ssue: July 2007

Monkey See, Monkey Do—A Study of

Decision-Making

by Alice G. Walton

• Red or Green?

• How Do They (We) Do It?

• Stay Tuned

• Probabilistic Inference Explained: the Log Likelihood Ratio

• 715 Unique Combinations: A Case Study

• Discussion Questions

• Journal Abstracts and Articles

• Bibliography

• Keywords

AFP/Getty Images

Researchers study monkeys because they are capable of behaviors that are similar or identical to human

behaviors, and because it's easy to motivate them by offering food or drink rewards.

Decisions, decisions... We make loads of decisions every day. Some are simple (do I

have time to run to the store before it closes?) and some are anything but, but most

require adding up the pros and cons of a situation and then coming up with the best

possible response to a question that may have no clear-cut answer (what do I want to be

when I grow up?). How does the brain do this "arithmetic" in a timely manner?

Researchers at the University of Washington's National Primate Research Center

published a paper in the June 28, 2007 issue of Nature suggesting that the monkey

brain—and by extrapolation, the human brain—assesses the odds in a process that in

some sense involves calculations with logarithms, and typically arrives at the best

answer. If this sounds difficult, even more astonishing is that while it might take minutes

or longer to actually figure out odds and calculate an answer by hand, the brain comes up

with a solution in the blink of an eye.

This decision-making behavior is called probabilistic inference—it's the act of evaluating

all the information one has available and then determining the most likely outcome. In

less technical language, it's making an informed guess based on what we already know,

even if the information is incomplete. (Below, in the section called Probabilistic

Inference Explained: the Log Likelihood Ratio, there's a real-world example so you can

see how this works.) It is this behavior that researchers Tianming Yang and Michael

Shadlen wanted to investigate in rhesus monkeys—not only to see whether the animals

were able to do it, but also to get an idea of what is going on in the brain that leads to this

complex behavior.

Red or Green?

Yang and Shadlen used rhesus monkeys because they are capable of behaviors that are

similar or identical to human behaviors, and because it's easy to motivate them by

offering food or drink rewards (not so different from what largely motivates many

people, for that matter). In the study, the monkeys were trained to make a decision—to

choose either a red or a green dot—based on other information also presented to them at

this time. Specifically, the monkeys were first trained to understand that various 2-

dimensional shapes were associated more or less strongly with either red or green dots.

Depending on what combination of these other shapes was shown to them, the likelihood

of a monkey choosing either green or red would change.

Courtesy of Tianming Yang

In the study, the monkeys were trained to make a

decision—to choose either a red or a green dot—

based on other information also presented to them

at this time. Specifically, the monkeys were first

trained to understand that various 2-dimensional

shapes were associated more or less strongly with

either red or green dots.

Courtesy of Michael Shadlen

Here's the set-up in a little more detail. In the first training period, the monkeys sat in

front of a computer monitor which would show, for example, a diamond shape. Then

they were presented with a green and a red dot. The monkeys learned from experience

that they got rewarded with a liquid treat only when they moved their eyes to the green

dot after seeing this diamond—so they learned that "diamond" means "choose green"

100% of the time. After they mastered this first part of the training, they were exposed to

another shape: a triangle. This shape also indicated that they should choose green, but

now the association of green with a treat held only 90% of the time. That is, choosing

green after seeing the triangle led to a treat 90% of the time, but the rest of the time,

choosing the red dot would lead to the reward. Clearly, green is still the better choice

here, if you're in the market for a reward. Training went on like this for ten different

shapes. You probably get the idea: one shape was always associated with a green dot, one

shape was always associated with a red dot, and the ones in the middle represented

various likelihoods of red or green being rewarded (so, a Pac-man shape might indicate

that green would be rewarded 60% of the time and red 40% of the time).

Now to the heart of the experiment. Once the monkeys learned the "meanings" of the

various shapes, the researchers showed them random samplings of four shapes in one

trial, along with the red and green dots, just like before. Because so many combinations

of shapes are possible (715, to be exact), Yang and Shadlen were confident that the

monkeys couldn't simply memorize combinations. So the monkeys now had some serious

reasoning to do. There were now four different pieces of information that the animals had

to use, not just one. How would you tackle this task? Is it possible to add up all the values

of the shapes and come up with a sum that would indicate either red or green? Yes, it is.

But actually calculating the odds mathematically would take a while, unless you're a

prodigy. Luckily, as Yang and Shadlen found, the brain is able to do this in an instant, by

computing a "Logarithm of the Likelihood Ratio," or "LogLR." This is simply a fancy

way of saying that the brain is able to combine all the information coming in and then

choose the most likely outcome. The researchers found that the monkeys were incredibly

accurate in making the choice that would lead to a reward most often—and they made the

choice in less than one second!

