Future For Commercial HPC

As I noted in an earlier post I have High Performance Computing requirements. Basically if you can give me thousands of processors, I can use them. The problem with HPC today is that it is one or more of the following (depending on where you are):

• academic and only open on a limited basis to researchers based on their proposals
• internal
• available but not cost effective (8 core @ $7000 / compute year at amazon)

This flies in the face of what we know:

• there are many thousands of under or un-utilized computers available
• the true cost of computing power + ancillary costs (power, people) can be scaled to a much lower #
• organizations should want to monetize this underutilized capacity
  

Why do I care about this? Well, I could use cheap computing power today, but also I used to be a parallel algorithm researcher back in the day, so have been waiting for this for a long time.

The solution needs to be to allow compute resource providers a means to auction their unused resources for blocks of time, immediate or future. HPC users that want to evaluate a massively parallel problem can collect a forward dated/timed group of nodes for execution, finding a group within their cost range or wait for lower cost nodes to become available.

How would this be accomplished?

1. Exchanges are set up for geographical areas where providers can offer gflop-hr futures and consumers can buy computing futures or alternatively sell their unused futures.
   
2. Contract requires standardized power metrics (SPECfprate2006 for instance)
3. Contract requires standardized non-CPU resource (min memory, disk)
   
4. Standard means of code and data delivery (binary form, encryption, etc)
   
5. Safe VM in which to run code
   
6. Checkpointing to allow for a computation to be moved (optional)
   

Research into auction-based scheduling and resource allocation began in the early 90s, perhaps earlier. The first paper I saw in this regard was in 1991. There are now hundreds of papers on this and a few academic experiments. There should be a big market for this amongst web hosting companies, etc.

Amazon and Google, although likely to be very efficient with resource utilization, are likely to have peak periods and slack periods like everyone else. The strategy would be to price resources lower during slack periods to attract "greedy" computations looking for cheap power.

I have specific ideas about how this would be implemented. Contact me if you are interested.

Feed Forward NN in "real life"

Turns out that the Nematode Caenorhabditis Elegans has a nervous system that is similar to a feed forward network. A feed forward network is one where neurons have no backward feedback from neurons "downsignal" (i.e. the neurons and synapses can be arranged as a directed acyclic graph). This is very analogous to the feed forward network first envisaged for Artificial Neural Networks.

The worm has exactly 302 neurons and ~5000 synapses, with little variation in connection between one worm and another. This implies on average less than 20 synapse connections per neuron. This is in contrast to the mammalian brain, where most neurons have a feedback loop back from other neurons downstream of the signal.

I am very enthusiastic about this area of research as it progresses us step-by-step closer to realizing mapping an organism brain onto a machine substrate. The nematode is quite tractable because of the fixed and very finite number of neurons.

ANNs are no longer in vogue, but I use feed forward ANNs for some regression problems. Of course my activation function is likely to be quite different from the biological equivalent. ANNs are not a very active area of research given their limitations, but one does find them convenient for massive multivariate regression problems where one does not understand the dynamics.

The regressions that I solve only have sparse {X,Y} pairs if at all and can only be evaluated as a utility function across the whole data set. This precludes the various standard incremental "learning" approaches. Instead I use a genetic algorithm to find the synapse matrix that maximizes the utility function.

SVM is more likely to be used in this era than ANNs for regression. Its drawback is that it requires one to do much trial and error to determine an appropriate basis function, transforming a nonlinear data set into a reasonably hyperlinear dataset in another space.

High Performance Computing on the Cheap

I have a couple of trading strategies in research that require extremely compute intensive calibrations that can run for many days or weeks on a multi-cpu box. Fortunately the problem lends itself to massive parallelism.

I am starting my own trading operation, so it is especially important to determine how to maximize my gflops / $. Some preliminaries:

• my calibration is not amenable to SIMD (therefore GPUs are not going to help much)
• I need to have a minimum of 8 GB memory available
• my problem performance is best characterized by the SPECfprate benchmark

I started by investigating grid solutions. Imagine if I could use a couple of thousand boxes on one of the grids for a few hours. How much would that cost?

Commercial Grids
So I investigated Amazon EC2 and the Google app engine. Of the two only Amazon looked to have higher performance servers available. Going through the cost math for both Amazon and Google revealed that neither of these platforms is costed in a reasonable way for HPC.

