.. module:: statsmodels.base.optimizer
.. currentmodule:: statsmodels.base.optimizer
Optimization
============
statsmodels uses three types of algorithms for the estimation of the parameters
of a model.
1. Basic linear models such as :ref:`WLS and OLS ` are directly
estimated using appropriate linear algebra.
2. :ref:`RLM ` and :ref:`GLM `, use iteratively re-weighted
least squares. However, you can optionally select one of the scipy
optimizers discussed below.
3. For all other models, we use
`optimizers `_
from `scipy `_.
Where practical, certain models allow for the optional selection of a
scipy optimizer. A particular scipy optimizer might be default or an option.
Depending on the model and the data, choosing an appropriate scipy optimizer
enables avoidance of a local minima, fitting models in less time, or fitting a
model with less memory.
statsmodels supports the following optimizers along with keyword arguments
associated with that specific optimizer:
- ``newton`` - Newton-Raphson iteration. While not directly from scipy, we
consider it an optimizer because only the score and hessian are required.
tol : float
Relative error in params acceptable for convergence.
- ``nm`` - scipy's ``fmin_nm``
xtol : float
Relative error in params acceptable for convergence
ftol : float
Relative error in loglike(params) acceptable for
convergence
maxfun : int
Maximum number of function evaluations to make.
- ``bfgs`` - Broyden–Fletcher–Goldfarb–Shanno optimization, scipy's
``fmin_bfgs``.
gtol : float
Stop when norm of gradient is less than gtol.
norm : float
Order of norm (np.Inf is max, -np.Inf is min)
epsilon
If fprime is approximated, use this value for the step
size. Only relevant if LikelihoodModel.score is None.
- ``lbfgs`` - A more memory-efficient (limited memory) implementation of
``bfgs``. Scipy's ``fmin_l_bfgs_b``.
m : int
The maximum number of variable metric corrections used to
define the limited memory matrix. (The limited memory BFGS
method does not store the full hessian but uses this many
terms in an approximation to it.)
pgtol : float
The iteration will stop when
``max{|proj g_i | i = 1, ..., n} <= pgtol`` where pg_i is
the i-th component of the projected gradient.
factr : float
The iteration stops when
``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps``,
where eps is the machine precision, which is automatically
generated by the code. Typical values for factr are: 1e12
for low accuracy; 1e7 for moderate accuracy; 10.0 for
extremely high accuracy. See Notes for relationship to
ftol, which is exposed (instead of factr) by the
scipy.optimize.minimize interface to L-BFGS-B.
maxfun : int
Maximum number of iterations.
epsilon : float
Step size used when approx_grad is True, for numerically
calculating the gradient
approx_grad : bool
Whether to approximate the gradient numerically (in which
case func returns only the function value).
- ``cg`` - Conjugate gradient optimization. Scipy's ``fmin_cg``.
gtol : float
Stop when norm of gradient is less than gtol.
norm : float
Order of norm (np.Inf is max, -np.Inf is min)
epsilon : float
If fprime is approximated, use this value for the step
size. Can be scalar or vector. Only relevant if
Likelihoodmodel.score is None.
- ``ncg`` - Newton conjugate gradient. Scipy's ``fmin_ncg``.
fhess_p : callable f'(x, \*args)
Function which computes the Hessian of f times an arbitrary
vector, p. Should only be supplied if
LikelihoodModel.hessian is None.
avextol : float
Stop when the average relative error in the minimizer
falls below this amount.
epsilon : float or ndarray
If fhess is approximated, use this value for the step size.
Only relevant if Likelihoodmodel.hessian is None.
- ``powell`` - Powell's method. Scipy's ``fmin_powell``.
xtol : float
Line-search error tolerance
ftol : float
Relative error in loglike(params) for acceptable for
convergence.
maxfun : int
Maximum number of function evaluations to make.
start_direc : ndarray
Initial direction set.
- ``basinhopping`` - Basin hopping. This is part of scipy's ``basinhopping``
tools.
niter : integer
The number of basin hopping iterations.
niter_success : integer
Stop the run if the global minimum candidate remains the
same for this number of iterations.
T : float
The "temperature" parameter for the accept or reject
criterion. Higher "temperatures" mean that larger jumps
in function value will be accepted. For best results
`T` should be comparable to the separation (in function
value) between local minima.
stepsize : float
Initial step size for use in the random displacement.
interval : integer
The interval for how often to update the `stepsize`.
minimizer : dict
Extra keyword arguments to be passed to the minimizer
`scipy.optimize.minimize()`, for example 'method' - the
minimization method (e.g. 'L-BFGS-B'), or 'tol' - the
tolerance for termination. Other arguments are mapped from
explicit argument of `fit`:
- `args` <- `fargs`
- `jac` <- `score`
- `hess` <- `hess`
- ``minimize`` - Allows the use of any scipy optimizer.
min_method : str, optional
Name of minimization method to use.
Any method specific arguments can be passed directly.
For a list of methods and their arguments, see
documentation of `scipy.optimize.minimize`.
If no method is specified, then BFGS is used.
Model Class
-----------
Generally, there is no need for an end-user to directly call these functions
and classes. However, we provide the class because the different optimization
techniques have unique keyword arguments that may be useful to the user.
.. autosummary::
:toctree: generated/
Optimizer
_fit_newton
_fit_bfgs
_fit_lbfgs
_fit_nm
_fit_cg
_fit_ncg
_fit_powell
_fit_basinhopping