# count#

Methods for estimating latent structures used for confident learning, including:

• Latent prior of the unobserved, error-less labels: py: p(y)

• Latent noisy channel (noise matrix) characterizing the flipping rates: nm: P(given label | true label)

• Latent inverse noise matrix characterizing the flipping process: inv: P(true label | given label)

• Latent confident_joint, an un-normalized matrix that counts the confident subset of label errors under the joint distribution for true/given label

Functions:

 calibrate_confident_joint(confident_joint, ...) Calibrates any confident joint estimate P(label=i, true_label=j) such that np.sum(cj) == len(labels) and np.sum(cj, axis = 1) == np.bincount(labels). compute_confident_joint(labels, pred_probs, *) Estimates P(labels,y), the confident counts of the latent joint distribution of true and noisy labels using observed labels and predicted probabilities pred_probs. Estimates P(labels, y), the confident counts of the latent joint distribution of true and noisy labels using observed labels and predicted probabilities pred_probs. This function computes the out-of-sample predicted probability [P(label=k|x)] for every example in X using cross validation. estimate_joint(labels, pred_probs, *[, ...]) Estimates the joint distribution of label noise P(label=i, true_label=j) guaranteed to: estimate_latent(confident_joint, labels, *) Computes the latent prior p(y), the noise matrix P(labels|y) and the inverse noise matrix P(y|labels) from the confident_joint count(labels, y). estimate_noise_matrices(X, labels[, clf, ...]) Estimates the noise_matrix of shape (K, K). Computes the confident counts estimate of latent variables py and the noise rates using observed labels and predicted probabilities, pred_probs. This function computes the out-of-sample predicted probability P(label=k|x) for every example x in X using cross validation while also computing the confident counts noise rates within each cross-validated subset and returning the average noise rate across all examples. get_confident_thresholds(labels, pred_probs) Returns expected (average) "self-confidence" for each class. num_label_issues(labels, pred_probs[, ...]) Estimates the number of label issues in the labels of a dataset.
cleanlab.count.calibrate_confident_joint(confident_joint, labels, *, multi_label=False)[source]#

Calibrates any confident joint estimate P(label=i, true_label=j) such that np.sum(cj) == len(labels) and np.sum(cj, axis = 1) == np.bincount(labels).

In other words, this function forces the confident joint to have the true noisy prior p(labels) (summed over columns for each row) and also forces the confident joint to add up to the total number of examples.

This method makes the confident joint a valid counts estimate of the actual joint of noisy and true labels.

Parameters
• confident_joint (np.array) – An array of shape (K, K) representing the confident joint, the matrix used for identifying label issues, which estimates a confident subset of the joint distribution of the noisy and true labels, P_{noisy label, true label}. Entry (j, k) in the matrix is the number of examples confidently counted into the pair of (noisy label=j, true label=k) classes. The confident_joint can be computed using count.compute_confident_joint. If not provided, it is computed from the given (noisy) labels and pred_probs.

• labels (np.array) – A discrete vector of noisy labels, i.e. some labels may be erroneous. Format requirements: for dataset with K classes, labels must be in 0, 1, …, K-1.

• multi_label (bool, optional) – If True, labels should be an iterable (e.g. list) of iterables, containing a list of labels for each example, instead of just a single label. The multi-label setting supports classification tasks where an example has 1 or more labels. Example of a multi-labeled labels input: [[0,1], [1], [0,2], [0,1,2], [0], [1], ...]. The major difference in how this is calibrated versus single-label is that the total number of errors considered is based on the number of labels, not the number of examples. So, the calibrated confident_joint will sum to the number of total labels.

Returns

calibrated_cj – An array of shape (K, K) of type float representing a valid estimate of the joint counts of noisy and true labels.

Return type

np.array

cleanlab.count.compute_confident_joint(labels, pred_probs, *, thresholds=None, calibrate=True, multi_label=False, return_indices_of_off_diagonals=False)[source]#

Estimates P(labels,y), the confident counts of the latent joint distribution of true and noisy labels using observed labels and predicted probabilities pred_probs.

This estimate is called the confident joint.

When calibrate=True, this method returns an estimate of the latent true joint counts of noisy and true labels.

Important: this function assumes that pred_probs are out-of-sample holdout probabilities. This can be done with cross validation. If the probabilities are not computed out-of-sample, overfitting may occur.

This function estimates the joint of shape (K, K). This is the confident counts of examples in every class, labeled as every other class.

Under certain conditions, estimates are exact, and in most conditions, the estimate is within 1 percent of the truth.

