probe_model#

t3toolbox.fitting.probe_model(geometry, x, ww, residual, weight=None, regularizer=None)#
def probe_model(
        geometry,                            # MANIFOLD / COREWISE (or the UNIFORM_* twin for a uniform x)
        x:          typ.Union[t3.TuckerTensorTrain, ut3.UniformTuckerTensorTrain],   # the current point
        ww:         typ.Sequence[NDArray],   # probe vectors, len=d, elm_shape=W+(Ni,)
        residual:   typ.Sequence[NDArray],   # r = probe(x) − y, len=d, elm_shape=W+C+(Ni,)
        weight:     typ.Optional[typ.Any] = None,   # per-mode residual weight ω, 1-D (d,); None = 1 (unweighted)
        regularizer: typ.Any = None,         # optional regularizer, e.g. optimizers.IdentityRegularizer(λ)
) -> typ.Union[GaussNewtonModel, UniformGaussNewtonModel]:

The Gauss-Newton model of a probe least-squares objective at x, on geometry.

Like apply_model() but the measurements are probes – vector-valued (one free mode each), so residual is a sequence of d arrays (elm_shape = W+C+(Ni,)). Optionally per-mode weighted: the objective is ½ Σ_i ‖ω_i r_i‖² over the d per-mode probe residuals, so a 1-D weight ω of shape (d,) up- or down-weights each mode’s data (e.g. inverse-scale / inverse-noise balancing). Plain probe has no order axis, so weight is a 1-D per-mode vector (a 2-D (d, 1) is rejected); for per-order weighting use probe_derivatives_model().

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.manifold as t3m
>>> import t3toolbox.fitting as fitting
>>> np.random.seed(0)
>>> x = t3.TuckerTensorTrain.randn((6, 7, 8), (2, 3, 2), (1, 2, 2, 1))
>>> ww = [np.random.randn(15, N) for N in (6, 7, 8)]
>>> r = [np.random.randn(15, N) for N in (6, 7, 8)]     # per-mode probe residual (a list of d)

A per-mode weight down-weights mode 0 and up-weights mode 2 in the objective ½ Σ_i ‖ω_i r_i‖²:

>>> model = fitting.probe_model(t3m.MANIFOLD, x, ww, r, weight=[0.5, 1.0, 2.0])
>>> print(model.gradient.is_gauged())
True
>>> p = t3m.MANIFOLD.randn(model.frame)
>>> bool(np.allclose(float(model.gn_quadratic(p)), float(p.corewise_inner(model.gn_hessian(p)))))
True

A 2-D weight is rejected – plain probe has no order axis:

>>> fitting.probe_model(t3m.MANIFOLD, x, ww, r, weight=[[0.5], [1.0], [2.0]])
Traceback (most recent call last):
ValueError: plain probe takes a 1-D per-mode residual weight of shape (d,)
Parameters:

  • x (t3toolbox.backend.common.typ.Union[TuckerTensorTrain, UniformTuckerTensorTrain])

  • ww (t3toolbox.backend.common.typ.Sequence[NDArray])

  • residual (t3toolbox.backend.common.typ.Sequence[NDArray])

  • weight (t3toolbox.backend.common.typ.Optional[t3toolbox.backend.common.typ.Any])

  • regularizer (t3toolbox.backend.common.typ.Any)

Return type:

t3toolbox.backend.common.typ.Union[GaussNewtonModel, UniformGaussNewtonModel]