Amazon charges 0.80 cents per compute hour, $580 / month or $7000 / compute year on one of their "extra-large high cpu" boxes. This configuration of box is a 2007 spec Opteron or Xeon. This would imply a dual Xeon X5300 family 8 core with a SPECfprate of 66, at best. $7000 per compute year is much too dear, certainly there are cheaper options.

Hosting Services
It turns out that there are some inexpensive hosting services that can provide SPECfprate ~70 machines for around $150 / month. That works out to $1800 / year. Not bad, but can we do better?

Just How Expensive Is One of these "High Spec" boxes?
The high-end MacPro 8 core X5570 based box is the least expensive high-end Xeon based server . It does not, however, offer the most !/$ if your computation can be distributed. The X5500 family performs at 140-180 SPECfprates, at a cost of > $2000 just for the 2 CPUs.

There is a new kid on the block, the Core i7 family. The Core i7 920, priced at $230 generates ~80 SPECfprates and can be overclocked to around 100. A barebones compute box can be built for around $550. I could build 2 of these and surpass the performance of a dual cpu X5500 system, saving $2000 (given that the least expensive such X5500 system is ~$3000).

Cost Comparison Summary
Here is a comparison of cost / 100 SPECfprate compute year, for the various alternatives. We will assume 150 watt power comsumption per cpu at 0.10 / Kwh, in addition to system costs.

1. Amazon EC2
   $10,600 / year. 100/66 perf x 0.80 / hr x 365 x 24
   
   
2. Hosting Service
   $2,700 / year. 100/70 perf x $150 x 12
   
   
3. MacPro 2009 8 core dual X5570
   $1070 / year. 100 / 180 perf x $3299 / 2 + $160 power
   
   
4. Core i7 920 Custom Build
   $430 / year. 100 / 80 perf x $550 / 2 + $88 power
   
   
5. Core i7 920 Custom Build Overclocked
   $385 / year. 100 / 100 perf x $550 / 2 + $100 power
   

The Core i7 920 build is the clear winner. One can build 5-6 of these for the cost of every X5570 based system. Will build a cluster of these.

Tick Databases

Ok, so the street has largely embraced KDB as a tick database for high-frequency algo. It is by far the worst DB I have every worked with in terms of reliability and functionality. The one thing it does have going for it is that it is fast.

Other than that, if you want to deal with the agony of a database that falls over on simple operations, has a largely unintelligable language Q (a dialect of APL) that noone cares for, and has next to nothing in the way of support from the vendor, be my guest.

KDB is a very (very!) raw database, not much more than a process or two around a a bunch of binary files, one for each timeseries per day.

Stay away.

Evolution of Distribution

For a number of problems, understanding the evolution of the distribution over time is important. The distribution tends to be stable over longer periods and unstable over shorter periods.

The distribution is going to be measured from a sample over some time period. One may want to take a blend of distributions measured over different time periods, combined as basis functions with weights summing to 1.

The interesting bit is predicting the distribution forward with some statistical accuracy. The order book and momentum indicators should tell us something about how the distribution is going to transform over the next period or based on when a certain price level is achieved.

We are going to use a GA to calibrate the transformation function against historical data. There are many different functions we could use, so we use a GP approach to play with the permutations.

GP for option pricing

As you probably know GP (Genetic Programming) is an extension of GA which rearranges algebraic or functional instruction trees to fit to a solution.


I had not thought of it previously, but could use such an approach with the right set of functional constructors to converge on an option pricing GP. Now if all we were trying to do was to replicate the Black / Scholes, CEV, or other gaussian distribution based model, would not be very interesting.

We know that the actual distribution are often non-gaussian. Could we produce a more accurate approximation of the hedging cost against a non-gaussian distribution (implying the true risk free price of the option) with GP?

Interestingly, Neural Networks are just special cases of a GP tree, so in the end GP is the most general approach to non-linear regression.

Tracking the Order Book

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As this article points out, trend following or using technical indicators in a vacuum can be doomed without analysis of the order book. When we want to buy into market movement, we want to make sure that the order book supports the direction indicated by technical signals and is not about to start a reversal.

Processing the order book from snapshot to shapshot, we can determine:

• ratio of bid to ask interest
• bid interest up/down
• ask interest up/down
• bid aggressed (using last traded price and reduction of bid size to determine)
• ask aggressed (using last traded price and reduction of ask size to determine)

Going further one can look at the complexion of orders at each level, determining what sort of players are behind the orders. Knowing this can add further bias to the weighting of direction.