tensap.approximation.tensor_approximation.tensor_learning package¶

Submodules¶

tensap.approximation.tensor_approximation.tensor_learning.canonical_tensor_learning module¶

Module canonical_tensor_learning.

class tensap.approximation.tensor_approximation.tensor_learning.canonical_tensor_learning.CanonicalTensorLearning(order, *args)¶

Bases: tensap.approximation.tensor_approximation.tensor_learning.tensor_learning.TensorLearning

Class CanonicalTensorLearning.

tensap.approximation.tensor_approximation.tensor_learning.tensor_learning module¶

Module tensor_learning.

class tensap.approximation.tensor_approximation.tensor_learning.tensor_learning.TensorLearning(loss)¶

Bases: tensap.approximation.learning.learning.Learning

Class TensorLearning.

See also tensap.Learning.

Attributes

orderint: Order of the tensor.
baseslist or numpy.ndarray: The functional bases used for by the approximation.
bases_evallist or numpy.ndarray: The evaluations of the bases on the training data.
bases_eval_testlist or numpy.ndarray: The evaluations of the bases on the test data.
algorithmstr: The choice of algorithm.
initialization_typestr: The type of initialization.
initial_guesstensap.Tensor: An initial guess for the solver.
tree_adaptationbool: Boolean indicating if tree adaptation is to be performed.
tree_adaptation_optionsdict: Options for the tree adaptation.
rank_adaptationbool: Boolean indicating if rank adaptation is to be performed.
rank_adaptation_optionsdict: Options for the rank adaptation.
tolerancedict: Tolerances for the solver.
linear_model_learning_parametersdict: Parameters for the linear solvers.
alternating_minimization_parametersdict: Parameters for the alternating minimization.
bases_adaptation_pathlist or numpy.ndarray: Paths for each basis for the basis adaptation.
store_iteratesbool: Boolean indicating if the iterates are to be stored.
rankint or list or numpy.ndarray: The rank of the expected approximation.
output_dimensionint: The dimension of the outputs of the function to be approximated.
_number_of_parametersint: The number of parameters of the approximation.
_exploration_strategynumpy.ndarray: The exploration strategy.
_warningsdict: Dictionnary containing the state of some warnings to be displayed.

Methods

`adapt_tree`(f, cv_error, test_error, output, …)	Tree adaptation algorithm.
`adaptation_display`(f, enriched_nodes)	Display during the adaptation.
`final_display`(f)	Display at the end of the computation.
`initial_guess_new_rank`(s_local, f, new_rank)	Computation of the initial guess with the new selected rank.
`initialize`()	Initialization of the learning algorithm.
`local_solver`()	Extraction of the solver for the adaptive algorithm
`new_rank_selection`(f)	Selection of a new rank in the adaptive algorithm.
`pre_processing`(f)	Initialization of the alternating minimization algorithm.
`prepare_alternating_minimization_system`(f, mu)	Preparation of the alternating minimization algorithm.
`randomize_exploration_strategy`()	Randomization of the exploration strategy.
`set_parameter`(f, mu, coef)	Update of the parameter mu of the tensor f.
`solve`(*args)	Solver for the learning problem with tensor formats.
`stagnation_criterion`(f, f0)	Computation of the stagnation criterion.

linear_model
risk_estimation

adapt_tree(f, cv_error, test_error, output, *args)¶

Tree adaptation algorithm.

Parameters

ftensap.Tensor: The current tensor approximation.
cv_errorfloat: The current cross-validation error.
test_errorfloat: The current test error.
outputdict: The outputs of the solver.
argstuple: Additional parameters.

Returns

tensap.TensorLearning: The TensorLearning object.
ftensap.Tensor: The current tensor approximation, perhaps with an adapted tree.
outputdict: The outputs of the solver.

abstract adaptation_display(f, enriched_nodes)¶

Display during the adaptation.

Parameters

ftensap.FunctionalTensor: The current approximation.
enriched_nodesnumpy.ndarray: The enriched parameters.

abstract final_display(f)¶

Display at the end of the computation.

Parameters

ftensap.FunctionalTensor: The current approximation.

Returns

None.

abstract initial_guess_new_rank(s_local, f, new_rank)¶

Computation of the initial guess with the new selected rank.

