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Predict

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Predict[data] fits a predictor to data and returns a PredictorFunction, which can be stored and applied to new inputs. Data is either a list of rules {features -> value, ...} or a matrix whose last column is the response. Method -> "LinearRegression" is the only method implemented and is the default; any other declines rather than silently linear-regressing. The returned object also answers "Method", "Coefficients" and "FeatureCount". A collinear feature set has no unique fit and returns unevaluated.

Examples (3)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (3)

In[1]:= p = Predict[{1. -> 3., 2. -> 5., 3. -> 7., 4. -> 9.}]
Out[1]= PredictorFunction["LinearRegression", <>]

In[2]:= {p[10.], p["Coefficients"], p["Method"]}
Out[2]= {21.0, {1.0, 2.0}, "LinearRegression"}

In[3]:= Predict[{{1., 1., 6.}, {2., 1., 8.}, {1., 2., 9.}, {3., 2., 13.}, {2., 3., 14.}}]["Coefficients"]
Out[3]= {1.0, 2.0, 3.0}

Options & behaviour

On verification

the 1-neighbour predictor is cross-checked against the existing independent Nearest builtin, on both sides of a midpoint, so neighbour selection is validated against separate code. Nearest supports only the one-neighbour scalar form here (its k form and point form decline), so that check covers selection at k = 1 and says nothing about the averaging, which is asserted directly instead.

Implementation notes

  • Data is either a list of rules {features -> value, …} or a matrix whose last column is the response — the shape data usually arrives in. Both give the same model; which was used is not remembered.
  • A one-feature model accepts a bare scalar as well as a one-element list, so p[3.] works for a single-variable regression.
  • A singular system returns unevaluated. Perfectly collinear features, or fewer observations than parameters, have no unique fit — a pseudo-inverse would return one of infinitely many answers and look like a successful fit.
  • "LinearRegression" is the only method implemented and the default. Any other declines rather than silently linear-regressing.
  • A wrongly-shaped input leaves the application unevaluated rather than guessing.
  • "NearestNeighbors" has no fitted parameters — the training set is the model. That is why it costs nothing to fit and everything to apply. The prediction is the mean response of the k nearest training rows; k defaults to 3, enough to average away one noisy response and few enough to stay local, and is clamped to the number of training rows. It answers "NeighborCount" and "TrainingData" as well as the shared properties.
  • "NeighborsNumber" on a "LinearRegression" is refused, not ignored — silently accepting a meaningless option would hide a real mistake. So is an unrecognised sub-option, and a non-positive k.

Attributes: Protected.

References

See also: PredictorFunction, Nearest