Re: Proof that neural nets work


John Moody <john.atwell.moody@xxxxxxxxx> wrote in message
news:1148301297.993268.319420@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

You can indeed use a neural net to PERFECTLY
predict a sequence of apparently "random" numbers, after some
amount of "training", if indeed those numbers are generated by
some unknown, but continuously and precisely applied discrete
function.

OK I'm with you so far....

But what happens if the function is both unknown and only applied
sometimes and not precisely? Or for that matter, what happens to
your "training" if, for example, you are currently perfectly predicting
the
sequence of an unknown "random" number generator and then they
re-seed the generator?

Yes, in fact, here's a very specific example: if the random numbers
are the result of RSA encoding the sequence 1,2,3,4,5,6,7....
(which are, in fact, an example of a type of pseudo random number
sequence similar to what computer
programs put out),
we KNOW it cannot be predicted by any existing computer algorithm. So
certainly
a neural network couldn't predict that, even though it's in principle
predictable.

Ah, so would it be fair to say that if there is an input to stock prices
that you are not using as an input to the neural net, the neural net will
not be able to predict future prices?

Now, a net like Stock100 that just runs automatically cannot really do
anything useful. You have to have human cognition first, to imagine a
.relation between various tickers and volumes. Then, a neural net can
tell you whether that relationship is real, and quantifiable.

That works in GoldenGem because, when you set sensitivity to zero, the
net is blinded to the blue curve (the present day stock values) and
only sees the red curve (the historical prices and volumes). So if the
green curve it produces is matching the blue curve, this means, it HAS
found a mathematical relationship.

Well, did it? Has anybody done this (knowing that I did this almost
twenty years ago, and many others claim to have done it)? If you, or
anybody did it, how closely did the "blue curve" (actual values) match
the "green curve" (predicted values)? How much price/volume data
did you feed it, what was the period of the data?

Well, I am starting from knowing little about the stock market, going
back to that big drop in
Microsoft a few weeks ago, and trying to see what tickers I can load
alongside Microsoft that
match the graph. I have a description on my university website of the
attempt, which proved
that the shares I loaded did not have anything to do with that drop
(disappointing). It is
http://www.maths.warwick.ac.uk/~moody/goldengem.html

It sounds like you are using price-only data for a collection of
"related" stocks for a relatively short period of time to attempt to
predict the price of one stock. I'm actually not sure, even though
you are kind of saying it in plain English, probably because my
mindset is such that I can't comprehend that particular "experiment"
at this point in my life (twenty years ago I might have understood).

But let's start with price data alone, and look at it from some other
angles. If we look at daily data (or really any period of data), we
"discover" that there IS a simple mathematical relationship, a
STATISTICAL relationship, between today's data and yesterday's
data, because if we plot a histogram of the change between the
two days, we get something sort of resembling a "normal curve",
with a lot of data points clustering around a very small change,
and very few for a large change.

OK I'm with you so far.

Likewise, from chaos theory, our first pass at "attractor reconstruction"
(n vs. n-1), shows a little fuzzy but easily discernable "attraction" of
today's stock prices to yesterday's stock prices. But just plain old
logic and common sense and any amount of experience says that
of course traders base their bids and asks in the market on the most
recent sales prices, just like people believe that if their next door
neighbor sold their house for $1,000,000, THEY should also get
$1,000,000...and they'll stick to that unless there are other factors
that cause or allow them to raise or lower the price.

This is making perfect sense to me so far...

Good, now we've proven something about the stock market: you
don't really have to have any particular knowledge about the specifics
of the market, just some "common sense", to begin to analyze the
market.

We've covered one big motivation of sellers in a market, to get at
least the prevailing market price for their good or service. Other
"common sense" motivations: how much do you NEED money rather
than the good or service, how much money did YOU pay for the
good and service (your "cost basis"), etc.

Now, as a BUYER of something in any market, what motivates
you to buy? Well, first, you have to have the MONEY to buy, then
if you are buying an "investment", which "investment" do you choose?
What does "common sense" tell you?

Note that EVERYTHING you NEED to predict the market
comes out of the motivations described above for buyers and
sellers, which is just based on "common sense".

