[Speaker] - Okay, so thank you for the introduction
and thank you all for being here.
So the speed-accuracy trade off is
something we encounter a lot in each time.
Often when you try to evaluate the quality
of an interaction,
we measure its speed and accuracy.
Right?
And want this to be as high as possible.
And if we want to increase the speed and accuracy,
we end up at the limit, above which,
if we try to increase accuracy,
we should decrease the speed,
and vice versa.
This is what's called the speed-accuracy trade off.
And in this talk I'm interested about
the speed-accuracy trade off in pointing movements.
And now this has famously been studied by Fitts.
And so what he did was, he made participants
sit in front of a board, with two targets
that have a certain size w.
And he made them repeatedly point
back and forth between them.
And now, Fitts, manipulated accuracy by
modifying the values of d and w.
Which is summarized by the index of difficulty.
So ID is the log of one plus the ratio d over w.
And what he found was that the movement time
was actually predicted by this index of difficulty,
and they found the linear relationship between
movement time and index of difficulty.
Now what's important for us in HCI
is that the parameters a and b of this
linear relationship, they vary according to the
participants and to the device.
So what, if we estimate these values
for a and b, then we can actually
evaluate the performance of the device or user.
And if we assume values for a and b,
so we used old values from existing experiments
for example, we can actually predict movement
time for a pointing task or as part
of a more complex interaction.
So Fitts law is widely is used in HCI.
I guess all of you have probably heard of it,
but still it suffers from many issues.
And in this presentation, I have
selected three problems.
So the first problem, is the problem of many
different formulations.
And now the question is, how many
different formulation can you think of?
And personally, I know about fifteen
probably more.
And now the second problem is that sometimes
participants miss the targets.
So typically what we do in HCI
is we look at the actual
distribution of endpoints,
which are all the, all the black bullet points.
We measure their standard deviation and
then we multiply this by a constant factor.
And this is our effective width, W, e,
and we replace the width by this effective width.
Now this was a solution, first given by
Crossman in the experiment of psychology,
then it was popularized by MacKenzie in HCI.
And in the paper we have a
critique of this solution.
So I will refer you to the paper,
it's a bit to long for this talk.
But actually this issue with target misses
points to, is that Fitts's experiment
actually fails to measure correct accuracy
in an accurate way, because of the target misses.
The third problem, is a problem which
I call the problem of regression.
So this is empirical data, that
you see all the time in Fit'z law.
So on the y axis, you have movement time
and on the x axis, you have the index of difficulty.
And here, each blue dot is the outcome of
a single movement.
Now, according to Fitts law, you would expect
that all these blue dots align quite
nicely, onto a straight line.
An you see, it's actually not really the case
and we can actually compute the
best straight line possible for this points,
which is the orange line here, and you
see the r squared value is quite low.
It's much too low for a typical
Fitts task for a task (muffled speaking).
Because what we actually do in HCI, usually
is we consider to average
movement time per condition.
So you can see here the blue scattered
parts is the same as previously.
Except here, a represented orange diamond
which are the average movement time per condition.
And in these align quite nicely
actually, and if you compute the best
straight line through this, you find
typical values of r squared that you find in HCI.
Except the parameters of the line are actually
more or less the same as before.
Now, I know some of you
would tell me that this is normal.
We are just re-using the noise that
we have in the data by averaging the measures.
But then the question is, what do
you do with data like this?
So this is, the data from the field
study, which is very high variability.
And of course, we can compute
linear regression and this will give
us the orange line that sits kind of
in the middle.
And you can see obviously, what can we do
with this information?
It's hard to interpret.
So the goal of this work, is to provide
the theoretical framework for
the speed-accuracy trade off, that's simple
but rigorous and not completely driven by
empirical considerations and hopefully
to help solve problems I've just shown.
And now what we are going to use this
information theory, for several reasons,
is first because Fitts Law was
actually originally conceived as an analogy
with the Shannon capacity formula, and because
the channel capacity theorem can actually be
interpreted as a speed-accuracy trade off.
So let's jump right into the, only result
I'm going to present today of information theory
which is the Capacity of the Gaussian Channel.
So first of all, what's the channel?
So a channel is just a pipe, it does
an input, x, and an output, y.
And in the case, this particular case
of the Gaussian Channel, the model is
that the output is a noisy
observation of the input.
For you see, y is the sum of x, the input
plus sum gaussian symbol.
And now we have a clever way
of having a mathematical formula
for the transmitted information
in despite of the information theory
which is called I.
