13.1.3. Solvers#

Solvers are the optimisation backends shared by the quantifier families. They turn a distribution-matching or likelihood objective into a prevalence vector, either over the binary interval \([0, 1]\) or over the full probability simplex \(\Delta^{k-1} = \{p : p_c \ge 0,\; \sum_c p_c = 1\}\). Compose and matching quantifiers delegate their final optimisation step to one of these functions, so the same solver code is reused across many methods.

13.1.3.1. Role and mechanism#

Every optimisation-based quantifier reduces prevalence estimation to

\[\hat{p} = \arg\min_{p \in \Delta^{k-1}} \mathcal{L}(p),\]

where \(\mathcal{L}\) is a loss comparing the test representation with the prevalence-mixed training representations. The solvers differ only in how they search that feasible set.

Solver	Search space	Mechanism / when used
`solve_binary`	\([0, 1]\)	Scalar search over the positive prevalence (grid, ternary, or bounded). Backbone of the binary matching methods.
`ternary_search`	interval	Derivative-free trisection for a unimodal objective; the engine behind `solve_binary(solver="ternary")`.
`solve_simplex`	simplex	SLSQP with the equality constraint \(\sum_c p_c = 1\) and box bounds; the multiclass workhorse.
`minimize_prevalence`	both	Dispatcher: routes binary problems to `solve_binary` and multiclass problems to `solve_simplex`.
`minimize_prevalence_blocks`	simplex (per block)	Minimises one estimate per representation block (e.g. a histogram bin group) and aggregates them by the median; the recipe behind HDy/HDx.

13.1.3.2. Choosing a solver#

Leave solver="auto" for most cases: it selects a bounded scalar search for binary problems and SLSQP for multiclass problems.
Use "grid" when the objective may be multi-modal and you want a global search; use "ternary" when it is unimodal and you want speed.
minimize_prevalence is the entry point a quantifier should call, so the same code runs unchanged in both the binary and multiclass settings.

13.1.3.3. Used by#

Binary matching (DyS, HDy, SORD) goes through solve_binary; the constrained-regression and density methods (GACC, MMD_RKHS, KDEyML, EDy) go through solve_simplex; the histogram sweep (HDy / HDx) uses minimize_prevalence_blocks.

13.1.3.4. Example#

import numpy as np
from mlquantify.solvers import minimize_prevalence

def objective(p):
    target = np.array([0.4, 0.6])
    return np.sum((p - target) ** 2)

prevalences, value = minimize_prevalence(
    objective=objective,
    n_classes=2,
    solver="slsqp",
    random_state=0,
)