from typing import Optional, Union
from sklearn.base import BaseEstimator
from sklearn.utils import check_random_state
import numpy as np
from cblearn import utils
from cblearn.embedding._base import TripletEmbeddingMixin
from cblearn.embedding import _torch_utils
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class FORTE(BaseEstimator, TripletEmbeddingMixin):
""" Fast Ordinal Triplet Embedding (FORTE).
FORTE [1]_ minimizes a kernel version of the triplet hinge soft objective
as a smooth relaxation of the triplet error.
This estimator supports multiple implementations which can be selected by the `backend` parameter.
The *torch* backend uses the ADAM optimizer and backpropagation [2]_.
It can executed on CPU, but also CUDA GPUs. We optimize using BFSGS and Strong-Wolfe line search.
.. Note::
The *torch* backend requires the *pytorch* python package (see :ref:`extras_install`).
Attributes:
embedding_: Final embedding, shape (n_objects, n_components)
stress_: Final value of the SOE stress corresponding to the embedding.
n_iter_: Final number of optimization steps.
Examples:
>>> from cblearn import datasets
>>> np.random.seed(42)
>>> true_embedding = np.random.rand(15, 2)
>>> triplets = datasets.make_random_triplets(true_embedding, result_format='list-order', size=1000)
>>> triplets.shape, np.unique(triplets).shape
((1000, 3), (15,))
>>> estimator = FORTE(n_components=2)
>>> embedding = estimator.fit_transform(triplets)
>>> embedding.shape
(15, 2)
>>> estimator.score(triplets) > 0.6
True
References
----------
.. [1] Jain, L., Jamieson, K. G., & Nowak, R. (2016). Finite Sample Prediction and
Recovery Bounds for Ordinal Embedding. Advances in Neural Information Processing Systems, 29.
.. [2] Vankadara, L. C., Haghiri, S., Lohaus, M., Wahab, F. U., & von Luxburg, U. (2020).
Insights into Ordinal Embedding Algorithms: A Systematic Evaluation. ArXiv:1912.01666 [Cs, Stat].
"""
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def __init__(self, n_components=2, verbose=False, random_state: Union[None, int, np.random.RandomState] = None,
max_iter=2000, batch_size=50_000, device: str = "auto"):
""" Initialize the estimator.
Args:
n_components :
The dimension of the embedding.
verbose: boolean, default=False
Enable verbose output.
random_state:
The seed of the pseudo random number generator used to initialize the optimization.
max_iter: Maximum number of optimization iterations.
batch_size: Batch size of stochastic optimization. Only used with *torch* backend, else ignored.
device: The device on which pytorch computes. {"auto", "cpu", "cuda"}
"auto" chooses cuda (GPU) if available, but falls back on cpu if not.
Only used with the *torch* backend, else ignored.
"""
self.n_components = n_components
self.max_iter = max_iter
self.verbose = verbose
self.random_state = random_state
self.device = device
self.batch_size = batch_size
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def fit(self, X: utils.Query, y: np.ndarray = None, init: np.ndarray = None,
n_objects: Optional[int] = None) -> 'FORTE':
"""Computes the embedding.
Args:
X: The training input samples, shape (n_samples, 3)
y: Ignored
init: Initial embedding for optimization
Returns:
self.
"""
self.fit_X_ = utils.check_query(X, result_format='list-order') # for data validation in .transform
triplets = utils.check_query_response(X, y, result_format='list-order')
self.n_features_in_ = 3
if not n_objects:
n_objects = triplets.max() + 1
random_state = check_random_state(self.random_state)
if init is None:
init = random_state.multivariate_normal(np.zeros(self.n_components),
np.eye(self.n_components), size=n_objects)
_torch_utils.assert_torch_is_available()
result = _torch_utils.torch_minimize_kernel('l-bfgs-b', _torch_forte_loss, init, data=(triplets.astype(int),),
device=self.device, max_iter=self.max_iter,
seed=random_state.randint(1),
batch_size=self.batch_size, line_search_fn='strong_wolfe')
if self.verbose and not result.success:
print(f"FORTE's optimization failed with reason: {result.message}.")
self.embedding_ = result.x.reshape(-1, self.n_components)
self.stress_, self.n_iter_ = result.fun, result.nit
return self
def _torch_forte_loss(kernel_matrix, triplets):
triplets = triplets.long()
diag = kernel_matrix.diag()[:, None]
dist = -2 * kernel_matrix + diag + diag.transpose(0, 1)
d_ij = dist[triplets[:, 0], triplets[:, 1]].squeeze()
d_ik = dist[triplets[:, 0], triplets[:, 2]].squeeze()
return (1 + (d_ij - d_ik).exp()).log().sum()