And what we try to do, is we try
to maximize this transmitted information
and this maximum transmitted information
is called the capacity, C.
And this maximum, you find it
over all possible input distribution.
So you look for all the x's that maximizes
the transmitted information.
And in the case of the Gaussian Channel, the
input that maximize this is also
the Gaussian distribution with variance P.
Now if you look at the famous
Shannon's Theorem Seventeen, it's
just an evaluation of the C in
the case of the Gaussian Channel.
And so you see, it's simply
the bandwidth times
log of one plus p over n
where p is the power of the input
and n is the power of the noise.
And this theorem expresses
a trade off between time through
the bandwidth parameter and bits.
Now Fitts directly applied this
formula, and he said well, in case
of human movements, my signal is
the average movement and the noise
is just a moving variability.
And then he said, because bandwidth is
expressed in Hertz , which is
the units are one over a time, he simply
identified bandwidth to one over a time.
And if you put all of this into
Shannon Capacity formula, you
actually find Fitts' first formula in 1954,
and then he added later in intercept
for Better Data '15.
So if we look, take a step back, there
are some questions that emerge.
So first of all, why do you
identify bandwidth with one over m,t?
It's not that simple.
And why would you equate a variance,
which is suppose to be proportional or
at least related to the square of the input, to
the amplitude, which is, would
be related to the input itself.
And what's the channel model of the
aiming task and what are the
input and output's.
And by this, we mean, basically
what's the link between
Channels Capacity formula
and aiming.
Cause to us, it's hard to draw
a link just from this.
So our model actually answers these questions.
So this is the name of the model, A Formal
Information-Theoretic Transmission Scheme.
And so the first abstract model
is very simple.
So there's a, the user has the intention of
aiming it towards the target and this
intention is not to a signal that send
it over a noisy channel to the muscle
which prefer movement.
And as we've seen just before, everything in
this work relies on the Channel model.
So what we are going to do,
is were going to integrate the task
constraints in the Channel model, okay.
So let's do this.
So if we loo at the task, or when we
have to hit a target, what we are going to do
is, we are going to aim at
the center of the target and then
we allow a variability that's the size
of the targets.
So this gives us first constraint on noise.
And then the fact that the
targets are separated by distance, D, gives
us second constraint on input
then if we take these two constraints together
this gives us third
constraint on the output.
So now we have assumed basically, that
the noise was bounded which we still
have to choose a distribution for noise
and this is not something that's easy.
So what we do is, we use something that's
used in physics, which is called
the Principle of Maximum Entropy,
which is basically says that if you
don't know how to choose your distribution,
your best bet is to go with the one
that maximizes the entropy.
So in our case, this is
the uniform distribution.
So we assume, so this is a
recap of the channel model, so it outer bounds
and the uniform distributed noise.
And so in the paper, we actually show
how we can compute the capacity of this
channel so we express the transmitted information
and then look for the best input.
And we show that the capacity is actually
log of one, plus d over w.
Which is exactly the idea
proposed by MacKenzie in '99.
And what's interesting is if
you look at the input that actually
reaches the capacity, its the
discreet uniform input.
And I've represented it just here, so the input
space are all the set of black bullet points.
So its as if you see the entire
available space was filled up
with targets of size w and when
you actually aim towards a target
you actually choose the right target.
And so we summered this
in the paper with a catch phrase, which
is that aiming is actually choosing.
So this is an interpretation.
So, I know some of you will have
maybe a tough time accepting the uniform
noise assumption, but the interesting
thing here, is that if you look a what
the uniform noise was given by the maximum
entropy principle, so in our case
it was actually the worse noise.
Right.
So this capacity is actually a lower bond.
And now the question is, suppose the noise
is not uniform, but for example Gaussian,
which most of you will agree is likely,
what is the error that we actually make
by assuming this capacity with uniform noise.
And now in the paper, we actually show that
this difference is at most zero point two bits.
So its actually quite small.
And you can find more details
about this in the paper.
So now we presented a model
for errorless task with uniform noise
and then we show how it can be
generalized to any abitrary noise
and I just show you an evaluation
with the Gaussian noise.
And so what about target misses.
So that's what I'm addressing now.
So sometimes participants miss
the target as I have said.
And in the paper, to talk about misses,
we distinguish errors from erasures.
And what we mean by errors, if you look at
how error, how the correction is computed
it takes into account the standard deviation,
and standard deviation basically considers
the distance from each
endpoint to the target center.
So with in this definition, all
movements involve metrical errors.
So this is what we mean by errors.
It's just that their amplitude varies.
