Retrieval (full book available online). The tradeoff can be explained mathematically, and also more intuitively. The mathematical explanation is as follows:
if we have a learning method that operates on a given set of input data (call it $x$) and a “real” underlying process that we are trying to approximate (call it $\alpha$), then the expected (squared) error is:
E[x-\alpha]^2 = Ex^2 – 2Ex\alpha + \alpha^2\\
= (Ex)^2 – 2Ex\alpha + \alpha^2 + Ex^2 – 2(Ex)^2 + (Ex)^2\\
= [Ex-\alpha]^2 + Ex^2 – E2x(Ex) + E(Ex)^2\\
= [Ex-\alpha]^2 + E[x-Ex]^2
Taking advantage of the linearity of expectation and adding a few extra cancelling terms, we end up with the representation:
Error = bias (E[x-\alpha]^2) + variance (E[x-Ex]^2)
Thats the mathematical equivalence. However, a more descriptive approach is as follows:
Bias is the squared difference between the true underlying distribution and the prediction of the learning process, averaged over our input datasets. Consistently wrong prediction equal large bias. Bias is small when the predictions are consistently right, or the average error across different training sets is roughly zero. Linear models generally have a high bias for nonlinear problems. Bias can represent the domain knowledge that we have built into the learning process – a linear assumption may be unsuitable for a nonlinear problem, and thus result in high bias.
Variance is the variation in prediction (or the consistency) – it is large if different training sets result in different learning models. Linear models will generally have lower variance. High variance generally results in overfitting – in effect, the learning model is learning from noise, and will not generalize well.
Its a useful analogy to think of most learning models as a box with two dials – bias and variance, and the setting of one will affect the other. We can only try and find the “right” setting for the situation we are working with. Hence the bias-variance tradeoff.
The FT has a nice article on financial amnesia, which talks about the desire of the CFA UK discipline to incorporate some financial history into their curriculum, ostensibly to implant enough of a sense of deja vu in budding financial managers when they encounter potential disaster scenarios that they may avoid repeating them.
I think this is a great idea – the only problem is that it probably wont have any sort of meaningful impact other than provide some fascinating course material for CFA students. The problem with an industry that makes its living from markets that essentially operate on two gears – fear and greed – is that despite all of the prior knowledge in the world, we will willingly impose a state of amnesia upon ourselves if we can convince ourselves that what is happening now is in some way different, or just different enough from whatever disasters happened before. The Internet bubble, tulip-mania, and the various property boom and busts that we have seen over the last decade share at their core a common set of characteristics, but they are different (or “new”) enough that we were able to live in a state of denial. The “fear and greed” mentality also means that even if you know you are operating in a bubble that will eventually burst, you carry on regardless, as you plan to be out of the game before it all goes bad (The Greater Fool theory).
Incidentally, if you want to read a beautifully written and entertaining account of financial bubbles by one of the greatest writers on this topic, you should read this book (“A Short History of Financial Euphoria” by J.K. Galbraith). It packs a huge amount of wit and insight into its relatively small page count.
NOTE: Galbraith also wrote the definitive account on the Great Crash of 1929, which rapidly became required reading around three years ago…it’s also excellent. Galbraith has a beautiful turn of phrase.