Parameters
• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• pred_probs (np.array, optional) – An array of shape (N, K) of model-predicted probabilities, P(label=k|x). Each row of this matrix corresponds to an example x and contains the model-predicted probabilities that x belongs to each possible class, for each of the K classes. The columns must be ordered such that these probabilities correspond to class 0, 1, …, K-1. pred_probs should have been computed using 3 (or higher) fold cross-validation.

• K (optional) – Number of unique classes. Calculated as len(np.unique(labels)) when K=None.

• thresholds (array_like, optional) –

An array of shape (K, 1) or (K,) of per-class threshold probabilities, used to determine the cutoff probability necessary to consider an example as a given class label (see Northcutt et al., 2021, Section 3.1, Equation 2).

This is for advanced users only. If not specified, these are computed for you automatically. If an example has a predicted probability greater than this threshold, it is counted as having true_label = k. This is not used for pruning/filtering, only for estimating the noise rates using confident counts.

• calibrate (bool, default True) – Calibrates confident joint estimate P(label=i, true_label=j) such that np.sum(cj) == len(labels) and np.sum(cj, axis = 1) == np.bincount(labels).

• multi_label (bool, optional) – If True, labels should be an iterable (e.g. list) of iterables, containing a list of labels for each example, instead of just a single label. The multi-label setting supports classification tasks where an example has 1 or more labels. Example of a multi-labeled labels input: [[0,1], [1], [0,2], [0,1,2], [0], [1], ...]. The major difference in how this is calibrated versus single-label is that the total number of errors considered is based on the number of labels, not the number of examples. So, the calibrated confident_joint will sum to the number of total labels.

• return_indices_of_off_diagonals (bool, optional) – If True, returns indices of examples that were counted in off-diagonals of confident joint as a baseline proxy for the label issues. This sometimes works as well as filter.find_label_issues(confident_joint).

Note

We provide a for-loop based simplification of the confident joint below. This implementation is not efficient, not used in practice, and not complete, but covers the gist of how the confident joint is computed:

# Confident examples are those that we are confident have true_label = k
# Estimate (K, K) matrix of confident examples with label = k_s and true_label = k_y
cj_ish = np.zeros((K, K))
for k_s in range(K): # k_s is the class value k of noisy labels s
for k_y in range(K): # k_y is the (guessed) class k of true_label k_y
cj_ish[k_s][k_y] = sum((pred_probs[:,k_y] >= (thresholds[k_y] - 1e-8)) & (labels == k_s))


The following is a vectorized (but non-parallelized) implementation of the confident joint, again slow, using for-loops/simplified for understanding. This implementation is 100% accurate, it’s just not optimized for speed.

confident_joint = np.zeros((K, K), dtype = int)
for i, row in enumerate(pred_probs):
s_label = labels[i]
confident_bins = row >= thresholds - 1e-6
num_confident_bins = sum(confident_bins)
if num_confident_bins == 1:
confident_joint[s_label][np.argmax(confident_bins)] += 1
elif num_confident_bins > 1:
confident_joint[s_label][np.argmax(row)] += 1

cleanlab.count.estimate_confident_joint_and_cv_pred_proba(X, labels, clf=LogisticRegression(), *, cv_n_folds=5, thresholds=None, seed=None, calibrate=True, clf_kwargs={})[source]#

Estimates P(labels, y), the confident counts of the latent joint distribution of true and noisy labels using observed labels and predicted probabilities pred_probs.

The output of this function is an array of shape (K, K).

Under certain conditions, estimates are exact, and in many conditions, estimates are within one percent of actual.

Notes: There are two ways to compute the confident joint with pros/cons. (1) For each holdout set, we compute the confident joint, then sum them up. (2) Compute pred_proba for each fold, combine, compute the confident joint. (1) is more accurate because it correctly computes thresholds for each fold (2) is more accurate when you have only a little data because it computes the confident joint using all the probabilities. For example if you had 100 examples, with 5-fold cross validation + uniform p(y) you would only have 20 examples to compute each confident joint for (1). Such small amounts of data is bound to result in estimation errors. For this reason, we implement (2), but we implement (1) as a commented out function at the end of this file.

Parameters
• X (np.array) – Input feature matrix of shape (N, ...), where N is the number of examples. The classifier that this instance was initialized with, clf, must be able to handle data with this shape.

• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• clf (estimator instance, optional) – A classifier implementing the sklearn estimator API.

• cv_n_folds (int, default 5) – The number of cross-validation folds used to compute out-of-sample probabilities for each example in X.

• thresholds (array_like, optional) –

An array of shape (K, 1) or (K,) of per-class threshold probabilities, used to determine the cutoff probability necessary to consider an example as a given class label (see Northcutt et al., 2021, Section 3.1, Equation 2).

