What is a good heuristic to detect if a column in a pandas.DataFrame is categorical?
I've been thinking about a similar problem and the more that I consider it, it seems that this itself is a classification problem that could benefit from training a model. 
I bet if you examined a bunch of datasets and extracted these features for each column / pandas.Series:

% floats: percentage of values that are float
% int: percentage of values that are whole numbers
% string: percentage of values that are strings
% unique string: number of unique string values / total number
% unique integers: number of unique integer values / total number
mean numerical value (non numerical values considered 0 for this)
std deviation of numerical values

and trained a model, it could get pretty good at inferring column types, where the possible output values are: categorical, ordinal, quantitative.
Side note: as far as a Series with a limited number of numerical values goes, it seems like the interesting problem would be determining categorical vs ordinal; it doesn't hurt to think a variable is ordinal if it turns out to be quantitative right? The preprocessing steps would encode the ordinal values numerically anyways without one-hot encoding.
A related problem that is interesting: given a group of columns, can you tell if they are already one-hot encoded? E.g in the forest-cover-type-prediction kaggle contest, you would automatically know that soil type is a single categorical variable.
I've been developing a tool that automatically preprocesses data in pandas.DataFrame format. During this preprocessing step, I want to treat continuous and categorical data differently. In particular, I want to be able to apply, e.g., a OneHotEncoder to only the categorical data.
Now, let's assume that we're provided a pandas.DataFrame and have no other information about the data in the DataFrame. What is a good heuristic to use to determine whether a column in the pandas.DataFrame is categorical?
My initial thoughts are:
1) If there are strings in the column (e.g., the column data type is object), then the column very likely contains categorical data
2) If some percentage of the values in the column is unique (e.g., >=20%), then the column very likely contains continuous data
I've found 1) to work fine, but 2) hasn't panned out very well. I need better heuristics. How would you solve this problem?
Edit: Someone requested that I explain why 2) didn't work well. There were some tests cases where we still had continuous values in a column but there weren't many unique values in the column. The heuristic in 2) obviously failed in that case. There were also issues where we had a categorical column that had many, many unique values, e.g., passenger names in the Titanic data set. Same column type misclassification problem there.