Representer Point Selection - L2

View source | 📰 Original Paper

Using a completely different notion of influence than the techniques in modules deel.influenciae.influence and deel.influenciae.trac_in, this is the first method to use the representer point theorem for kernels to attribute an influence to data-points in the training dataset. In particular, it posits that the classification function can be approximated by:

\[ \Phi (x_t, \theta) = \sum_i^n k (x_t, x_i, \alpha_i) \]

\[ \alpha_i = - \frac{1}{2 \lambda n} \frac{\partial L (x_i, y_i, \theta)}{\partial \Phi (x_i, \theta)} \]

where \(\Phi\) is the function that transforms the points \(x_t\) in the embedding of the network's last layer to the logits for the classification. However, this function must be learned with a strong \(\ell^2\) regularization, and thus requires creating a surrogate model.

In particular, it will be the \(\alpha_i\) for the predicted label \(j\) the equivalent of the influence of the data-point.

This method does not require us to compute inverse-hessian-vector products, so it can be computed with a certain efficiency once the surrogate model has been learned.

Notebooks

• Using Representer Point Selection - L2 (RPS_L2)

RepresenterPointL2

A class implementing a method to compute the influence of training points through the representer point theorem for kernels.

__init__(self,
         model: keras.engine.training.Model,
         train_set: tf.Dataset,
         loss_function: Union[Callable[[tf.Tensor, tf.Tensor], tf.Tensor], keras.losses.Loss],
         lambda_regularization: float,
         scaling_factor: float = 0.1,
         epochs: int = 100,
         layer_index: int = -1)

Parameters

• model : keras.engine.training.Model

  • A TF2 model that has already been trained

• train_set : tf.Dataset

  • A batched TF dataset with the points with which the model was trained

• loss_function : Union[Callable[[tf.Tensor, tf.Tensor], tf.Tensor], keras.losses.Loss]

  • The loss function with which the model was trained. This loss function MUST NOT be reduced.

• lambda_regularization : float

  • The coefficient for the regularization of the surrogate last layer that needs to be trained for this method

• scaling_factor : float = 0.1

  • A float with the scaling factor for the SGD backtracking line-search optimizer for fitting the surrogate linear model

• epochs : int = 100

  • An integer for the amount of epochs to fit the linear model

• layer_index : int = -1

  • layer of the logits

compute_influence_values(self,
                         train_set: tf.Dataset,
                         device: Optional[str] = None) -> tf.Dataset

Compute the influence score for each sample of the provided (full or partial) model's training dataset.

Parameters

• train_set : tf.Dataset

  • A TF dataset with the (full or partial) model's training dataset.

• device : Optional[str] = None

  • Device where the computation will be executed

Return

• train_set : tf.Dataset

  • A dataset containing the tuple: (batch of training samples, influence score)

compute_influence_vector(self,
                         train_set: tf.Dataset,
                         save_influence_vector_ds_path: Optional[str] = None,
                         device: Optional[str] = None) -> tf.Dataset

Compute the influence vector for each sample of the provided (full or partial) model's training dataset.

Parameters

• train_set : tf.Dataset

  • A TF dataset with the (full or partial) model's training dataset.

• save_influence_vector_ds_path : Optional[str] = None

  • The path to save or load the influence vector of the training dataset. If specified, load the dataset if it has already been computed, otherwise, compute the influence vector and then save it in the specified path.

• device : Optional[str] = None

  • Device where the computation will be executed

Return

• inf_vect_ds : tf.Dataset

  • A dataset containing the tuple: (batch of training samples, influence vector)

compute_top_k_from_training_dataset(self,
                                    train_set: tf.Dataset,
                                    k: int,
                                    order: deel.influenciae.utils.sorted_dict.ORDER = ) -> Tuple[tf.Tensor, tf.Tensor]

Compute the k most influential data-points of the model's training dataset by computing Cook's distance for each point individually.

Parameters

• train_set : tf.Dataset

  • A TF dataset containing the points on which the model was trained.

• k : int

  • An integer with the number of most important samples we wish to keep

• order : 2>

  • Either ORDER.DESCENDING or ORDER.ASCENDING depending on if we wish to find the top-k or bottom-k samples, respectively.

Return

• training_samples, influences_values : Tuple[tf.Tensor, tf.Tensor]

  • A tuple of tensor.

    - training_samples: A tensor containing the k most influential samples of the training dataset for the model provided.