Parameters

s_localtensap.TensorLearning: The local solver.
ftensap.FunctionalTensor: The current approximation.
new_ranknumpy.ndarray: The new tensor rank.

Returns

s_localtensap.TensorLearning: The local solver with the initial guess in s_local.initial_guess.

abstract initialize()¶

Initialization of the learning algorithm.

Returns

tensap.TensorLearning: The TensorLearning object.
ftensap.FunctionalTensor: The initialization of the solver.

abstract local_solver()¶

Extraction of the solver for the adaptive algorithm

Returns

s_localtensap.TensorLearning: The local solver.

abstract new_rank_selection(f)¶

Selection of a new rank in the adaptive algorithm.

Parameters

ftensap.FunctionalTensor: The current approximation.

Returns

new_ranknumpy.ndarray: The new tensor rank.
enriched_nodesnumpy.ndarray: The enriched parameters.
tensor_for_initializationtensap.Tensor: A tensor used for the initialization of the next iteration.

abstract pre_processing(f)¶

Initialization of the alternating minimization algorithm.

Parameters

ftensap.Tensor: The current tensor approximation.

Returns

tensap.TensorLearning: The TensorLearning object.
ftensap.Tensor: The pre-processed tensor approximation.

abstract prepare_alternating_minimization_system(f, mu)¶

Preparation of the alternating minimization algorithm.

Parameters

ftensap.FunctionalTensor: The current approximation.
muint: The number of the parameter to be optimized.

Returns

tensap.TensorLearning: The TensorLearning object.
Anumpy.ndarray: The matricized partial evaluation of f.
bnumpy.ndarray: The target training data.
ftensap.FunctionalTensor: The current approximation.

abstract randomize_exploration_strategy()¶

Randomization of the exploration strategy.

Returns

alpha_listnumpy.ndarray: The randomized exploration strategy.

abstract set_parameter(f, mu, coef)¶

Update of the parameter mu of the tensor f.

Parameters

ftensap.FunctionalTensor: The current approximation.
muint: The number of the optimized parameter.
coefnumpy.ndarray: The new value of the parameter mu of f.

Returns

ftensap.FunctionalTensor: The updated approximation.

solve(*args)¶

Solver for the learning problem with tensor formats.

Parameters

*argsmisc: Additional arguments, if needed.

Returns

ftensap.FunctionalTensor: The learned approximation.
outputdict: The outputs of the solver.

Raises

NotImplementedError: If the required solver is not implemented.
ValueError: If the required data is not provided.

abstract stagnation_criterion(f, f0)¶

Computation of the stagnation criterion.

Parameters

ftensap.FunctionalTensor: The current approximation.
f0tensap.FunctionalTensor: The previous approximation.

Returns

stagnationfloat: The value of the stagnation criterion.

tensap.approximation.tensor_approximation.tensor_learning.tree_based_tensor_learning module¶

Module tree_based_tensor_learning.

class tensap.approximation.tensor_approximation.tensor_learning.tree_based_tensor_learning.TreeBasedTensorLearning(tree, is_active_node, *args)¶

Bases: tensap.approximation.tensor_approximation.tensor_learning.tensor_learning.TensorLearning

Class TreeBasedTensorLearning.

See also tensap.TensorLearning.

Attributes

treetensap.DimensionTree: The dimension tree of the tree-based tensor.
is_active_nodelist or numpy.ndarray: Booleans indicating if each node is active.

