One of the most, common applications of,
Bayesian networks, or rather, one of
the earliest ones that are still very much
in use today, is for the purpose of
diagnosis. And by diagnosis, I mean both
medical as well as fault diagnosis.
Now, this dates back into the early'90s,
in, the PHD thesis of Heckermann, et al., won the
ACM dissertation award. And a system
called Pathfinder, which looked at, a
range of different pieces of evidence in
order to help a doctor diagnose, a set of
diseases. And specifically, it was focused
initially on lymph node pathologies, so 60
different diseases, all sorts of different
symptoms, and they tried out a bunch of
different rules, methods for solving these
problems. So the first one they actually
tried, this way back in the early days of
artificial intelligence, and they tried a
rule based system. And, it didn't work
really well. The second version of
Pathfinder used the naive Bayes model,
which assumes that all of the symptoms are
independent given the disease. And even
that really simple model got superior
performance to the rule based system that
they initially tried. Pathfinder three
still used Naïve Bayes but it used Naïve
Bayes with better knowledge engineering.
That is they actually, they actually
understood some of the issues behind what
makes a system like this work well and
what. Made and they've fixed it. So
specifically one of the things that turns
out to be really fundamental for the
performance of any probabilistic modeling
system is not to put in zero probabilities
ever except for things that are
definitions because once you put in a zero
no matter how much evidence on the
contrary you have you will never ever be
able to get rid of it. Because anything
times zero is still zero. And so here in
the initial pathfinder tool they put in
some incorrect zero probabilities for
things that were very unlikely but not
impossible and it turns out that, that
gave rise about ten percent of
incorrect diagnosis in the system. And also
did better calibration of conditional
probability which turns out to be
important for knowledge engineering of the
Bayesian network. So for example it turns
out that it's a lot easier to compare for
a physician, to compare the probability of
a finding, a piece of evidence between two
diseases as opposed to the probability of
two different findings within a single
disease. It's much, it's much easier to
say "oh this is much more likely in this
context than in that context" and it turns
out that when they ask the physician to
calibrate this way, they got much better
estimate of the probabilities. Remind you
this was way before they had learning so
it was all hands constructed. And then,
finally Pathfinder four was the full
Bayesian network in all of its full
glory. It no longer made incorrect
assumptions about independencies between
different, say, symptoms. I'll give them a
disease. And that gave us an, both allowed
them to make the model more correct and
also it turns out as an unexpected side
effect by allowing, say, a symptom
variable to have more parents than just
the single disease variable it actually
gave rise to considerably more accurate
estimation of the probabilities because
the doctor could kind of think about
different cases and didn't have to average
them all out in his head. And this is one
of the, I think, really compelling aspects
of Bayesian network models which is that the
Bayesian network model actually turned out
to agree with the experts in an expert
panel of physicians in 50 out of the 53
cases. And these were hard cases. These
were ones that you really needed the
expert opinions on. It wasn't one that
just an average doctor could necessarily
diagnose correctly. And this is as
compared to 47 out of 53 for the naive
Bayes model. Also and significantly less
than that for the rule-based system. Mind
you, and this is an interesting and
important. Aspect is that the Bayesian
network actually outperformed the
physicians who designed the model. And I
mean it didn't outperform the expert panel
but it outperformed the  physician who designed it
Because it was better at putting together all
these different numbers in a way that a
doctor just can't fit all of these
different findings into his or her brain
at the same time. So we talked about, the
CPCS network. It's, one of my, favorite
networks, because it's kinda big and hairy,
and sorta kinda scary to look at. But
anyway, the actual number of variables in
this network is about 500. And each of
them has, on average, about four values.
So the total number of parameters, if you
were to specify a full joint distribution,
is about 400-500, so that's about, it's
about four to the 500, or two to the power
of 1000, which is more than the number of
atoms in the universe. So obviously,
one couldn't specify this as a complete
joint distribution. Not to mention that
the probability of each and every one of
these is about, is as close to zero as makes no
difference. Because it's the probability
of, you know, 500 different, I mean
events involving 500
variables. If you were to if you were to
actually construct a CPD for each of these
for each of these variables the number of parameters would be about 133 million.
Which is fairly better than two to the
1000 still much too large. And so it turns
out that they made additional simplifying
assumptions that we'll talk later on that
allowed them to avoid a complete table
representation of the CPD's and rather do
a more compact one and that gave rise to
about a thousand parameters. Which is
still a lot but not but actually is
tractable to deal with. So we already
talked about the fact that these medical
diagnosis systems have emerged from
research and Microsoft built a medical
diagnosis system. Various other people
have built one as well. This has been a
little bit slow on the uptake in the
medical field because it doesn't fit
naturally into a physicians, pipeline.
Maybe now, with the advent of medical, of
electronic health records, there will be
more data entered into the computer so,
these systems will be more common use.
But, until very recently most doctors just
wrote stuff down on paper and so there, it
was very difficult to put this into the
standard production pipeline for
diagnoses. And then finally fault
diagnosis has been a much, more direct
application of these, of these systems,
because here we don't have an issue, of,
of how doctors typically do their
diagnostic pipeline. So within the
Window's operating system, there are
thousands of these little troubleshooters
that help you diagnose problems with your
printer, with, with Excel, with your
email, and each of these has a little
Bayesian network inside that answers
probability questions, given observations
about what, What the system, the, the,
about the, about the model involving, in
this case, for example, the printer. And
there's also a big website out there that
does, car repair. And, you put in the make
and model of, and year of the car. And
what are the main problems within it.
Figures it out and tells you what to look
at, and what the most likely complaints
is. And the reason behind the benefits of
this, people don't use Bayesian networks
are cool even though they are, they use
this because it provides a very flexible
user interface for the user. You
instantiate the evidence of the Bayesian
network out comes the probability, you
don't want to answer the question right
now, that's okay, you can answer it later.
It's just means that it's an observation
that you didn't get the condition on. And,
and then for the designer this type of
system is really easy to design and
maintain. Because if for example something
changes a little bit in your printer
structure. If you were to design a
standard menu-base system you'd have to go
and rebuild the entire tree that asks you
know wh, what is the besides what is the
first question to ask, what is the second
question to ask. What is the most likely
diagnosis. Here in the Bayesian network, you change
one probability, maybe add an edge, and
everything just emerges from that in a
very straight-forward way so it's much
more modular and more maintainable than,
than a hardwired menu-based system. And
that's what the people who use these
systems will you tell is that, why, that's
why they chose this path as opposed to As
opposed to the hard-wired methodology.