Apr

2

On a sailboat there are dozens of lines, but not a single rope. You've got your mainsheet, anchor rode, jib halyard, downhauls, uphauls, outhauls, and reef lines. They are all attached by simple knots. In fact the simplest knots are the best. They hold best and they are undone quickly and easily, which is very important to be able to release a line at the appropriate moment. Some knots are so simple, it is a matter of merely crossing two lines over each other and applying the appropriate pressure to be able to hold upwards of a five ton vessel with one hand.

I had a few landlubbers on my boat the other day. They tied a line to a fitting and it looked like a rat's nest, a tangle jumble of lines, impossible to undo, with questionable holding power. Their model, more is better, is flawed. A simple square knot or bowline cannot be beat for simplicity, ease of release, and reliable holding. Trading has the same needs: simple models and a simple position that can easily be unwound in a jam but that will hold well in a storm.

The problem of pattern recognition is quite fascinating and similar to the problems of knot classification and application. A jumble of indicators all crisscrossing this way and that is often not the best. In creating predictive models, statistically speaking, simplicity is best to avoid the problem of curve fitting the past, and reducing predictive power.

Humans are quite good at recognizing patterns, even ones that don't exist. Humans can recognize faces, even in disguise, remember a loved one's perfume, the smell of a certain flower, read hand written scribbles, spot fake antiques, recognize dangerous driving conditions, and spot good opportunities in financial markets. Now, machines can do almost none. Why? There is obviously a learning process, and a judging process. B.D. Ripley, in Pattern Recognition and Neural Networks, discusses these problems. He is careful to distinguish that the term neural networks is not an attempt to recreate a human brain in the box. Rather it is the process of creating statistical models to recognize and rate pattern recognition algorithms in terms of the their predictive power outside the learning set.

On a sailboat there are dozens of lines, but not a single rope. You've got your mainsheet, anchor rode, jib halyard, downhauls, uphauls, outhauls, and reef lines. They are all attached by simple knots. In fact the simplest knots are the best. They hold best and they are undone quickly and easily, which is very important to be able to release a line at the appropriate moment. Some knots are so simple, it is a matter of merely crossing two lines over each other and applying the appropriate pressure to be able to hold upwards of a five ton vessel with one hand.

I had a few landlubbers on my boat the other day. They tied a line to a fitting and it looked like a rat's nest, a tangle jumble of lines, impossible to undo, with questionable holding power. Their model, more is better, is flawed. A simple square knot or bowline cannot be beat for simplicity, ease of release, and reliable holding. Trading has the same needs: simple models and a simple position that can easily be unwound in a jam but that will hold well in a storm.

The problem of pattern recognition is quite fascinating and similar to the problems of knot classification and application. A jumble of indicators all crisscrossing this way and that is often not the best. In creating predictive models, statistically speaking, simplicity is best to avoid the problem of curve fitting the past, and reducing predictive power.

Humans are quite good at recognizing patterns, even ones that don't exist. Humans can recognize faces, even in disguise, remember a loved one's perfume, the smell of a certain flower, read hand written scribbles, spot fake antiques, recognize dangerous driving conditions, and spot good opportunities in financial markets. Now, machines can do almost none. Why? There is obviously a learning process, and a judging process. B.D. Ripley, in Pattern Recognition and Neural Networks, discusses these problems. He is careful to distinguish that the term neural networks is not an attempt to recreate a human brain in the box. Rather it is the process of creating statistical models to recognize and rate pattern recognition algorithms in terms of the their predictive power outside the learning set.

The Bayesian models figure prominently in many pattern recognition texts such as Ripley's, but also in Bishop's, Pattern Recognition and Machine Learning.

One of the issues is the use of parametric and non-parametric models. Often it seems that the data do not fit a normal model easily, and a non-parametric model may give better prediction. Ripley states the following,

"The normal distribution is a convenient abstraction, but all careful studies show that real distributions do not quite follow a normal distribution but have slightly heavier tails. In addition we should consider the possibility of outliers, that is examples which do not belong to the class under consideration….If the distributions are non-normal, then we need to take into consideration that the tails will be longer, and assuming a t distribution will be more appropriate."

A continuing issue is how to combine normal densities with outliers, like 2/27, to arrive at robust estimators. The traditional statistical approach to model selection includes the iterative process of backward selection by eliminating features until the best remains, or forward selection by starting with none and adding one at a time.

One method of arriving at a non-parametric model is through the use of Monte Carlo with replacement to ascertain the parameters of the learning set. Ripley finds that it may give superior predictions over a parametric model. Before computers, the difficulty of computing non-parametric models must have been insurmountable. But with fast computers why is greater use not made of non-parametric models?

We recently had some discussion on creating some rule of thumb benchmarks for easy computation based on non-parametric models created through Monte Carlo methods. This is an example of how recent market activity might be modeled simply.

A way to incorporate cycles might be with a rolling testing learning period to give estimators and in a Bayesian framework use those estimators going forward. That way the distribution parameters will morph to reflect the current regimes rather than be stuck with a fixed system. The Bayesian Information Criteria, which penalize size severely, might be used to determine a good leaning set/lookback size.

From Pitt T. Maner III:

With respect to pattern recognition, this reminds me of the thief knot used by sailors in days past.

Isn't it amazing, too, how easy it is for random lines to get tangled or knotted up and not break and yet how compounded simple knots done with willful intent can come unraveled in the blink of an eye and fail their purpose. It's one topological mystery.


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