Methods

`adapt_tree`(f, cv_error, test_error, output, …)	Tree adaptation algorithm.
`adaptation_display`(f, enriched_nodes)	Display during the adaptation.
`canonical_correction`(f, rank)	Rank-r canonical correction.
`canonical_initialization`(rank)	Rank-r canonical initialization.
`create_basis_adaptation_path`(ranks, alpha)	Creation of the basis adaptation path.
`enriched_edges_to_ranks_random`(f, new_rank)	Enrichment of the ranks of specified edges of the tensor f using random additions for each child / parent couple of the enriched edges.
`final_display`(f)	Display at the end of the computation.
`initial_guess_new_rank`(s_local, f, new_rank)	Computation of the initial guess with the new selected rank.
`initialize`()	Initialization of the learning algorithm.
`local_solver`()	Extraction of the solver for the adaptive algorithm
`make_ranks_admissible`(f, rank)	Adjustment of the ranks to make the associated tree-based tensor f rank-admissible, by enriching new edges associated with nodes of the tree until all the rank admissibility conditions are met.
`new_rank_selection`(f)	Selection of a new rank in the adaptive algorithm.
`pre_processing`(f)	Initialization of the alternating minimization algorithm.
`prepare_alternating_minimization_system`(f, mu)	Preparation of the alternating minimization algorithm.
`randomize_exploration_strategy`()	Randomization of the exploration strategy.
`rank_one_correction`(f)	Rank one correction.
`set_parameter`(f, mu, coef)	Update of the parameter mu of the tensor f.
`solve`(*args)	Solver for the learning problem with tensor formats.
`stagnation_criterion`(f, f0)	Computation of the stagnation criterion.
`tensor_train`(order, *args)	Call of the constructor of the class TreeBasedTensorLearning, with a tree and active nodes corresponding to the Tensor-Train format in dimension order.
`tensor_train_tucker`(order, *args)	Call of the constructor of the class TreeBasedTensorLearning, with a tree and active nodes corresponding to the Tensor-Train Tucker format in dimension order.
`unique_tol`(inp, tol)	Unique values within tolerance, with sorted output.

create_basis_adaptation_path_dmrg
create_basis_adaptation_path_dmrg_low_rank
linear_model
risk_estimation

adapt_tree(f, cv_error, test_error, output, *args)¶

Tree adaptation algorithm.

Parameters

ftensap.Tensor: The current tensor approximation.
cv_errorfloat: The current cross-validation error.
test_errorfloat: The current test error.
outputdict: The outputs of the solver.
argstuple: Additional parameters.

Returns

tensap.TensorLearning: The TensorLearning object.
ftensap.Tensor: The current tensor approximation, perhaps with an adapted tree.
outputdict: The outputs of the solver.

adaptation_display(f, enriched_nodes)¶

Display during the adaptation.

Parameters

ftensap.FunctionalTensor: The current approximation.
enriched_nodesnumpy.ndarray: The enriched parameters.

canonical_correction(f, rank)¶

Rank-r canonical correction.

Parameters

ftensap.FunctionalTensor or None: The current approximation.
rankint: The rank of the canonical correction.

Returns

ftensap.FunctionalTensor: The corrected approximation.

Raises

NotImplementedError: If the method is not implemented.

canonical_initialization(rank)¶

Rank-r canonical initialization.

Parameters

rankint: The rank of the canonical initialization.

Returns

tensap.TreeBasedTensor: The rank-r canonical initialization..

create_basis_adaptation_path(ranks, alpha)¶

Creation of the basis adaptation path.

Parameters

ranklist or numpy.ndarray: The alpha-ranks of the current approximation.
alphaint: The current node.

Returns

pathnumpy.ndarray: The basis adaptation path.

create_basis_adaptation_path_dmrg(ranks, alpha)¶

create_basis_adaptation_path_dmrg_low_rank(ranks, alpha)¶

static enriched_edges_to_ranks_random(f, new_rank)¶

Enrichment of the ranks of specified edges of the tensor f using random additions for each child / parent couple of the enriched edges.

Parameters

ftensap.TreeBasedTensor: The tree-based tensor to enrich.
new_ranklist or numpy.ndarray: The new tree-based rank.

Returns

ftensap.TreeBasedTensor: The enriched tree-based tensor.

final_display(f)¶

Display at the end of the computation.

Parameters

ftensap.FunctionalTensor: The current approximation.

Returns

None.

initial_guess_new_rank(s_local, f, new_rank)¶

Computation of the initial guess with the new selected rank.

Parameters

s_localtensap.TensorLearning: The local solver.
ftensap.FunctionalTensor: The current approximation.
new_ranknumpy.ndarray: The new tensor rank.

Returns

s_localtensap.TensorLearning: The local solver with the initial guess in s_local.initial_guess.

initialize()¶

Initialization of the learning algorithm.

