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The Human Mind is a Bayes Logic Machine
lexxyz writes "Apparently the human mind can predict the distribution type for a given sample of results.
A study found in The Economist has shown that a group of minds working on single pieces of data, can together generate the statistical model used to represent a given sample. Note that it takes a group of people to be able to accurately predict the behaviour of something, not a single individual"
From the fine article:
Phew! Once I read that, I realized I didn't have to read the rest of the article having now taken a large enough "sparse" sample.An added benefit, I already know what all of the posts are going to say, including this one!
An added benefit, I already know what all of the posts are going to say, including this one!
Impossible:
9EF5A76EB34EDCC29CC88F18722CF99A
This is the md5 of a phrase. You can use google to see what it is, but it would be completely impossible for you to know I would post that exact hash.
Furthermore, there is actually no solid evidence that the future exists, only the present (and the qualified jury is still out on that one).
The dangers of knowledge trigger emotional distress in human beings.
A study found in The Economist has shown that a group of minds working on single pieces of data, can together generate the statistical model used to represent a given sample. Note that it takes a group of people to be able to accurately predict the behaviour of something, not a single individual.
hugh?
The key to successful Bayesian reasoning is not in having an extensive, unbiased sample, which is the eternal worry of frequentists, but rather in having an appropriate "prior", as it is known to the cognoscenti. This prior is an assumption about the way the world works--in essence, a hypothesis about reality--that can be expressed as a mathematical probability distribution of the frequency with which events of a particular magnitude happen.
So is this more evidence that creativity and regular intelligence do not get along too well?
Religion for nerds. Stuff that really matters
A study found in The Economist has shown that a group of minds working on single pieces of data, can together generate the statistical model used to represent a given sample. Note that it takes a group of people to be able to accurately predict the behaviour of something, not a single individual.
Well, that's a somehwat misleading summary. These people were not knowingly collaborating. Each person would have had to answer the questions independently (not knowing what the other respondants' answers were) in order for Bayes to be applicable. Each person's response counts as a piece of evidence or clue in inferring the underlying probability distribution. Their answers are combined using Bayes's rule by an external third party (the researchers). So, yes, this technically counts as a group of minds working together, but I think the way it this summary was worded might give people the wrong impression.
Think about it this way: if you lock a bunch of people in a room toegther and have them come up with an answer, the "strong" personalities in the room are likely to have a heavy influence on the "weaker" ones. People who aren't really firm in their opinions are going to influenced -- whether they realize it or not -- by people who sound confident. The article makes a big to-do about the fact that Bayesian techniques allow you to get good answers with a small number of people working on the problem. But the key is that those people have to be working independently because it's going to be damn difficult to identify and subtract out the cross-correlation of members influencing each other.
I'm making (what I hope to be) an important point. I think business people who read this article or even slashdotters who read the above summary may get the impression that small meetings are a great way to arrive at strikingly effective solutions. That's not what Bayes techinques are about. If you want to put a small group of people to work on a problem, you'd better separate them , otherwise Bayes's rule is not strictly applicable.
GMD
watch this
WOW!!
Imagine a beowulf cluster of these!!!
Good point. Maybe a better one though: who stole your sense of humor?
I call prior art on psychohistory
"Imagination is more important than knowledge."
It's not all about data and results. It's also about pre-formed boundaries, or domains within which answers usually (and some might say 'logically') fall.
This is one of those elementary, goosey sorts of tomes (if you RTFA) where a bunch of nerds go around with a bad hypthosis and come to an 'enlightened' conclusion.
Consider the techniques that surround Wolfram's expostuations-- that the world is algorhmic, and language ill-describes these algorithms, loosely defining them as processes. These setup boundaries within which we derive domains where answers must lay.
Proving that with just a few data points within a tight algorithm that you'll get the right answer is just hilarious-- of course you will. The domain fits, and so the answer must. The domain gets defined by a number of experience points as hidden references that allow the frequentists to get magic (e.g. hidden and historical) inferences to the answer. This is where the phenomenon of the trick question makes us all so frustrated.
My point? Inference has predefined boundaries, and so of course Bayesian logic doesn't require a bunch of data to lead to a correct conclusion because the boundaries are already so tightened that only those that randomly guess, and don't use historical data points (e.g. their freaking memories) are going to blow the answers.
Sigh.
---- Teach Peace. It's Cheaper Than War.
While the article concludes:
Which is not really the same. To say that our minds *are* this type of logic machine indicates that we have no features *except* those of a Bayes logic machine, something that is hardly supported by the evidence that the predictions of *many* people (not just one) fall along the proper probability distributions for those frequencies they tested. I.E. that we apparently assume a poisson distribution for some things that have a poisson distribution, whether or not we know what that is, etc.