How Do They (We) Do It?

Courtesy of Michael Shadlen

Based on previous studies, the team suspected there might be a connection between the LIP

area and the kind of decision-making that the monkeys were doing, probabilistic inference

behavior.

What's going on in the brain that allows such speedy and accurate calculation? This is the

second question that Yang and Shadlen asked. The cerebral cortex is the part of the brain

that does the heavy lifting—the serious thinking—and it's also the part of the brain that is

the most highly developed in human and nonhuman primates. The researchers in this

study were interested in a particular area of the cerebral cortex called the lateral

intraparietal (or LIP) area.

Based on previous studies, the team suspected there might be a connection between the

LIP area and the kind of decision-making that the monkeys were doing, probabilistic

inference behavior. To investigate this possibility, Yang and Shadlen took recordings

from individual neurons in the LIP area with tiny electrodes as the monkeys were

performing the task, and then plotted the neurons' activity against the LogLR. What they

found was that there was an incredible match between the neurons' rates of firing and the

LogLR. That is, as LogLR increases or decreases, the activity of the neurons in the LIP

area also increases or decreases. This finding is very exciting since it seems to pinpoint

an area in the brain that may play a role in the kind of complex reasoning and decision-

making that was shown in the study. The LIP area appears to be a pretty nifty little piece

of brain tissue.

But what is the LIP area actually doing? This part is still a bit unclear. Is it the part of the

brain that actually pieces together all the incoming information to arrive at a final

decision, or does it simply "announce" that decision, much like a jury foreman? The

authors point out that the answer is not known at this time, and it will take more research

to answer such questions. The LIP area is part of a system used for guiding eye

movements, but it is also activated when one is about to make a movement. What's

interesting is that various parts of the brain are often similarly multifunctional, so that one

circuit can be responsible for making a choice about an action and executing that action.

Stay Tuned

What will the researchers do next? One question to address might be: would the results

have been different if the monkeys were asked to touch the red or green targets with their

hands, rather than moving their eyes to them? There are many other questions that remain

unanswered—you can probably think of some yourself. However, even with the

uncertainty that remains, the experiments tells us a little bit more about how this

complicated, yet every-day behavior—decision-making—may work in monkeys, and in

humans.

Probabilistic Inference Explained: the Log Likelihood Ratio

Photos.com

To explore how probabilistic inference works in the real world, let's look at your chances of

getting into the college of your choice.

To explore how probabilistic inference works in the real world, we'll consider the

following example. Say you're trying to figure out how likely it is that a college you're

thinking of applying to will admit you. You know that they have an overall admit rate of

24%; the other 76% are rejected (we won't get into waiting list complications). But you

can use some other factors to improve your assessment of the odds. You have an

impressive resume when it comes to extracurriculars, and you know—you have a spy in

the admissions office—that 80% of the admitted students typically have strong

extracurriculars; however, 40% of the rejected students also have strong extracurriculars.

Your SAT scores are about the same as 80% of the admitted students—but 50% of the

rejected students had those scores too. Finally, you happen to have a parent who went to

the college; 24% of the admitted students also did—but 18% of the rejected students were

alumni children. Before explaining how to apply the Log Likelihood Ratio to our

assembled data, it may be worth clearing up a possible source of confusion. If you've

studied probability , you may have learned that probabilities are supposed to sum to 1.

This is certainly true if you are talking about a collection of possible events that are

mutually exclusive and together exhaust all possibilities—like the possible outcomes of

tossing a coin. In the example above, .24 and .76 sum to 1, since an applicant will be

either accepted or rejected, with no other possibilities allowed. But for the other factors,

the numbers don't need to sum to one because we're comparing percentages of admitted

students who have a certain characteristic with percentages of rejected students who have

that characteristic. At the risk of belaboring the point, if 90% of admitted students like ice

cream then we could deduce that 10% of admitted students don't, but it's quite possible

for 90% of rejected students to also like ice cream: the numbers don't have to add to 1.

On to LogLR. The math for this calculation is done by adding all the logarithms of the

ratios that we've gathered together (don't freak out, it's not that bad!). If the answer is

greater than zero, then chances are you'll get in; if not, then start expanding that list of

schools to apply to. Our first ratio comes from the over-all admit rate: it's 24/76. We take

the (common) log of this, and get -0.50. (The log of anything less than 1 will be

negative!). OK—we knew it wasn't so easy getting in. Now let's look at the plus factors.

For extracurriculars, we get 80/40 = 2, and 2 has a log of .30. For SAT scores, the ratio is

80/50 = 1.6, with a log of .20. For the alumni link, we get a ratio of 24/18 = 1.33, with a

log of .12. If we add up the four logs, we get a positive score of .12: hooray! Still, you'd

probably be advised to put a few safeties on your list—we're talking probabilities, not

certainties.

