|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/glm/proximal_hessian.py#L107-L220) | One step of (the outer loop of) the GLM fitting algorithm. tfp.glm.fit_sparse_one_step( model_matrix, response, model, model_coefficients_start, tolerance, l1_regularizer, l2_regularizer=None, maximum_full_sweeps=None, learning_rate=None, name=None ) This function returns a new value of `model_coefficients`, equal to `model_coefficients_start + model_coefficients_update`. The increment `model_coefficients_update in R^n` is computed by a coordinate descent method, that is, by a loop in which each iteration updates exactly one coordinate of `model_coefficients_update`. (Some updates may leave the value of the coordinate unchanged.) The particular update method used is to apply an L1-based proximity operator, "soft threshold", whose fixed point `model_coefficients_update^*` is the desired minimum model_coefficients_update^* = argmin{ -LogLikelihood(model_coefficients_start + model_coefficients_update') + l1_regularizer * ||model_coefficients_start + model_coefficients_update'||_1 + l2_regularizer * ||model_coefficients_start + model_coefficients_update'||_2**2 : model_coefficients_update' } where in each iteration `model_coefficients_update'` has at most one nonzero coordinate. This update method preserves sparsity, i.e., tends to find sparse solutions if `model_coefficients_start` is sparse. Additionally, the choice of step size is based on curvature (Fisher information matrix), which significantly speeds up convergence.


| ## Args || |---|---| | `model_matrix` | (Batch of) matrix-shaped, `float` `Tensor` or `SparseTensor` where each row represents a sample's features. Has shape `[N, n]` where `N` is the number of data samples and `n` is the number of features per sample. | | `response` | (Batch of) vector-shaped `Tensor` with the same dtype as `model_matrix` where each element represents a sample's observed response (to the corresponding row of features). | | `model` | [`tfp.glm.ExponentialFamily`](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/ExponentialFamily)-like instance, which specifies the link function and distribution of the GLM, and thus characterizes the negative log-likelihood which will be minimized. Must have sufficient statistic equal to the response, that is, `T(y) = y`. | | `model_coefficients_start` | (Batch of) vector-shaped, `float` `Tensor` with the same dtype as `model_matrix`, representing the initial values of the coefficients for the GLM regression. Has shape `[n]` where `model_matrix` has shape `[N, n]`. | | `tolerance` | scalar, `float` `Tensor` representing the convergence threshold. The optimization step will terminate early, returning its current value of `model_coefficients_start + model_coefficients_update`, once the following condition is met: `||model_coefficients_update_end - model_coefficients_update_start||_2 / (1 + ||model_coefficients_start||_2) < sqrt(tolerance)`, where `model_coefficients_update_end` is the value of `model_coefficients_update` at the end of a sweep and `model_coefficients_update_start` is the value of `model_coefficients_update` at the beginning of that sweep. | | `l1_regularizer` | scalar, `float` `Tensor` representing the weight of the L1 regularization term (see equation above). | | `l2_regularizer` | scalar, `float` `Tensor` representing the weight of the L2 regularization term (see equation above). Default value: `None` (i.e., no L2 regularization). | | `maximum_full_sweeps` | Python integer specifying maximum number of sweeps to run. A "sweep" consists of an iteration of coordinate descent on each coordinate. After this many sweeps, the algorithm will terminate even if convergence has not been reached. Default value: `1`. | | `learning_rate` | scalar, `float` `Tensor` representing a multiplicative factor used to dampen the proximal gradient descent steps. Default value: `None` (i.e., factor is conceptually `1`). | | `name` | Python string representing the name of the TensorFlow operation. The default name is `"fit_sparse_one_step"`. |



| ## Returns || |---|---| | `model_coefficients` | (Batch of) `Tensor` having the same shape and dtype as `model_coefficients_start`, representing the updated value of `model_coefficients`, that is, `model_coefficients_start + model_coefficients_update`. | | `is_converged` | scalar, `bool` `Tensor` indicating whether convergence occurred across all batches within the specified number of sweeps. | | `iter` | scalar, `int` `Tensor` representing the actual number of coordinate updates made (before achieving convergence). Since each sweep consists of [`tf.size(model_coefficients_start)`](https://www.tensorflow.org/api_docs/python/tf/size) iterations, the maximum number of updates is `maximum_full_sweeps * tf.size(model_coefficients_start)`. |