dwavesystems / dwavesystems/dwave-scikit-learn-plugin

Consider multiplying the quadratic biases in `SelectFromQuadraticModel.correlation_cqm()` by `1-alpha`.

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Dominant language
Python
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Description

Currently, it is possible to construct a dataset where, even with `alpha=1`, a fixed or random column is chosen because of the penalties in the quadratic term. This contradicts [the docstring](https://github.com/dwavesystems/dwave-scikit-learn-plugin/blob/7db7d03c7b2b17db6309907069ade9aee0e4157a/dwave/plugins/sklearn/transformers.py#L132-L140) which claims
```
alpha:
Hyperparameter between 0 and 1 that controls the relative weight of
the relevance and redundancy terms.
``alpha=0`` places no weight on the quality of the features,
therefore the features will be selected as to minimize the
redundancy without any consideration to quality.
``alpha=1`` places the maximum weight on the quality of the features,
and therefore will be equivalent to using
:class:`sklearn.feature_selection.SelectKBest`.
```
One solution is to multiply the quadratic/redundany terms by `1-alpha` to ensure that they are zeroed when `alpha=1`.

For instance we could replace https://github.com/dwavesystems/dwave-scikit-learn-plugin/blob/7db7d03c7b2b17db6309907069ade9aee0e4157a/dwave/plugins/sklearn/transformers.py#L210-L212 with
```python
diag = np.array(correlations[:, -1] * (-2 * alpha * num_features), copy=True)

correlations *= (1-alpha)

# our objective
# we multiply by 2 because the matrix is symmetric
np.fill_diagonal(correlations, diag)
```

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Research direction

Read dwave/plugins/sklearn/transformers.py, focusing on SelectFromQuadraticModel.correlation_cqm() and its alpha docstring. Check how the diagonal and quadratic redundancy terms are assembled, then verify that alpha=1 leaves only the quality terms and matches the documented SelectKBest behavior.

Written by the indexing model from the issue text.

Assessment

Tech stack
numpy, python, scikit-learn
Domain
machine-learning
Issue type
Bug
Difficulty
2/5
Estimated time
1-3 hours
Activity status
Stale
Clarity
Clearly specified
Newbie friendliness
55/100

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