I have dataset of 250000 points which has 15 features. Each feature takes values from 0 to 100.
So, I want to fit a probability distribution to this dataset to identify outliers like wrong data entry.
For univariate, I could follow this approach. How to do this for multi variate?
How to measure the goodness of fit? Answer with code are appreciated.
When you deal with multivariate data, there is not that much choice of distributions. You might try the multivariate normal and see it it is a reasonable model for your data. Otherwise, you have the multinomial, but then you hit the curse of dimensionality.
You could arrange your observations in a 15 dimensional contingency table, but notice that even if you reduce your 0 to 100 values to "low" and "high" --which would be terribly rough--, you would still have 2^15 = 32768 cells. If you reduce your values to three levels, "low", "medium", "high", which is still quite rough, you would have 3^15 = 14348907 cells, the vast majority of them empty, since you "only" have 250000 observations. Therefore, an observation alone in a cell would no longer be evidence of it being an outlier.
In short, unless you have some more structure in your data, it is hard to think of a way of detecting outliers.
