XPost: comp.soft-sys.matlab   
   From: not@here.com   
      
   "Dmitry A. Kazakov"  wrote in message   
   news:1vtiaoer4qm9a.3en2er7uxwqc.dlg@40tude.net...   
   > On Sun, 17 Apr 2005 11:42:00 +0100, Fuzzy wrote:   
   >   
   > > "Dmitry A. Kazakov"  wrote in message   
   > > news:c1x9d15twfhw$.36vug05uapdd$.dlg@40tude.net...   
   > >>   
   > >> The point is that the metric does not come from fuzzy. Look how it   
   happens   
   > >> in statistic to highlight the pattern:   
   > >>   
   > >> Variant 1. First you postulate that y=ax+b. Then you postulate that   
   > >> observed x's and y's are x+err and y+err, where err's distribution is   
   also   
   > >> postulated. From that you find a and b minimizing the probability of   
   error.   
   > >>   
   > >> Variant 2. You again postulate y=ax+b. Then you say that x's and y's   
   are   
   > >> exact, but a and b are random (vary from cow to cow). Further you   
   postulate   
   > >> a distribution of a and b and estimate the distribution's parameters to   
   > >> minimize the probability of error.   
   > >>   
   > >> In both cases and all their mixtures the metric is *postulated*: you   
   > >> pretend to know/presume/surmise how the cow works (y=ax+b). This   
   knowledge   
   > >> does not come to you from the probability theory, it does from the   
   > >> farm-yard.   
   > >>   
   > >> Nothing changes here if you replace one type of uncertainty with   
   another   
   > >> and switch to fuzzy. Mathematical apparatus may change, instead of   
   least   
   > >> squares you could expect C-norm. But the rest will be same.   
   > >>   
   > >> What you have described as an example with cows looks like the variant   
   1.   
   > >> With the variant 2 there might be difficulties with its justification.   
   If   
   > >> the parameters of the cow are not random, but fuzzy, then what does it   
   > >> physically mean? Note to make a prediction you'd describe a herd of all   
   > >> cows, not a particular cow. Should we treat it as if a cowboy forgot   
   his   
   > >> spectacles and now is guessing what's the cow? [ You cannot get rid of   
   > >> randomness here, but you could mix fuzziness in. ]   
   > >   
   > > No, that was a red herring introduced to imply that some sort of   
   "averaging"   
   > > across cows "may" be possible to aid the model formulation. The cowboy   
   always   
   > > knows the cow and we are interested in predicting a specific cows   
   response given   
   > > the data to a new batch of feed.   
   >   
   > OK.   
   >   
   > > Where I thought fuzzy would help is the possibility of belonging to more   
   > > than one set.   
   >   
   > Yes. Moreover, fuzzy allows you to describe non-singleton data, missing   
   and   
   > contradictory data. (There is also a price of this flexibility.)   
   >   
   > > The cow would probably have some preference AND dislike for   
   > > each batch - as the distribution perhaps may not be normal. Maybe a   
   simple   
   > > y=ax+b doesn't cut it, perhaps the response is more sophisticated, may   
   have   
   > > non linearities etc.   
   >   
   > Absolutely.   
   >   
   > > This is becuase the estimated value will serve as a parameter in a   
   larger   
   > > model - say a cow health model - and the dislike it has for a feed may   
   be   
   > > more informative than the preference it has for a feed.   
   > >   
   > > Either way if we *assume* that the responses are fuzzy, a moot point,   
   >   
   > They usually are.   
   >   
   > > I am   
   > > looking for any techniques to be able to model the data as given to   
   predict   
   > > a response given new output. I am looking for suitable ways to transform   
   the   
   > > historical data to be able to produce a "preference model", given that   
   the   
   > > data bay be sparse, incomplete and unevenly distributed. I hoped using   
   the   
   > > fuzzy paradigm may facilitate making an "educated guess" when, perhaps   
   we   
   > > dont have enough data to use standard techniques.   
   >   
   > Right. This is exactly the application field of fuzzy.   
   >   
   > But I must repeat it again, you need a model. Any choice is based on the   
   > model. For example, if you take a fuzzy decision tree and do some training   
   > on your fuzzy data set. This assumes that you have chosen the model:   
   > training on trees implicitly introduces a distance in the feature space   
   > which is then used for generalizations. This distance may fit or not the   
   > reality. It is quite easy to build examples where trees perform badly   
   > wrong...   
   >   
   > Basically, you can use practically any machine learning technique that   
   > supports generalization on the fuzzy case. Though mathematically it might   
   > be tricky, but there is nothing new, there cannot be anything new. Fuzzy   
   is   
   > not a new method of machine learning, it is a framework which allows you   
   to   
   > handle fuzzy data. No more, no less.   
      
      
   But that doesn't get me much further! :)   
      
   I am looking for references and/or examples of *how* to go about it.   
      
   I can make up some method to transform the historical data to be able to be   
   used in a fuzzy model to predict new data.   
   But I was after information as to how to go about it, which methods show   
   success in which environment - the pitfalls and restrictions etc as shown by   
   the development of a working model. Something practical.   
      
   Cheers   
      
   --- SoupGate-Win32 v1.05   
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