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Friday, March 24, 2006
Tuesday, March 21, 2006
Sunday, March 19, 2006
Artificial Intelligence
On Intelligence is a well written book 
that offers a peak at how you think and how things may think in the future.
I started working with Neural nets when I was 20 trying to predict derivatives prices. I learned a lot about neural nets and genetic algorithms even more about the difficulty of predicting various markets.
I have been fascinated by neural nets, genetic algorithms and machine learning. All of which is derived from some of the earliest theory work done in control systems. Thanks Norbert Wiener.
Jeff Hawkins book is great stuff, for 2 reasons, one is clarity of communication, the second for the key ideas themselves. Basically the thesis is that human intelligence is a function of the neocortex performing a massively repetitive prediction algorithm.
The prediction algorithm is looking at bits and pieces of things and then matching them up with an invariant memory model. Invariant memories, the second key concept to Hawkins thesis are the ability to recognize things regardless of context or orientation. For example you can recognize a dog, from any direction, size or species. That is a great trick! and incredibly powerful computationally.
The repetitive nature of the algorithm (embedded in your physical neurons) combined with massive feedback and feed forward loops is the thesis for consciousness and learning. Hawkins approach seems very interesting. He forgoes a bunch of the fairly un-interesting philosophical traps of consciousness and awareness thrown out by types such as Daniel Dennet. Hawkins has fairly limited time for the Turing test as well. As an engineer he is more interested in a solution than its "philosophical impacts".
I agree with this. Alan Turing was a brilliant mathematician and thinker, but the Turing test itself is too anthropic to be of any use to science. It is interesting from a philosophy perspective but pointless from an engineering and science perspective.
The human ego is fragile and many of us tend to respond to the potential of conscious machines with a strong state of denial. The same type of mentality that was upset when we lost our place at the center of the universe, or as a unique species. Science gets in the way of our self importance sometimes.
If you are interested at all in the potential future of artificial intelligence or even potential storage architectures of the future, Hawkins book may be for you. Even media as it gets richer will need to be able to sort and search images and complex data sets. Hawkins start up www.numenta.com is probably going to create something very interesting in the next few years. Keep watching.
Sunday, March 12, 2006
Saturday, March 11, 2006
Voronoi geometric brilliance
There is a form of spatial plot known as a Voronoi plot. A diagram is shown here.
The picture was borrowed from the brilliant people at Wolfram research. they make mathematica. Stephen Wolfram is behind the firm. If you get a chance take a look at his book A new kind of science. I will make some comments on it later. It is profound and a peak into a fascinating future of math, physics and complex systems understanding, that we have just started to understand.
The Voronoi tessellation or plot has many applications. If you have a look at the diagram to the left, you will notice points and vertices which create closed spaces or cells. This optimal (packing) plot is found in many places in natures and natural phenomenae where physical spaces and points of growth grow to define "boundaries".
Like many things in nature that are beautiful, the beauty emerges from a set of rules, governing symmetry, growth and pattern while allowing for diversity, strength and emerging complexity across scales. Imagine if you will each point to be the nucleus of a cell and the edges to be cellular walls.
One of the best sites to explore the Voronoi concepts is The Voronoi website. the Voronoi concept is used not only in small physically bounded regions such as biological cells but also in astronomy to identify likely galactic clusters (see paper here) and here as well
The concept also lends itself to many forms of optimization and problem solving for crude or abstract bounded set problems. The nature of an auto clustering algorithm on a 2d plane is very powerful. It is my belief that using iterative resolution voronoi plots, will be a way in the future for image recognition as it is the most logical to way to detect variance without use crude spectral analysis.
These 2 images are an example of high noise dataset reduced using a Voronoi map see here. The feature set is reduced significantly. My guess is that the delta of various plot resolutions would very effective for measuring and detecting crude sets or image identification. This is far more effective and probably efficient than edge detection and then spectral mapping.
As a clustering approach, something feels right to me about the Voronoi approach and I wouldn't be surprised to see it showing up in a lot of places in the future. As more analog data needs to be compared and contrasted in complex sets, this approach makes sense. Now that is all good and well for understanding "static" data matches or comparing static data over a dynamic range.
The other interesting application will be Voronoi plots involving Cellular Automata. Most CA models use simple regular boundaries, typically 2-dimensional squares. Wolfram's first work involved this. However, most phenemonae exhibit radial irregular boundary conditions that don't work for traditional lattice models etc. The Voronoi method of modeling things allows for "noise" within the micro boundary and positioning of elements, but gives a quick solution to synthesis and modeling. As of today no, language of Voronoi plots has evolved. My belief is it will. This is a rich field for exploration, Voronoi dynamics, fractal metrics and perhaps even a voronoi excited state model yielding something equivalent to a Feigenbaum constant remain to be discovered.
And here for a big finish is a really cool app call the Bubble Harp Scott Snibbe has made some fascinating works here. They aren't toys, they are windows on a rich and fascinating world. For fun install the bubble harp app and hold down your mouse as you create vertices. the resulting action almost looks like a beating heart :). The Voronoi concept is beautiful and will be profoundly revealing for years to come.