In other words, while we might have the *capability* of a Bayes logic machine, there is no indication that we are *limited* to only the realizations such a machine can provide.
Mod article (-1, Typical Slashdot Hype)
"Proving that with just a few data points within a tight algorithm that you'll get the right answer is just hilarious-- of course you will. The domain fits, and so the answer must. The domain gets defined by a number of experience points as hidden references that allow the frequentists to get magic (e.g. hidden and historical) inferences to the answer. This is where the phenomenon of the trick question makes us all so frustrated."
So how long does my group have to camp this spot before my production unit can start crafting? And how will this effect my guild's power gaming marketers?
-Rick
"Most people in the U.S. wouldn't know they live in a tyrannical state if it walked up and grabbed their junk." - MyFirs
...is to pose the unanswered questions to this collective Bayesian mind:
Given how old the universe is, how long does the universe have until the universe collapses back on itself? Hey, at least we'll have the probability of the right answer!
I'll form my OWN solar system! With blackjack! And hookers!
Back in 1995, when I was at Carnegie Mellon, a researcher did a project in the planetarium at the Carnegie science museum. He had programmed a "joystick" to receive reflections from a set of reflective paddles held by the people in the audience. Each paddle had two different sides (red and green); depending on which side you held up, a different signal got sent back to the main processor (positive or negative, respectively). The overall "direction" taken by the game was determined by the sum of the responses - so if everyone held up "red", it as a 100% positive; but if everyone held up "green", it was 100% negative; and so on, with straight linear interpretation.
The first game was Pong. Up and down were controlled directly, if cumulatively, by the audience. You would think that control would be spotty, and that controls would overshoot. Instead, the audience was INCREDIBLY accurate in its overall response; even when the game got very fast, the audience played very, very well against the computer.
There were several games presented, but the last was a flight simulator, flying a plane through a set of rings. The left half of the audience controlled up and down; the right half controlled left and right. Again, you would think this would be nearly impossible to control - but the audience never missed a single ring, even when the game got fast.
Individually, it's doubtful that many members of the audience could have played any of the games as well as we saw the group play cumulatively. It was a clear and very effective demonstration that there was some sort of statistical model at play in the interplay of all those minds.
Your production unit lacks motivation.
Your marketers will quit because they're bored and going broke.
---- Teach Peace. It's Cheaper Than War.
My mind can predict future events usually 3 month in advance.I believe that everyone has this ability.I also believe in evolution. ,you cant change the future.
The precogs in the movie minority report is a good example.I see short clips of the future also.But unlike the movie
I witnessed this procces in action several times.It seems to try every possible outcome to predict an event while time stops.I think that understanding the true nature of time is fundemental in understanding how the mind really works..
http://web.mit.edu/cocosci/Papers/prediction10.pd
It begins:
These questions have specific "right" answers, which can be achieved based on having the proper mental model for how lifespans and movie grosses are distributed. See how good a job you could do, without peeking, just based on your prior knowledge about the world.
Inference has predefined boundaries, and so of course Bayesian logic doesn't require a bunch of data to lead to a correct conclusion because the boundaries are already so tightened that only those that randomly guess, and don't use historical data points (e.g. their freaking memories) are going to blow the answers.
I'm not sure I agree with you. What is remarkable about these experiments is not that the population gets the right answer, where right answer here is a number, like 42. It's that the population correctly modelled the prior distribution that a Bayesian would use to infer the correct answer. Not only can they get 42, but they can decide whether it's 42 with Gaussian, Laplacian, Bernoulli, whatever, noise, with it's attendant parameters. In other words, take a population, give it a context and a data point, and it will succeed at the model selection problem (which prior do I use?), and provide the correct parameters for the model.
Of course, all this hinges on whether the 'true' model for the context is really a well-defined (in the mathematical sense) distribution.
So long, and thanks for all the Phish
http://www.monzy.org/audience/
p df
http://www.monzy.org/audience/ICMI-2002-finalpub.
http://movis.net/research/audience/techniques.pdf
http://www.cuug.ab.ca/CUUGer/9705/confernc.html
Alright, I understand that there are circumstances in which the errors of the individuals in a population average towards zero, but it's clearly not a very broadly applicable effect. It is interesting to consider the question, "what are the structural requirements on problems, which allow error-cancellation to be applied to refine the result", and consider how this might be applied to political organization, to cancel out errors such as the current POTUS.