    - influences_values: The influence score corresponding to these k most influential samples.

estimate_influence_values_in_batches(self,
                                     dataset_to_evaluate: tf.Dataset,
                                     train_set: tf.Dataset,
                                     influence_vector_in_cache: deel.influenciae.common.base_influence.CACHE = ,
                                     load_influence_vector_path: Optional[str] = None,
                                     save_influence_vector_path: Optional[str] = None,
                                     save_influence_value_path: Optional[str] = None,
                                     device: Optional[str] = None) -> tf.Dataset

Estimates the influence that each point in the provided training dataset has on each of the test points. This can provide some insights as to what makes the model predict a certain way for the given test points, and thus presents data-centric explanations.

Parameters

• dataset_to_evaluate : tf.Dataset

  • A TF dataset containing the test samples for which to compute the effect of removing each of the provided training points (individually).

• train_set : tf.Dataset

  • A TF dataset containing the model's training dataset (partial or full).

• influence_vector_in_cache : 0>

  • An enum indicating if intermediary values are to be cached (either in memory or on the disk) or not.

    Options include CACHE.MEMORY (0) for caching in memory, CACHE.DISK (1) for the disk and CACHE.NO_CACHE (2) for no optimization.

• load_influence_vector_path : Optional[str] = None

  • The path to load the influence vectors (if they have already been calculated).

• save_influence_vector_path : Optional[str] = None

  • The path to save the computed influence vector.

• save_influence_value_path : Optional[str] = None

  • The path to save the computed influence values.

• device : Optional[str] = None

  • Device where the computation will be executed

Return

• influence_value_dataset : tf.Dataset

  • A dataset containing the tuple: (samples_to_evaluate, dataset).

    - samples_to_evaluate: The batch of sample to evaluate.

    - dataset: Dataset containing tuples of batch of the training dataset and their influence score.

predict_with_kernel(self,
                    samples_to_evaluate: Tuple[tf.Tensor, ...]) -> tf.Tensor

Uses the learned kernel to approximate the model's predictions on a group of samples.

Parameters

• samples_to_evaluate : Tuple[tf.Tensor, ...]

  • A single batch of tensors with the samples for which we wish to approximate the model's predictions

Return

• predictions : tf.Tensor

  • A tensor with an approximation of the model's predictions

top_k(self,
      dataset_to_evaluate: tf.Dataset,
      train_set: tf.Dataset,
      k: int = 5,
      nearest_neighbors: deel.influenciae.utils.nearest_neighbors.BaseNearestNeighbors = ,
      influence_vector_in_cache: deel.influenciae.common.base_influence.CACHE = ,
      load_influence_vector_ds_path: Optional[str] = None,
      save_influence_vector_ds_path: Optional[str] = None,
      save_top_k_ds_path: Optional[str] = None,
      order: deel.influenciae.utils.sorted_dict.ORDER = ,
      d_type: tensorflow.python.framework.dtypes.DType = tf.float32,
      device: Optional[str] = None) -> tf.Dataset

Find the top-k closest elements for each element of dataset to evaluate in the training dataset The method will return a dataset containing a tuple of: (Top-k influence values for each sample to evaluate, Top-k training sample for each sample to evaluate)

Parameters

• dataset_to_evaluate : tf.Dataset

  • The dataset which contains the samples which will be compare to the training dataset

• train_set : tf.Dataset

  • The dataset used to train the model.

• k : int = 5

  • the number of most influence samples to retain in training dataset

• nearest_neighbors : deel.influenciae.utils.nearest_neighbors.BaseNearestNeighbors =

  • The nearest neighbor method. The default method is a linear search

• influence_vector_in_cache : 0>

  • An enum indicating if intermediary values are to be cached (either in memory or on the disk) or not.

    Options include CACHE.MEMORY (0) for caching in memory, CACHE.DISK (1) for the disk and CACHE.NO_CACHE (2) for no optimization.

• load_influence_vector_ds_path : Optional[str] = None

  • The path to load the influence vectors (if they have already been calculated).

• save_influence_vector_ds_path : Optional[str] = None

  • The path to save the computed influence vector.

• save_top_k_ds_path : Optional[str] = None

  • The path to save the result of the computation of the top-k elements

• order : 2>

  • Either ORDER.DESCENDING or ORDER.ASCENDING depending on if we wish to find the top-k or bottom-k samples, respectively.

• d_type : tensorflow.python.framework.dtypes.DType = tf.float32

  • The data-type of the tensors.

• device : Optional[str] = None

  • Device where the computation will be executed

Return

• top_k_dataset : tf.Dataset

  • A dataset containing the tuple (samples_to_evaluate, influence_values, training_samples).

    - samples_to_evaluate: Top-k samples to evaluate.

    - influence_values: Top-k influence values for each sample to evaluate.

    - training_samples: Top-k training sample for each sample to evaluate.