This kind of calculation takes a little too long when you actually do all the math—you

probably wouldn't want to do this every time you had to make a decision. Now think

about how quickly the brain does this kind of work every day, as shown by Yang and

Shadlen's experiment, where similar calculations were done almost instantaneously!

715 Unique Combinations: A Case Study

Photos.com

The monkeys saw four shapes at a time, and there were 10 different shapes, adding up to 715

unique combinations. Can you come up with the same number?

The authors of the study point out that, since the monkeys see four shapes at a time, and

there are 10 different shapes, there are 715 unique combinations. How did they arrive at

this number?

We can label each of the shapes with a number, from 0 to 9. Now, if you think of

counting in the decimal system, there are 10,000 numbers—not 715—from zero (= 0000

) to 9,999. But (as we learn in first or second grade), a 5 in the 'ones' position is different

from a 5 in the 'tens' or 'hundreds' or 'thousands' position; position value matters when

we're counting numbers, but for this experiment, the monkeys didn't care where a shape

was on the screen, just whether that shape was there or not. So, for example, 5512 and

1525 and 2155 (or their equivalents in terms of shapes), would all be considered the

same, or at least, would all yield the same LogLR.

So, let's count the number of combinations another way, where position doesn't matter.

There are several different cases; we'll enumerate those cases, calculate how many of

each there are, and then add them up.

Case 1: All four shapes are the same. Since there are 10 different shapes, we can have 10

different, or unique, situations with all shapes the same. So, for this case, 10.

Case 2: Three of the shapes are the same, and the fourth is something else. Say three of

the shapes are diamond—what about the fourth? It can be any of the 9 other shapes, so

we have 9 possibilities, starting with three diamond shapes. (We can't have the other

shape be a diamond, because that would give us 4 diamonds, and we already counted that

in case 1.) If we take three of any other shape, we have the same situation. So, we have

10 times 9 (ten choices for the shape that is repeated three times, and for each of those ten

possibilities, nine other choices). So, for this case, the total is 90.

Case 3: Two of the shapes are the same.

Subcase A: We have two pairs—for example, two diamonds and two triangles. If this is

the situation, basically we are picking twice (once for each pair) out of 10 possibilities

(the 10 shapes). Picking k items out of a total of n possibilities is an exceptionally

common situation that arises in math, and the answer is given by the binomial coefficient,

which is: n!/(k!(n-k)!) . (The exclamation point stands for "factorial"—e.g. 10! means

that we start with 10 and then multiply it by every positive integer less than it: 10 x 9 x 8

x 7 ... x 2 x 1.) So, with 10 pick 2, the formula reads 10!/(2! x 8!). If we work this out

(canceling 8 x 7 x 6 ... etc. from top and bottom to make life easier), the number we get is

(10 x 9)/2 = 45. So, 45 for this subcase.

Subcase B: We have one pair, and two other (distinct) shapes. Ten distinct pairs are

possible. For each pair, we must choose 2 other shapes—so, we are picking 2 from 9

possibilities (not 10, since we can't choose the same shape as the pair itself). So, we have

10 times 9 pick 2, or 10 x (9!/(2! x 7!)). Multiply this out and we get 360, for this

subcase.

Case 4: All four shapes are different. This is 10 pick 4, so we use our formula again:

10!/(4! x 6!). After canceling the 6! from top and bottom, we have (10 x 9 x 8 x 7)/(4 x 3

x 2 x 1). This equals 210.

Now, we add up all the cases: 10 + 90 + 45 + 360 + 210. The total is 715—as it should

be.

Discussion Questions

If you were the researchers in this study and you were designing a follow-up project,

what would it be?

Think about some more questions that should be asked/answered if you were to do some

research in this area.

Journal Abstracts and Articles

(Researchers' own descriptions of their work (summary or full-text) on scientific journal

websites).

"Probabilistic Reasoning by Neurons" www.nature.com/ nature/ journal/ v447/ n7148/

abs/ nature05852.html.

Bibliography

Cisek, Paul. "The currency of guessing." Nature (447). June 28, 2007. Page 1061.

Shadlen, Michael N. Research Abstract, Howard Hughes Medical Institute, (month day

year) [accessed month day year]: www.hhmi.org/ research/ investigators/ shadlen.html.

Yang, Tianming & Michael N. Shadlen. Probabilistic reasoning by neurons. Nature

(447). June 28, 2007. Page 1075.

Keywords

decision-making, probabilistic inference, Tianming Yang, Michael Shadlen, National

Primate Research Center, Logarithm of the Likelihood Ratio