The question is: if you are feeding a neural net price-only stock data,
are you giving it everything it NEEDS to make a prediction?
I would of course ask the same question of any "TA" or "FA"
fanatic that claims that "FA" or "TA" respectively is a waste of time...

Now, as a practical matter, after running the neural net on the
same amount of data as was required to come to the above
conclusions, can it actually provide a more profitable prediction
than from what we learned (or already knew) above? If not,
then we're actually a step behind with the neural net, because
we haven't LEARNED anything, due to the "black box" nature
of the predictions...

OK it is REALLY GREAT that you raised this point and I hope you'll be
happy with my answer. On
my goldengem website, I have a practise exercise. The practise exercise
is to first get used
to training the net with the days slider at zero (so it is predicting
TODAYS price, based on
all prices and shares. You get to see the net realize "Hey, you're just
asking me for one of the
prices you yourself have input!" and it matches perfectly.

What an accomplishment!

Then, you ease the slider to the right and let it settle again. So,
it's starting from a point of
being trained to know that today's price of the share you are looking
at, probably is going to
have a lot to do with today's price, and then you move it a little.

If there is no relationship, what you see is the same graph shifted to
the right. In other words,
if it cannot do better, usign other loaded volumes and shares (and the
loaded volume of the target share)
than just to say 'it is probably going to be the same price as last
time you checked,' it will do exactly
that.

But, sometimes it does a lot better...throughout historical time it is
able to match tomorrow's price knowing
todays prices and volumes.

The term "sometimes" is troubling to me...replace that with a
correlation coefficient and some confidence intervals and I'd
be a happy camper.

BUT there is still another thing that can go wrong. Since you are
teaching it as it goes along, it may
be just doing what you tell it it should be doing (match the future
target price).

BUT if you set sensitivity to zero, and it still matches throughout
historical time, this means that there WAS
a mathematical relationship, it CAN throughought historical time,
determine tomorrow's price from today's data.

STILL there is a possibility of a further problem: the match throughout
historical time may have been an
unlikely coincidence. To minimize probability of that, use a minimum
number of loaded shares.

Finally, there is always the possibility that circumstances will change
(ie oil wil lbe discovered, a press
story will come out) and a valid existing relationship will change.

I am sort of proud of what I just wrote there, because I think I may
have really nailed your
question. Let me know if not, I think it was a great question anyway.

Well, not really, but the last sentence is really an important point.
"News" has a great impact on "predicting" the market; in fact, the
whole key is the difference between "predictable news" (which of
course really isn't "news" at all) and actual "news".

Look, my mathematical background, such as it is, lies more in
statistics and probability, and I'm always using tools from those
areas to discern if I'm on the "right path" with a particular
inquiry into the nature of the market.

If there is a high correlation between the predicted results and
the actual results over many decades of data, great, it's close to
Miller Time(TM), but first I have to come up with a trading strategy
and money management scheme to maximize my new-found
advantage.

But if there isn't, well then, because my goal is to make money, I spend
just a LITTLE time using my "common sense" or "intuition" to try to figure
out why it didn't work, but just a LITTLE time, because TIME IS MONEY,
and if it doesn't work, IT DOESN'T WORK, AND I WANT TO FIND
SOMETHING THAT DOES.

You see, this is what separates the men from the boys when it
comes to effective market analysis. If all you have is hammer,
then every problem looks like a nail, and if all you have is some
pre-conceived notions about neural nets, or charting, or "TA",
or fundamentals, or egregious lesbian criminal theft, you'll ignore
the stark statistical proof that none of those things "work" very
well...

I've tested neural nets, I've tested hundreds of chart, "TA",
fundamental strategies, but because I've got a finite life span
and don't wish to spend it trying to pump oil from dry holes,
I found it quickest to go back to "common sense" as described
above, and select and analyze my data using that filter.

Yeah, that's one of the keys to fooling around with neural nets, or
really doing anything to try to "predict" the stock market. You gotta
first know what data is important, and the question is, how do you
come to THOSE conclusions? It's kind of like a chicken and egg
thing...

Yes, I guess it also must come down to some people having an intutiive
idea what to do and using the net to extend it just a little, to handle
more capacity for calculation than their own mind. But the creativity
etc comes from the human mind....

