Binary classification vs. continuous output with neural networks Wikipedia says in binary classification:

Tests whose results are of continuous values, such as most blood
  values, can artificially be made binary by defining a cutoff value,
  with test results being designated as positive or negative depending
  on whether the resultant value is higher or lower than the cutoff.

Is there some guidance as to whether this is a desirable thing to do or not?  I have data where the output value is continuous in the training set and I'm interested to know how strong the output variable is.   Ideally an accurate continuous value would be the best, but I also would be satisfied with binary classification.  My layman's assumption is that the binary classification task would be a little simpler.  Is there any guidance as to whether to prefer continuous output vs binary classification?
 A: It is a bad idea. It increases both type I and type II error. It also invokes "magical thinking" - that is, that something magical happens at the cutoff value. For example, with newborns, it is common to say babies under 2.5 kg are "low birth weight" and those above 2.5 kg are not. This treats a baby of 2.49 kg as being the same as one of 1.4 kg, but vastly different from a baby of 2.51 kg. Similarly, the 2.51 kg baby is treated just like a baby of 4.5 kg.  
It is true that people sometimes need to make "yes/no" decisions based on the output of a statistical model. But the statistical model and its results should be a guide and a tool, not a straitjacket. 
A: If you convert a continous variable to binary you throw out a lot of detailed information.  So in my opinion it is advisable not to do it.  For tree classifiers binary splits are used but the information in the continuous variable if used to get the first split and the variable can be split again if it is very important to the classification.  I don't think it works that way with neural networks.
A: Peter Flom's answer here suggests that discretizing your output variable is going to hurt. If so, you obviously shouldn't do it! This is definitely the conventional wisdom for predictor variables. However, having thought about it for a little while, I'm not even sure how one could fairly compare the two situations for outputs. I suppose you could replace each discretized class with its mean value and compare the mean-squared errors, but that seems a little biased. If Peter Flom (or anyone else) has references or suggestions, I'd be very interested in seeing them!
Your specific application might determine whether one or the other is more appropriate. An automatic defibrillator needs to decide whether or not to shock the patient; it can't show estimates of what the pulse is/should be, then tell you to ask a doctor.  On the other hand, a cardiologist or sports coach might be interested in having those numbers. From your question, it sounds like continuous output might be preferable. That's certainly a more flexible option. If you were soliciting customers, knowing which ones will buy your product is nice, but being able to predict how much each will spend is even better. For example, you might offer Bill Gates lots of free samples, whereas I get a leaky pen. There are ways to rank discretized outputs (e.g., using the activation function), but that might not be exactly what you want.
However, you might be better off modeling some situations as discrete, even if your actual measurements are continuous. Suppose you were trying to predict a person's electricity usage from their activities. Power is definitely a continuous variable. However, I suspect many appliances use a lot of power (when  on) or very little (when off). There might be some variance, either due to measurement error or other factors (e.g., it's especially hot, so the computer's fan runs a little bit harder). Depending on your predictors, you might do better predicting COMPUTER=ON, TV=OFF, STEREO=ON and then substituting known values for each of those. You'd have to look at a histogram to see if your output variable has many narrow, isolated peaks or if it's more continuous. 
Finally, it may depend on your audience. Peter Flom makes an excellent point about how people treat values that are on opposite sides of a threshold as drastically different. A 2.501 kg baby probably has a very similar prognosis to a 2.499 kg baby, even if only one officially has a "Low Birth Weight" diagnosis. Sometimes one needs a threshold or it's just convenient shorthand. One alternative, frequently used with children, is to report percentiles (e.g., "he's a little more than 2.5 kg, but still in the 5th percentile so we ought to keep an eye on him"). On the other hand, some sharp thresholds are reasonable: $H_2O$ behaves very differently at -1 and +1 degrees. You'll have to decide based on the nature of your audience and your data. 
