4 ms·
I can't speak for all of machine learning, but classic statistics has some probabilistic assumptions and uses those to prove some theorems about the results of
by graycat 7y ago
I can't speak for all of machine learning, but classic statistics has some probabilistic assumptions and uses those to prove some theorems about the results of how statistical methods manipulate data.
E.g., in regression analysis, the assumptions are (i) there really is a linear mode with the variables to be used; (ii) typically the data will not fit the model exactly and instead there are errors; (iii) the errors are in the sense of probability independent, all have the same distribution which is Gaussian with mean zero. Then estimate the regression coefficients and get, say, a F ratio statistic on the fit and t-tests on the coefficients. For details can see, say, Mood, Graybill, and Boas, or Morrison, or Draper and Smith, or Rao, etc. If you need detailed references, request them here, but these are all classic references going back decades. In that case, maybe some of current machine learning does qualify as statistics.
Here regression was just an example, however, apparently especially close to much of current machine learning. But there is no end of (i) having data, (ii) having some probabilistic assumptions, (iii) manipulating the data, (iv) getting results, and (v) proving some theorems about the probabilistic properties of the results.
Might argue that in machine learning the results of the training data on the model yields some estimates of some probabilistic properties that can be used to make probabilistic statements about the results of the trained model on future real data.
- graycat 7y agoErrata: Replace "mode" with "model"!
- srean 7y agoTo a rough approximation they differ in the theorems/results they care about. In statistics one would care about consistent estimate of parameters -- as sample size goes to infinity and the model is such and such here is an estimator that will converge (according to some interesting mode of convergence) to the true parameter generating the data. In ML one wouldnt care much about recovering the parameters. The results/theorems of interest would be that with large enough samples the predictions and the new data will converge (according to some interesting mode of convergence). If this comes at a cost of doing poorly in terms of parameter recovery, ML wouldnt be bothered. According to ML the cycloids and epicycloid based geocentric model of planetary motion would be perfectly acceptable.
- alexgmcm 7y agoThere are non-parametric statistical methods too though (such as bootstrap methods) which don't make such assumptions.
- graycat 7y agoHave two calculus teachers, A and B, each with 20 students. Look at the final exam numbers. Put all the numbers in a bucket, stir briskly, draw out 20 numbers (test scores) and average, average the other 20, and get the difference in the averages. Do this many times. Get the empirical distribution of the differences in the averages. Now look at the difference in the actual average for A and B. If this is out in a tail of the empirical distribution, then we reject the null hypothesis that the two teachers are equally good. For this non-parametric, distribution-free, resampling, two-sample test, to make theorems about it, which should, will likely need at least an independence assumption and likely an i.i.d. (independent, identically distributed) assumption. Else maybe each student of teacher B is an older sibling of a student of teacher A!!!! In a nutshell, what's going on in statistical hypothesis testing is that we make the null hypothesis, and that gives us enough assumptions, e.g., i.i.d., to calculate the probability of our calculated test statistic, e.g., the difference in the two averages, being way out in a tail. Without some such null hypothesis assumptions, we have no basis on which to reject anything, are not testing anything. There's chance of getting all twisted out of shape philosophically( here: E.g., I outlined one statistical hypothesis test for the two teachers A and B. Okay, now consider ALL reasonably relevant* hypothesis: Maybe we on the test I outlined, the two teachers look very different, not equal, maybe teacher B better. But in ALL those hypothesis tests, maybe in one of the tests the two teachers look equally good or even teacher A looks better. Now what do we do? That is, there is a suspicion that teacher B looked better ONLY because of the particular test we chose. Maybe there has been some research to clean up this issue.
- graycat 7y agoSorry, was way too busy and typed way too fast and had LOTS of typing errors.