-I like my women like I like my tea: green-
The news piece is just plain wrong in the intro. Frequentist interpretations of probability are widely discredited and have been for quite some time (on the order of 50 years I believe). The modern interpretation of probability comes out of normative decision theory, which is based on subjective probabilities - i.e., your beliefs about the world (see here for some general background). Your beliefs should be coherent, which means consistent with observable facts, but they are not objective.
To understand this better, consider weather forcasts. My weather guy says there is a 10% chance of rain tomorrow. Unless you believe that the universe branches and follows all possible outcomes of all events (i.e., kind of the "Sliders" thing with universes in which WWII comes out differently and so forth), then a strictly frequentist view just isn't valid.
The accepted theoretical construct for defining and interpreting probabilities is in terms of betting behavior. If you construct the right kind of lottery, then the amount of money I am willing to bet on a particular outcome relates directly to my belief about that outcome (i.e., my subjective probability).
As for the research itself, I have to read the academic article to draw an informed opinion. The news writeup was too vague and possibly misleading. Just because the average guess of a bunch of people is accurate is not evidence that any of them are using Bayesian reasoning. I know damn well that humans model the world and our inferences are informed by these models. And if you give me a little more information I can draw even better inferences. But that doesn't prove anything about how I improved my guess. I trust the researchers did something more sophisticated than was reported in the news writeup.
And no, I am not a decision theorist. I just play one on TV. :)
Look at the citation on the frequency distribution graphs. They source the illustration to Wikipedia. I don't think I've ever seen a respectable publication cite Wikipedia as a source for a story about something OTHER than Wikipedia itself. Granted, they didn't cite a "fact" but rather used a graphic, but that's still something of a vote of confidence form the Economist.
Make cheese not war 8:)
After reading the article and, of course, ignoring the complex math behind the entire thesis, I have to say that it seems so obvious.
>> "That might explain the emergence of superstitious behaviour, with an accidental correlation or two being misinterpreted by the brain as causal. A frequentist way of doing things would reduce the risk of that happening. But by the time the frequentist had enough data to draw a conclusion, he might already be dead."
The human mind has to perform an unthinkable (pun fully tended!) amount of computations in order to assess and understand his environment. This is our primary survival mechanism and, well, what makes us human. So it would make sense that our brain is designed to correlate cause and effect from past experiences, and ultimately predict the most likely outcome, based on very little and limited information. After all, it would be great if we could sit down and think everything over until we fully comprehend its implications, and to take our time to gather and analyze all available information, but that is a luxury that no organism can take in the natural world.
Of course, this still does not explain how humans think, nor does it prove that the human mind is in fact a Bayesian engine, but it offers the somewhat counter-intuitive notion that accurate predictions can be made based on very little information, and gathering extensive amounts of data first might not always be the best approach.
It also says something about our ability for induction and intuition. That first "gut-feeling" we get about something -- that usually tends to be right -- is nothing magical or ethereal, but perhaps the most probable outcome of a very rapid and complex statistical computation of significant pieces of currently available data, and as it now seems, mathematically provable or reproducible, and therefore should not be ignored.
-dZ.
Carol vs. Ghost
and if humans think bayesian ... ;)
that's the reason why I delete more spam instead of my bayesian filter ; the implementation is flawed
--- I am known for the ones who want to find me on the net. Is that a privacy risk or a privilege? One might wonder..
One other interpretation of probability is that it represents real propensities in the world, I think this is particularly relevant in the case of quantum physics. This rests on the idea that causality includes stochastic determination, so that when you say there is a 10% chance of rain tomorrow, you are actually talking about some real propensity of the world.
I also don't think your example is a good way of debunking frequentist interpretations. A frequentist would argue that the weather forecast should be interpreted in the following way: Out of every day that has occurred in the past of which the conditions of the antecedent day are similar to the conditions of today (i.e. out of the relevant sample), 10% have been rainy, so if there is some distribution that days are converging on, then there is a 10% chance tomorrow will be one of the rainy days, i.e. will fall into that part of the distribution. This does not require reference to possible worlds theory (which is something I find personally repugnant).
Anyway I think it's a bit overly strong to say that frequentist interpretations of probability are discredited, and I also think it's overly strong to suggest that subjectivist interpretations have completely won out.
Well, how many more "studies" do we need to come to the conclusion that the brain is a database engine that applies statistical rules to the queries it processes? all the brain does is actually pattern matching on the input, then produces an output, then the whole experience is fed back again to the brain etc.
Scientists know this for years! I once saw in the show "Incredible But True" an artificial mini brain based on a neural network that could optically recognize persons.
Of course there is a reason machines will never reach human-like behaviour: the brain's purpose is to "survive", something machines do not have.
