I'm working on a model for publishing in a journal. I'm removing outliers from results of my models. Suppose that I have 100 trained neural network, inserting out-of-sample data to these models and obtaining results. In this step I'm removing outliers (based on abs(x-mean(x))>= 2*s.d and use average of remaining results. How can I prove we need removing outliers in my paper? What statistically procedure or graphical presentation we need?
Update. X-axis is every out-of-sample and Y-axis is outputs for every sample. Output range is 0-1 (50 samples from 8000 samples presented in figure). In this figure green filled circles are geomean, red filled circles are averaging after removing outliers using above formula and blue filled circles are arithmetic mean. We have three outputs here. Which averaging method is suitable in this case? How can I prove that? I think we based on below figures we have appropriate mean value when removing above 2 s.d outliers. What do you think?
Run your model BOTH with and without the observations you think are outliers (whatever criterion you use for identify outliers). If you get more or less the same results, don't remove outliers. Note that removal of observations, for whatever reason, reduces your sample size, and tends to weaken the inferences you draw.
There isn't *any* general way of stating what constitutes an ``outlier''-it assumes prior knowledge of what the signal is expected to be and what the model is expected to deliver and the only issue that can be meaningfully addressed is the distribution of the deviation between the two, under the assumptions. In particular, it isn't true that this deviation has a Gaussian distribution-it can and must be reconstructed from its moments and the relations between moments quantify what the distribution is. So the average value need not be a good approximation to the typical value, for instance.
Univariate -> boxplot. outside of 1.5 times inter-quartile range is an outlier.
Bivariate -> scatterplot with confidence ellipse. outside of, say, 95% confidence ellipse is an outlier.
Multivariate -> Mahalanobis D2 distance.
Otherwise:
Run a logistic regression (on Y=IsOutlier) to see if there are any systematic patterns.
Remove ones that you can demonstrate they are not representative of any sub-population.
Outliers...
What is outliers? If we're talking in a statistical point of view outliers are the same you cut in your work, but if we're talking in an experimental point of view perhaps outliers are the true data... So I think that remove outliers are a very delicate procedure.
mariano
Removing outliers is not a recommended approach is statistical analysis, unless we justify the removal of such values.
The detection of outliers depends in both the nature of data and model you are looking for. One may use median instead of mean or use a robust model.
One common way to prove the necessity for removing outliers is to run your model with and without suspected outliers, if you find a significant difference in the results of two models then these outliers are also influential. Then you either use robust models or remove such points.
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