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A alternative-NEP on masking and missing values

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A alternative-NEP on masking and missing values

The principle of this aNEP is to separate the APIs for masking and for missing values, according to

  • The current implementation of masked arrays
  • Nathaniel Smith's proposal.

This discussion is only of the API, and not of the implementation.

Authors:

  • Matthew Brett
  • Nathaniel Smith

Rationale

The purpose of this aNEP is to define two interfaces -- one for handling 'missing values', and one for handling 'masked arrays'.

An ordinary value is something like an integer or a floating point number. A missing value is a placeholder for an ordinary value that is for some reason unavailable. For example, in working with statistical data, we often build tables in which each row represents one item, and each column represents properties of that item. For instance, we might take a group of people and for each one record height, age, education level, and income, and then stick these values into a table. But then we discover that our research assistant screwed up and forgot to record the age of one of our individuals. We could throw out the rest of their data as well, but this would be wasteful; even such an incomplete row is still perfectly usable for some analyses (e.g., we can compute the correlation of height and income). The traditional way to handle this would be to stick some particular meaningless value in for the missing data, e.g., recording this person's age as 0. But this is very error prone; we may later forget about these special values while running other analyses, and discover to our surprise that babies have higher incomes than teenagers. (In this case, the solution would be to just leave out all the items where we have no age recorded, but this isn't a general solution; many analyses require something more clever to handle missing values.) So instead of using an ordinary value like 0, we define a special "missing" value, written "NA" for "not available".

Therefore, missing values have the following properties: Like any other value, they must be supported by your array's dtype -- you can't store a floating point number in an array with dtype=int32, and you can't store an NA in it either. You need an array with dtype=NAint32 or something (exact syntax to be determined). Otherwise, they act exactly like any other values. In particular, you can apply arithmetic functions and so forth to them. By default, any function which takes an NA as an argument always returns an NA as well, regardless of the values of the other arguments. This ensures that if we try to compute the correlation of income with age, we will get "NA", meaning "given that some of the entries could be anything, the answer could be anything as well". This reminds us to spend a moment thinking about how we should rephrase our question to be more meaningful. And as a convenience for those times when you do decide that you just want the correlation between the known ages and income, then you can enable this behavior by adding a single argument to your function call.

For floating point computations, NAs and NaNs have (almost?) identical behavior. But they represent different things -- NaN an invalid computation like 0/0, NA a value that is not available -- and distinguishing between these things is useful because in some situations they should be treated differently. (For example, an imputation procedure should replace NAs with imputed values, but probably should leave NaNs alone.) And anyway, we can't use NaNs for integers, or strings, or booleans, so we need NA anyway, and once we have NA support for all these types, we might as well support it for floating point too for consistency.

A masked array is, conceptually, an ordinary rectangular numpy array, which has had an arbitrarily-shaped mask placed over it. The result is, essentially, a non-rectangular view of a rectangular array. In principle, anything you can accomplish with a masked array could also be accomplished by explicitly keeping a regular array and a boolean mask array and using numpy indexing to combine them for each operation, but combining them into a single structure is much more convenient when you need to perform complex operations on the masked view of an array, while still being able to manipulate the mask in the usual ways. Therefore, masks are preserved through indexing, and functions generally treat masked-out values as if they were not even part of the array in the first place. (Maybe this is a good heuristic: a length-4 array in which the last value has been masked out behaves just like an ordinary length-3 array, so long as you don't change the mask.) Except, of course, that you are free to manipulate the mask in arbitrary ways whenever you like; it's just a standard numpy array.

There are some simple situations where one could use either of these tools to get the job done -- or other tools entirely, like using designated surrogate values (age=0), separate mask arrays, etc. But missing values are designed to be particularly helpful in situations where the missingness is an intrinsic feature of the data -- where there's a specific value that should exist, if it did exist we'd it'd mean something specific, but it doesn't. Masked arrays are designed to be particularly helpful in situations where we just want to temporarily ignore some data that does exist, or generally when we need to work with data that has a non-rectangular shape (e.g., if you make some measurement at each point on a grid laid over a circular agar dish, then the points that fall outside the dish aren't missing measurements, they're just meaningless).

Initialization

First, missing values can be set and be displayed as np.NA, NA:

>>> np.array([1.0, 2.0, np.NA, 7.0], dtype='NA[f8]')
array([1., 2., NA, 7.], dtype='NA[<f8]')

As the initialization is not ambiguous, this can be written without the NA dtype:

>>> np.array([1.0, 2.0, np.NA, 7.0])
array([1., 2., NA, 7.], dtype='NA[<f8]')

Masked values can be set and be displayed as np.IGNORE, IGNORE:

>>> np.array([1.0, 2.0, np.IGNORE, 7.0], masked=True)
array([1., 2., IGNORE, 7.], masked=True)

As the initialization is not ambiguous, this can be written without masked=True:

>>> np.array([1.0, 2.0, np.IGNORE, 7.0])
array([1., 2., IGNORE, 7.], masked=True)

Ufuncs

By default, NA values propagate:

>>> na_arr = np.array([1.0, 2.0, np.NA, 7.0])
>>> np.sum(na_arr)
NA('float64')

unless the skipna flag is set:

>>> np.sum(na_arr, skipna=True)
10.0

By default, masking does not propagate:

>>> masked_arr = np.array([1.0, 2.0, np.IGNORE, 7.0])
>>> np.sum(masked_arr)
10.0

unless the propmask flag is set:

>>> np.sum(masked_arr, propmask=True)
IGNORE

An array can be masked, and contain NA values:

>>> both_arr = np.array([1.0, 2.0, np.IGNORE, np.NA, 7.0])

In the default case, the behavior is obvious:

>>> np.sum(both_arr)
NA('float64')

It's also obvious what to do with skipna=True:

>>> np.sum(both_arr, skipna=True)
10.0
>>> np.sum(both_arr, skipna=True, propmask=True)
IGNORE

To break the tie between NA and MSK, NAs propagate harder:

>>> np.sum(both_arr, propmask=True)
NA('float64')

Assignment

is obvious in the NA case:

>>> arr = np.array([1.0, 2.0, 7.0])
>>> arr[2] = np.NA
TypeError('dtype does not support NA')
>>> na_arr = np.array([1.0, 2.0, 7.0], dtype='NA[f8]')
>>> na_arr[2] = np.NA
>>> na_arr
array([1., 2., NA], dtype='NA[<f8]')

Direct assignnent in the masked case is magic and confusing, and so happens only via the mask:

>>> masked_array = np.array([1.0, 2.0, 7.0], masked=True)
>>> masked_arr[2] = np.NA
TypeError('dtype does not support NA')
>>> masked_arr[2] = np.IGNORE
TypeError('float() argument must be a string or a number')
>>> masked_arr.visible[2] = False
>>> masked_arr
array([1., 2., IGNORE], masked=True)

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