Re: "We Believe in Design"

On 5/25/05, Denyse O'Leary <oleary@sympatico.ca> wrote:
>
> "Perhaps someone needs to take the lead and write a similar essay, "We
> Believe in Design" where we explain our belief in this concept that flows
> directly out of the doctrine of Creation, ..."
>
> Yes, that sounds like an excellent idea. It will be interesting to see
> whether this kind of essay is greeted with hostility.
>

Although the following isn't the essay required, I'd like to take some time
to explain why I believe in design. Before I start, I'd like to say that I
thought Glenn Morton's essay that he posted on this list at:

http://home.entouch.net/dmd/casino.htm

is excellent and really summarises a lot of what my thoughts have been on
this subject. Glenn suggests in this essay that the design in biology is in
the sculpting of dna sequence space so there are clear paths of viability
from one species to the next:

Now when one organism evolves to another, there must be a path of viability
in this space (or a cavern of viability) To put things in a 2 dimensional
perspective (see diagram) if one wants to evolve an animal from point A in
the sequence space to point B, there must be a clear path where all the
points allow for viability. There can be gaps in the path, which require 2
mutations to jump over, but such blockages, lower the probability that one
will get from A to B.

Here is the diagram. The occasional period is in there for spacing purposes
only.

6 A d d d d d
5 l l d d d d
4 d l d d d d
3 l l d B d d
2 l d d l d d
1 l l l l d d
1 2 3 4 5 6
where l is a dna sequence space point leading to life and d is a DNA
sequence leading to death. The place I posit design is in the design or
layout of these caverns of viability. God could have pre-programmed life's
evolution via this approach turning what is considered a product of pure
chance into a quasi-deterministic event.

This last observation of Glenn's (that the event becomes
quasi-deterministic) exactly stacks up with my own professional experience
in learning systems (and to an extent, genetic algorithms).

I have spent nearly 15 years in the field of neural networks (7 of which
were in doing a part-time PhD in the subject as a full-time job - quite a
nightmare). I'll talk about Neural Nets and their learning algorithms, which
can be viewed in a similar fashion to an evolutionary process. It is just
about possible to use a Genetic Algorithm to train a neural net (there are
some examples around), though more normal to use a conventional optimiser
based on gradient descent, which is deterministic (though the initial guess
of the parameters to be optimised is usually done with a random number
generator). However, an optimiser that uses small changes to progress
towards a (local) optimum is very much akin to an evolutionary algorithm,
only more efficient. Once can look upon an evolutionary algorithm as a way
of exploring the gradient of a fitness surface - the generation of mutations
about a given point generates a cloud of possibilities, and the selection
pressure that results means the cloud of points (population) tends to move
in the direction of the gradient of the fitness surface.

With neural networks, a fascinating mathematical theorem was published in
1984 which showed that a fairly simple type of neural network ( a
"Multi-Layer Perceptron" or MLP) can in principle learn to reproduce any
mathematical mapping of numerical data from M-dimensional space to
N-dimensional space. This means that it is termed a "universal function
approximator", and as such can be used in all sorts of applications where we
want to find a mapping, but we don't actually know the underlying physics,
but have a lot of empirically measured data. Neural nets are commonly used
on Optical Character Recognition software used in scanners, and also have
applications in medical diagnosis, financial modelling, and a host of other
applications. (Credit card fraud detection was a particularly fascinating
one I worked on for some time, which revealed some fascinating insights into
the criminal mind!)

Unfortunately the promise (universal function approximator) leads many
people to throw away their brains when trying to use neural networks for
their particular set of data. There are a lamentable number of such papers
I've seen at conferences where the presenter has had some data and decided
to throw it at a neural network, and then presented mediochre results. One
of the worst examples I saw was a woman presenting a paper about predicting
the minimum temperature based on the previous day's meteriological readings
(for an airport authority). Having started the talk with a colourful slide
of her children playing snowballs after an unexpected snowfall, and saying
"wouldn't it be good if we could predict this?", she presented a very
mediochre set of results, largely because there wasn't nearly enough data to
get any sensible result. But there was this strong indication from her that
the neural network, because it was inspired by the architecture of the
brain, would somehow magically "learn" the underlying patterns in the data
and enable sensible predictions to be made. Alas! a simple eyeball of the
data revealed that a "predictor" that said that tomorrow's minimum
temperature will be the same as today's minimum temperature, would have done
just as well as her fancy neural network (not much good, in other words!).

So why did this fail? It was simply because of a lack of "intelligent
design" in preparing the data. Just because mathematically the neural net is
a universal function approximator, in practice (with a finite amount of
data), it rarely will. The error surface (fitness surface if you like) for a
neural net is full of plateaus where it will get stuck, and steep ravines
where multiple changes are required to make progress (so a Genetic algorithm
where single point mutations occur is of little use). So it is
alwaysrecommended "best practice" to apply sensible pre-processing to
the data. In
some cases this may be as simple as scaling the numbers fed into it, but
more often than not much more sophisticated tricks are used. There is an
application that I think got FDA approval called PapNet, that identified
cancerous cells from cervical smear tests, for example. You feed the image
in from the smear, and out comes a likelihood of it containing abnormal
cells. Now the naive way it could be done is to convert the image into, say
a 64x64 grayscale set of pixels and feed in all the pixel values (4096 of
them) into a neural net, and get it to predict the likelihood of cancer
(which would have previously been manually determined by a clinician to make
the data to train the net). Now, in principle such a neural network could be
made to work because of the universal function approximation theorem.
However in practice, it is extremely unlikely to do so, and will not learn
anything useful, that will give good predictions from new images. Instead,
the inputs are derived from sensible image processing of the cells on the
slide, giving about half-a-dozen numerical parameters such as circumference,
area, ratio of circumference to area, moments and so forth. The idea behind
this is that it turns an extremely difficult learning process into a very
easy one that is much more likely to work quickly. This, if you like, is a
direct analogue of Glenn's idea of the design of sequence space in DNA. In
the neural network, the sequence space of the model parameters is also
"designed" so that a gradient based algorithm can traverse it easily.

It's my experience that any form of optimisation (be it neural networks, or
genetic algorithms, or simulated annealing, or as in my current work,
optimisations of complex chemical plants via simulation), requires
"intelligent design" in the modelling. Not to do this, and just to pick any
old mathematical model and hope that your magic optimiser will solve your
problem, is a recipe for disaster.

In a nutshell, the way I see it is that if intelligent design is necessary
to get any of these things to work properly, then since nature contains many
marvellous things that appear to be designed ( even Dawkins uses the word
"designoid", noting the eye's resemblance to a camera), then likewise the
sequence space of DNA, as Glenn says, is likely to have been intelligently
designed. As Glenn says, you can't prove it was so, but the evidence from
how we get biologically inspired computer algorithms to work suggests
strongly that it was.

Iain.
Received on Thu May 26 18:05:05 2005