Optimization routines¤

Solve a GLM with iteratively reweighted least squares (IRLS).

Arguments:

• X: Covariate matrix with shape (n, p).
• y: Outcome vector with shape (n,).
• offset: Offset vector with shape (n,), or a scalar offset.
• eta: Initial linear predictor \(\eta\) with shape (n,), excluding the separately supplied offset. IRLS adds the offset when constructing the complete initial predictor.
• family: GLM family implementing jaxqtl.distribution.ExponentialFamily.
• solver: Linear solver implementing jaxqtl.infer.AbstractLinearSolve.
• max_iter: Maximum IRLS iterations.
• tol: Absolute tolerance on the change in total negative log likelihood. A small change triggers the gradient check; it does not establish convergence on its own.
• step_size: Initial step size for each IRLS update. Rejected updates are retried with successively halved step sizes.
• disp_init: Initial dispersion estimate.
• gtol: Tolerance on the per-observation gradient infinity norm. Coefficient gradients are divided by each design column's root-mean-square magnitude. NB2 also requires a small projected alpha-space gradient, respecting its dispersion bounds. Defaults to 1e-3.

Returns:

A jaxqtl.infer.SolveResult containing fitted coefficients, dispersion, and convergence metadata.

Failure Modes:

converged is false on exhausted backtracking, an iteration limit, or an unchanged nonstationary state.

Solve an unweighted least-squares problem.

This is used as a fast path for Gaussian models.

Arguments:

• X: Covariate matrix with shape (n, p).
• y: Outcome vector with shape (n,).
• solver: Linear solver implementing jaxqtl.infer.AbstractLinearSolve.

Returns:

A jaxqtl.infer.SolveResult with disp set to 1 and num_iters set to 1.