:orphan:

Examples gallery
================

End-to-end runnable examples. Each script is executed at doc-build time and
its output is captured as a rendered page. Click through to read the
walkthrough or download the source.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Runnable companion to docs/migration_from_sparse_ho.md. We don&#x27;t import sparse_ho (it&#x27;s optional, not on PyPI) — instead each section shows the sparse-ho idiom in a comment and the sparho equivalent in runnable code. The prose guide has the full translation table.">

.. only:: html

  .. image:: /examples_built/images/thumb/sphx_glr_plot_migration_from_sparse_ho_thumb.png
    :alt:

  :doc:`/examples_built/plot_migration_from_sparse_ho`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Migrating from sparse-ho to sparho</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Held-out logistic loss on a binary classification problem with an L1 penalty. The Problem is (LogisticLoss, L1, X, y) with y ∈ {−1, +1}; the rest of the bilevel machinery is unchanged.">

.. only:: html

  .. image:: /examples_built/images/thumb/sphx_glr_plot_sparse_logreg_thumb.png
    :alt:

  :doc:`/examples_built/plot_sparse_logreg`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Sparse logistic regression</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="WeightedL1 carries one regularization strength per feature: a length-``p`` vector α. Grid search over the resulting p-dimensional hyperparameter space is intractable, but the implicit-differentiation hypergradient is just a vector, and hoag_search steps along it the same way it would for a scalar α.">

.. only:: html

  .. image:: /examples_built/images/thumb/sphx_glr_plot_weighted_lasso_thumb.png
    :alt:

  :doc:`/examples_built/plot_weighted_lasso`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Weighted Lasso (per-feature α)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The canonical sparho example: tune the Lasso regularization strength α to minimize the mean-squared error on a fixed held-out set, using one gradient-based outer search instead of a grid sweep.">

.. only:: html

  .. image:: /examples_built/images/thumb/sphx_glr_plot_held_out_lasso_thumb.png
    :alt:

  :doc:`/examples_built/plot_held_out_lasso`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Held-out Lasso with HOAG</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Stein&#x27;s Unbiased Risk Estimator (SURE) lets you tune the Lasso regularization strength when no held-out set exists — denoising, signal recovery, single-fold settings — by directly estimating the prediction MSE from the training data.">

.. only:: html

  .. image:: /examples_built/images/thumb/sphx_glr_plot_sure_lasso_thumb.png
    :alt:

  :doc:`/examples_built/plot_sure_lasso`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SURE-tuned Lasso (no held-out set)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="K-fold cross-validation is wrapped by CrossVal, which averages the value and the hypergradient across folds. With warm_start=True each fold reuses its previous-iteration β* as the next inner solve&#x27;s starting point — a substantial speed-up when the inner solver dominates.">

.. only:: html

  .. image:: /examples_built/images/thumb/sphx_glr_plot_cv_lasso_thumb.png
    :alt:

  :doc:`/examples_built/plot_cv_lasso`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cross-validated Lasso</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="GroupL1 is sparho&#x27;s block-sparsity penalty: features split into groups G_k get shrunk together by a block soft-threshold, so either all coordinates in a group are zero or all are nonzero. Useful whenever features come in natural batches — dummy-encoded categoricals, multi- output regression coefficient rows, multi-frequency Fourier bases, etc.">

.. only:: html

  .. image:: /examples_built/images/thumb/sphx_glr_plot_group_lasso_thumb.png
    :alt:

  :doc:`/examples_built/plot_group_lasso`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Group-Lasso with HOAG</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples_built/plot_migration_from_sparse_ho
   /examples_built/plot_sparse_logreg
   /examples_built/plot_weighted_lasso
   /examples_built/plot_held_out_lasso
   /examples_built/plot_sure_lasso
   /examples_built/plot_cv_lasso
   /examples_built/plot_group_lasso



.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_