jaxopt.projection.projection_sparse_simplex
- jaxopt.projection.projection_sparse_simplex(x, max_nz, use_approx_max_nz=False, value=1.0)[source]
Projection onto the simplex with cardinality constraint (maximum number of non-zero elements).
\[\underset{p}{\text{argmin}} ~ ||x - p||_2^2 \quad \textrm{subject to} \quad p \ge 0, p^\top 1 = \text{value}, ||p||_0 \le \text{max_nz}\]- Parameters
x (
Array) – vector to project, an array of shape (n,).max_nz (
int) – max nonzero values to keepuse_approx_max_nz (
bool) – when set to True, use jax.lax.approx_max_k to return max values and their indices in an approximate manner (default: False).value (
float) – value p should sum to (default: 1.0).
- Return type
Array- Returns
projected vector, an array with the same shape as
x.
References
Sparse projections onto the simplex Anastasios Kyrillidis, Stephen Becker, Volkan Cevher and, Christoph Koch ICML 2013 https://arxiv.org/abs/1206.1529