Saturday, March 04, 2006
Network theory is cool and connected
Network Theory is fascinating stuff. 
The thing I find most interesting about the mathematics and applied mathematics of network theory, like graph theory is the fact that only in the 20th century have we really taken a look at networks.
Network theory is deceptively simple and yet powerfully revealing, quite a bit like a good bikini :) Basically from a purely mathematical construct a network has 2 components Nodes, and connections. That is it, the graph shows some basic networks. The amazing things is the dynamics of networks. In theory any causal event or chain of causal events can be modeled with network theory. Social interactions can be model led with Network theory. Yes you really are only 6 people away from all the people on the planet (six degrees of separation)
Most natural phenomenae exhibit a unique aspect or type of network in that the connections and connectedness of the nodes follows a power law, this type of network is known as a scale free network, now before you think this all theory and math, please realize that the connectedness of the web follows a scale free network model. Most dynamic systems with independent components settle into some form of a scale free network. Thus understanding them is important. Whether modeling the spread of disease in a population of people, the transmission of ideas or the dynamics of some biological systems scale free networks hold the key. During the summer of 2002, I read a few papers and books on the topic, two of the best, I would recommend are Sync by Stephen Strogatz
and Linked by Laszo Barbasi. Both of these men are fine mathematicians in their own right and great popularizers of science. They have excellent skills at communicating and sharing some of the amazing worlds and phenomenae they have discovered.
The more interconnected we as a culture and species become the more important it is to understand network theory. I think network theory will eventually become as important as thermodynamics. The thesis being that modeling individuals nodes or components will be useless, but understanding complex systems in aggregate will allow for powerful understanding and control of those systems. Network theory and the emerging metrics and models associated with it will lead to whole new theories of "things" and relationships. Much like thermodynamics allowed us to scale up from Newtonian reductionism and ultimately harness energy, Network theory could very well allow us to model and control some of the most powerful networks of all. The list is long, but could include, neurochemical, social, environmental and communications networks. The implications and impacts will be profound. And it will have started with a Connection and a node. Check out these books if you get a chance, I personally fascinated by social networks, memetic spread and of course financial networks.
One of my friends from Starlab is Keith Still, he works primarily in Crowd simulations and modelling. He is considered one of the experts in this realm. Keith is doing soem really interesting stuff in terms of modelling autonomous agents in an environment to assess their behaviour, anyone interested in crowds, safety or cellular automata may be interested in visiting his page or emailing him. Keith is a great guy and very generous with his time.
Hedge Fund ahead. Beware.
Hedge Funds are something to be very wary of. 
If you invest in one read this post. If you have friends who invest in one have a look.
I spent part of Saturday reading on the beach with my wife. One of the more gripping reads was Systemic Risk and Hedge Funds by Nicholas Chan, Mila Getmansky, Shane M. Haas and the esteemed Andrew W. Lo.
One of the more interesting papers I have come across in finance for some time. A copy of it is available Download systemic2.pdf .
Wow what can I say but great work. Some fascinating insites into the style and performance aspects of funds. Some highlights that most people already know. Funds under management are now $1 trillion they were only, $200 billion in 1997. Some more interesting research is strong indications that the average hedge fund has a half-life (survival) of 30 months.
The analysis of highest risk and lowest risk fund types is fascinating. Hint: managed futures are dangerous.
Lo does a great job of explaining the dangers of selling options (volatility) that many funds use. Lo constructs what many managers and investors would consider a model portfolio Sharpe Ratio over 1.90 with returns double the S&P 500 over 7 years. The approach is simple and explained. The approach yields a 2,300% return over the period The approach is also statistically pointed to ruin.
Attention: Volatility is mean reverting and at historic lows. When Volatility comes back it will be short, sharp and Cruel to many funds!
Hedge funds are famously opaque. This paper does one of the best jobs of showing the hidden flaws and approaches of many funds. For every George Soros, there are literally hundreds of train wrecks for investors. I am speaking as one who once designed and put together a set of still born quantitative offshore funds. Ouch! Lesson learned when I was a green 27-28 living in London.
The hedge fund business still lives by the 2% and 20% performance payment. As more than one participant has stated, "hedge funds are more about being a compensation class than a true asset class."
The crux of the paper mentioned above is that hedge funds have in built risks that are not just limited to themselves but the banking system as a whole, systemic risk. This is an area, I have studied for years. I am impressed with the approaches for assessing proxies for systemic risk using a chain of logical analysis involving auto-correlations among fund performance and cross correlations among style and asset classes. The approach is not rock solid, but by far one of the more interesting ways of statistically teasing out the hidden games and trading profiles of hedge funds. Unfortunately the potential for systemic risk due to hedge fund phase locking is real, but un measurable.
I won't go into further details about the paper, only to say that it is worth the read. The authors should be commended as producing a tour de force. I would be interested in the authors comments on systemic risk and phase locking in regards to Basel 2 risk capital accords. If you think Phase locking and regime change (in the financial sense) is scary with $1 trillion in hedge funds, consider the implications for the entire global banking system.
Should any people out there be curious or want to speak about Hedge funds and systemic risk, feel free to ping me.