Returns

tensap.TensorLearning: The TensorLearning object.
ftensap.FunctionalTensor: The initialization of the solver.

local_solver()¶

Extraction of the solver for the adaptive algorithm

Returns

s_localtensap.TensorLearning: The local solver.

static make_ranks_admissible(f, rank)¶

Adjustment of the ranks to make the associated tree-based tensor f rank-admissible, by enriching new edges associated with nodes of the tree until all the rank admissibility conditions are met.

Parameters

ftensap.TreeBasedTensor: The current approximation in tree-based tensor format.
ranknumpy.ndarray: The proposed tree-based rank.

Returns

ranknumpy.ndarray: The admissible tree-based rank (if possible).
dnumpy.ndarray: The enriched nodes.

new_rank_selection(f)¶

Selection of a new rank in the adaptive algorithm.

Parameters

ftensap.FunctionalTensor: The current approximation.

Returns

new_ranknumpy.ndarray: The new tensor rank.
enriched_nodesnumpy.ndarray: The enriched parameters.
tensor_for_initializationtensap.Tensor: A tensor used for the initialization of the next iteration.

pre_processing(f)¶

Initialization of the alternating minimization algorithm.

Parameters

ftensap.Tensor: The current tensor approximation.

Returns

tensap.TensorLearning: The TensorLearning object.
ftensap.Tensor: The pre-processed tensor approximation.

prepare_alternating_minimization_system(f, mu)¶

Preparation of the alternating minimization algorithm.

Parameters

ftensap.FunctionalTensor: The current approximation.
muint: The number of the parameter to be optimized.

Returns

tensap.TensorLearning: The TensorLearning object.
Anumpy.ndarray: The matricized partial evaluation of f.
bnumpy.ndarray: The target training data.
ftensap.FunctionalTensor: The current approximation.

randomize_exploration_strategy()¶

Randomization of the exploration strategy.

Returns

alpha_listnumpy.ndarray: The randomized exploration strategy.

rank_one_correction(f)¶

Rank one correction.

Parameters

ftensap.FunctionalTensor or None: The current approximation.

Returns

ftensap.FunctionalTensor: The corrected approximation.

Raises

NotImplementedError: If the method is not implemented.

set_parameter(f, mu, coef)¶

Update of the parameter mu of the tensor f.

Parameters

ftensap.FunctionalTensor: The current approximation.
muint: The number of the optimized parameter.
coefnumpy.ndarray: The new value of the parameter mu of f.

Returns

ftensap.FunctionalTensor: The updated approximation.

stagnation_criterion(f, f0)¶

Computation of the stagnation criterion.

Parameters

ftensap.FunctionalTensor: The current approximation.
f0tensap.FunctionalTensor: The previous approximation.

Returns

stagnationfloat: The value of the stagnation criterion.

static tensor_train(order, *args)¶

Call of the constructor of the class TreeBasedTensorLearning, with a tree and active nodes corresponding to the Tensor-Train format in dimension order.

tensap.approximation.tensor_approximation.tensor_learning package¶

Submodules¶

tensap.approximation.tensor_approximation.tensor_learning.canonical_tensor_learning module¶

tensap.approximation.tensor_approximation.tensor_learning.tensor_learning module¶

tensap.approximation.tensor_approximation.tensor_learning.tree_based_tensor_learning module¶

Module contents¶

tensap

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Related Topics

`adapt_tree`(f, cv_error, test_error, output, …)	Tree adaptation algorithm.
`adaptation_display`(f, *args)	Display during the adaptation.
`final_display`(f)	Display at the end of the computation.
`initial_guess_new_rank`(s_local, f, *args)	Computation of the initial guess with the new selected rank.
`initialize`()	Initialization of the learning algorithm.
`local_solver`()	Extraction of the solver for the adaptive algorithm
`new_rank_selection`(f)	Selection of a new rank in the adaptive algorithm.
`pre_processing`(f)	Initialization of the alternating minimization algorithm.
`prepare_alternating_minimization_system`(f, mu)	Preparation of the alternating minimization algorithm.
`randomize_exploration_strategy`()	Randomization of the exploration strategy.
`set_parameter`(f, mu, coef)	Update of the parameter mu of the tensor f.
`solve`(*args)	Solver for the learning problem with tensor formats.
`stagnation_criterion`(f, f0)	Computation of the stagnation criterion.