Now on the other hand, if we look at GUI, what
matters is really whether or not
the click falls inside of the intended area.
So here, if I want to click on sponsors
I can click anywhere inside
this light gray orange box.
And it doesn't matter where
the click takes place.
And this Dichotomous hit or miss notion
corresponds to the notion of erasures.
So in the paper, we treat the mistakes as
erasures and we show that the
calculation of the capacity is
actually very simple.
And it's simply one minus epsilon.
So which is actually the
success rate times the i,d.
And you see that the i,d, corresponds
to the accuracy as prescribed by w and
the success rate is just the correction
for the misses.
If we compare the two corrections, so the
Crossman- Mackenzie correction
and the the one that comes
from the erasure model
an important difference is that
the Crossman-Mackenzie correction
assumes the Gaussian distribution for the
errors, where as in our case, there's
no such assumptions.
So actually we have a non- parametric
formulation here.
Another nice thing is that if you look
at the condition for null error rates
the Crossman-Mackenzie correction
is actually undefined.
And in our case, it's simply reduces
to the index of difficulty, so this is
simply interpreted as the
index of difficulty is the
transmitted information when there
are no errors.
So it's very simple interpretation.
So this is, I basically presented the
complete model for movement time in Fitts task.
But we never actually ask ourselves
which movement time are we
talking about.
Cause, if we think about what channel
capacity gives us, it should give us
a minimum movement time, cause
the channel capacity is expressed as a maximum.
But what we do in HCI, is usually
what we ask participants to
work as rapidly as possible then
we trust them to actually do it
then we compute the average time.
So this is something that's kind of like an
average-minimum time.
And so what we argue in the paper
is that we, there's a lot to be gained
if we separate these two metrics into
an average time metrics, which would
be given by the linear regression as usual
and the minimum time metric, which would
correspond to the information theoretic
interpretation of Fitts law.
And to show an example of how this
looks like, so this is a data sample
from a point in field study.
So you see that the orange line
is the one that you get from linear
regression kind of sits in the middle, and the
minimum time metric is given
by the the black line.
So you see this gives a lot more information.
You can actually compare to
different metrics and this gives
a lot more useful information
than just the orange line that
sits in the middle.
So to conclude, our model links
the index of difficult to a channel capacity,
where everything is defined and interpreted.
Now on the downside,
it's kind of a black box model for endpoints.
It's only concern with movement time, it's not
concerned about the full trajectories.
It's not really based on any empirical
findings about the nervous system and it's
based on abstract information theory and we
don't take feedback into account.
Now a third problem is that we
never actually tell you in the
paper, how to compute the minimum
time regression and, so actually
this is, was work done in 2016, 2017
and it was published in 2018.
So you can find the references here and since
then, we've actually made a lot of progress.
So we have come up with a new
scheme, which we call Fitts 2.
Which is basically a scheme for full trajectory
with feedback control.
So you can find most of it in the pre-print, or
inside my thesis, which is online since December.
And then we also provided recently, a new
regression technique, which is a formal
method to determine this minimum time metric.
So again I refer you to pre-print for this.
Thank you for your attention, and I will be
taking questions.
(Applause)
[Announcer] - It's time for one quick question.
[Interviewer] - I have a question for you, would
you advise from now on if you want
to characterize new input devices
and you want to give like an
index of difficulty or performance measure
are you actually specifying that
you should not normally compute minimum
time but also average time, should we
actually give two measures?
[Speaker] - Yeah, I think there's a lot to be
gained actually by separating
these two measures and the difference
between those two might give
you interesting results, for example
if I did this in a controlled, if I had
shown you the same thing in
a controlled study, the average time
metric and the minimum time metric
would be almost identical.
In the field study, they are very far apart.
And actually, just computing the two
and looking at the difference can
actually give you an idea of how much the
participants actually invested their
efforts during the experiments.
Because sometimes we know participants, they
get bored and especially in experiments like
Fitts task and this actually, if you
notice that the two lines are quite close
it can give you some assurance that
the participants were actually engaging
the task and things like this.
So this is one idea, of course there are
probably other things that
can be envisioned.
[Interviewer] - Yeah, perhaps that a variance
among participants or experiments, some
input devices might just...
[Speaker] - Yes.
[Interviewer] - have more variance than others.
[Speaker[ - Exactly, some Input devices might
create more variance than others and this would
also be noticeable with this.
[Interviewer] - Okay, Thank you, very,
very challenging (mumbles).
(Applause)
[Announcer] - Okay, with this we conclude
the session on behavior monitoring.
Time for a break.