Well, you don't want to get too "creative", because that really is the
downfall of the human "intuition". The nature of humans in trading the
markets is to ignore "common sense" and obvious data and go with
their "gut feel", and to the extent they "analyze" the markets at all they
just hilariously (and sadly, depending on just how much they needed
the money) try to rationalize previous market movements to fit some
pre-conceived emotionally-derived "model" of the market. Then,
after "guessing" wrong long enough, they tend to slink away dejected
muttering, "It's all a crapshoot anyway, nobody can win."

The point that a naked human mind has limited powers to calculate
the odds of a game is well-taken, quite obviously true, and has been
proven many times. Yet it is that first "common sense" notion that
is rejected by most market participants; take a poll here, and you'll
find that most think that "the human mind is capable of perceiving
subtle patterns that no computer could see".

This may indeed be true, but it is also true that the human mind
can perceive subtle patterns, like fluffy dogs in clouds, that don't
exist at all...

However, I still believe that "natural stupidity" is the best stupidity
of
all. At least a computer can't talk itself into a completely retarded
trade
the way a human can, which is why I do like to take the advice of
my computer as much as possible, if only to "avoid mistakes"...

Yes. I was thinking, you know how they say averages (like S&P average)
do
better than investors and trusts? One reason could be that when
a share price bottoms out it gets replaced by a share at the top,
whereas
an actual fund manager has to produce funds to cover the difference.

Hmmmm...that's a thinker...what about the index ETFs? They actually
have to buy and sell shares according to changes in the indexes...

Another
reason might be humans buy when something is fashionable (hence
overpriced).

Yes, exactly, people have a fundamental motivation when buying
an "investment", and this does lead them to make "mistakes"...the
goal of out-performing the market is to capitalize on those mistakes,
or at least don't make them yourself...

But if a person has an idea that a connection might
exist, that certain share activity might predict certain other, the way
to make that rigoruos, and quantify it, and get a prediction based on
that would be defniitely to use a neural net.

Yeah, that's the general drill, more specifically you're gonna have to
quantify any results you get statistically, and then ponder why the
results
are the way they are, and after you've done all that, you might have
been better off taking a different tack.

I DID get "interesting" results from neural nets in trying to "predict"
the
market, but did feel that I needed to try different approaches to really
r>efine effective strategies. One of the problems I haven't even
addressed
i>s the quality of a lot of the relevant data (or the data I "think" is

relevant),
and how well does a neural net work when fed a diet of politically
motivated BS.

Well, since I've used neural nets in the past, I'd recommend them
to everybody, on the basis that if I've done something it must be
brilliant
and useful. Hell, I've thought about digging out my old neural net
software and running some tests on the data sets I currently use for
market "predictions" and see how closely the numbers match up
against my money-flow model algorithms...

We're curious to learn about your algorithms.

It's a top-down model that basically goes from broad monetary
aggregates->"savings"->investment class->stock market->stock
sectors->individual stocks. Each step includes some amount of
"common sense" forecasts about future money flows, and a dynamic
summation analysis of previous actual changes and forecasts,
looking for "discrepancies", which may be either the result of
bad data (yuck) or (hopefully) what I call "potential", which
is the difference between where an aggregate or stock price
"should be" and where it actually is, generally due to the
"informational/trading friction" inherent in all markets.

The easiest way to describe "potential" is the classic example
of an "undervalued" stock, where the company is growing its
revenues and earnings nicely but the stock is languishing well
below "fair value". Another upstream example would be if
interest rates are rising, but instead of taking the safe returns
of a money market, with yields getting close to perceived
long-term stock market returns, people are still investing
instead in the stock market.

Since I am carefully summing the forecasted, current, and previous
flows at each level down to the thousands of individual stocks, I
can chose the stocks with the greatest "potential" at a some semi-arbitrary
cutoff point (for years I've basically refused to invest in stocks unless
I could "predict" they would go up at least 100% a year) without
making the "mistakes" of ignoring large-scale monetary aggregate
changes, sector rotation, etc.

Generally, I move in at certain points when "trend" starts to move in
the direction of "potential"...

Wow I really loved this thread, hope it's OK if I copy it onto my
website?

It's all archived anyway so knock yourself out...

---
William Ernest Reid
Post count: 367



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