By the way, the human brain does not do computations like a computer. Even when adding numbers, the brain does a pattern matching on the input: we know, for example, that 1+2=3, from experience, whereas a computer uses an 'adder' electronic circuit to do the same.
First one to come up with an operating system that works like a brain, i.e. gathering experiences and doing pattern matching on those experiences using statistics will win big time.
And so, the number 42 as an example. Life is a dice roll.
Consider the homeopaths that believe that water has the 'signature' or inference of ingredients mixed in it.... tinctures as it were. This is memory long after the connection.... an impression. If you have enough impressions, you're allowed boundaries to be defined. Humans have thousands of impressions daily from the moment of sentience/self-awareness. These impressions, cause and effects, algorithms tried, tested, discarded, accepted, rejected, faith, dogma all add up to boundaries. After a while the filtration mechanism for the process of taking a seeming single data point, cross correlating it with all of the aformentioned heuristics, and if the light bulb doesn't go off in metaphorical answer, then an insufficient number of those boundaries were tested, or the new algorithmic instance has been created. All the possibilities on the dice thrown, all adding up to your meaning of life.
In other words, the poor data couldn't escape processing, and was hurled by the answer.
---- Teach Peace. It's Cheaper Than War.
For more on this topic, check out The Wisdom of Crowds by James Surowiecki.
Surowiecki gives many examples of how aggregated knowledge of a lot of fools usually beats the experts. The research cited in TFA begins to explain the mechanism by which that works.
The "Scientific Method" is a myth perpetrated by elementary school science textbooks. Actual, practicing scientists (of which I am one) do not adhere to any cookbook "method", and in particular hypotheses (let alone their predictions) do not always precede data. In fact, it is quite common for it to be the other way around, especially when you don't know much about the system being studied (exploratory data analysis) or when new statistical methodologies allow you to reanalyze data in a better way.
Now, it is important to make new predictions about data that the hypothesis wasn't fit to, but a completely different issue is being discussed here. In fact, in this case the analysis method was decided upon before the data (not that it has to be); it's just that the data collection method was screwed: it allowed respondents to give non-numerical answers ("infinity") when the analysis method required finite positive values.
That's not because the statistical analysis method was made after the data was collected, it's because the statistical analysis method (p-values) are bogus; the inference method they're based on is not logically coherent. You can mathematically prove that the Bayesian method is coherent, and that p-values can grossly overestimate "significance".
Now, there are cases where the choice of statistical method has to be made before the data is taken (such as stopping rules in frequentist sampling theory), but those also arise because of incoherent methodology. Stopping rules, for instance, don't appear in any methodology that adheres to the likelihood principle (of which Bayesian methods are a subset).
One of the fundamental modern Bayesian papers is Jaynes' "How Does the Brain Do Plausible Reasoning?", which can be found on the web along with lots of other interesting things. Jaynes' conclusion is that we must be Bayesians under the skull. It's a compelling paper, even now.
These experimental results are exactly what Jaynes theory predicts, which is a very nice confirmation of his work. But they are not the "discovery" of anything--they are empirical confirmation of something we already knew. When light-bending by gravity was measured it was not a discovery, it was the confirmation of a theoretical prediction. This is the same.
Blasphemy is a human right. Blasphemophobia kills.
Ugh! There I go again.
Free Software: Like love, it grows best when given away.
I think you need to also factor in the fact that both the thinking itself, and the perception of the outcome of an event, are both filtered through a given individual's biases and prejudices. Mind you, I'm not discussing simply the traditional use of the word "prejudice," but also (as easy examples) anyone who's a conspiracy theorist adherent, or dogmatic democrat/republican, and so forth. As a previous /. story (last week?) pointed out, domgatic political adherents actually stop thinking about, and instead simply start believing, their biases. I imagine that that had something to do with the need to have a statistical sampling in order to get valid results, as humans tend to be an ornery, anecdotal lot.
"The White House is not an intelligence-gathering agency," -- Scott McClellan, Whitehouse spokesman.
http://www.singinst.org/GISAI/index.html/ General Intelligence and Seed AI.
and
http://www.singinst.org/CFAI/index.html/ Creating Friendly AI.
Both really drive home the complexity of creating AI. The human brain isn't merely a "database engine that applies statistical rules to the queries it processes" . It's a carefully networked collection of highly specialized modules, of which one could be called the Bayesian Statistical Module. Bayesian statistical analysis is quite important to AI, but as Eliezer Yudkowsky (the author of the two listed papers) states, "It is necessary, but not sufficient."
Mediocrity knows nothing higher than itself; but talent instantly recognizes genius. -- Sir Arthur Conan Doyle
You don't understand. I never said the brain does not have modules. I just described the way modules work.