This is for advanced users only. If not specified, these are computed for you automatically. If an example has a predicted probability greater than this threshold, it is counted as having true_label = k. This is not used for pruning/filtering, only for estimating the noise rates using confident counts.

• seed (int, optional) – Set the default state of the random number generator used to split the cross-validated folds. If None, uses np.random current random state.

• calibrate (bool, default True) – Calibrates confident joint estimate P(label=i, true_label=j) such that np.sum(cj) == len(labels) and np.sum(cj, axis = 1) == np.bincount(labels).

• clf_kwargs (dict, optional) – Optional keyword arguments to pass into clf’s fit() method.

Returns

Tuple of two numpy arrays in the form: (joint counts matrix, predicted probability matrix)

Return type

tuple

cleanlab.count.estimate_cv_predicted_probabilities(X, labels, clf=LogisticRegression(), *, cv_n_folds=5, seed=None, clf_kwargs={})[source]#

This function computes the out-of-sample predicted probability [P(label=k|x)] for every example in X using cross validation. Output is a np.array of shape (N, K) where N is the number of training examples and K is the number of classes.

Parameters
• X (np.array) – Input feature matrix of shape (N, ...), where N is the number of examples. The classifier that this instance was initialized with, clf, must be able to handle data with this shape.

• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• clf (estimator instance, optional) –

A classifier implementing the sklearn estimator API.

• cv_n_folds (int, default 5) – The number of cross-validation folds used to compute out-of-sample probabilities for each example in X.

• seed (int, optional) – Set the default state of the random number generator used to split the cross-validated folds. If None, uses np.random current random state.

• clf_kwargs (dict, optional) – Optional keyword arguments to pass into clf’s fit() method.

Returns

pred_probs – An array of shape (N, K) representing P(label=k|x), the model-predicted probabilities. Each row of this matrix corresponds to an example x and contains the model-predicted probabilities that x belongs to each possible class.

Return type

np.array

cleanlab.count.estimate_joint(labels, pred_probs, *, confident_joint=None, multi_label=False)[source]#

Estimates the joint distribution of label noise P(label=i, true_label=j) guaranteed to:

• Sum to 1

• Satisfy np.sum(joint_estimate, axis = 1) == p(labels)

Parameters
• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• pred_probs (np.array) – An array of shape (N, K) of model-predicted probabilities, P(label=k|x). Each row of this matrix corresponds to an example x and contains the model-predicted probabilities that x belongs to each possible class, for each of the K classes. The columns must be ordered such that these probabilities correspond to class 0, 1, …, K-1. pred_probs should have been computed using 3 (or higher) fold cross-validation.

• confident_joint (np.array, optional) – An array of shape (K, K) representing the confident joint, the matrix used for identifying label issues, which estimates a confident subset of the joint distribution of the noisy and true labels, P_{noisy label, true label}. Entry (j, k) in the matrix is the number of examples confidently counted into the pair of (noisy label=j, true label=k) classes. The confident_joint can be computed using count.compute_confident_joint. If not provided, it is computed from the given (noisy) labels and pred_probs.

• multi_label (bool, optional) – If True, labels should be an iterable (e.g. list) of iterables, containing a list of labels for each example, instead of just a single label. The multi-label setting supports classification tasks where an example has 1 or more labels. Example of a multi-labeled labels input: [[0,1], [1], [0,2], [0,1,2], [0], [1], ...].

Returns

confident_joint – An array of shape (K, K) representing an estimate of the true joint of noisy and true labels.

Return type

np.array

cleanlab.count.estimate_latent(confident_joint, labels, *, py_method='cnt', converge_latent_estimates=False)[source]#

Computes the latent prior p(y), the noise matrix P(labels|y) and the inverse noise matrix P(y|labels) from the confident_joint count(labels, y). The confident_joint can be estimated by compute_confident_joint <cleanlab.count.compute_confident_joint> by counting confident examples.

Parameters
• confident_joint (np.array) – An array of shape (K, K) representing the confident joint, the matrix used for identifying label issues, which estimates a confident subset of the joint distribution of the noisy and true labels, P_{noisy label, true label}. Entry (j, k) in the matrix is the number of examples confidently counted into the pair of (noisy label=j, true label=k) classes. The confident_joint can be computed using count.compute_confident_joint. If not provided, it is computed from the given (noisy) labels and pred_probs.

• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• py_method ({"cnt", "eqn", "marginal", "marginal_ps"}, default "cnt") – py is shorthand for the “class proportions (a.k.a prior) of the true labels”. This method defines how to compute the latent prior p(true_label=k). Default is "cnt", which works well even when the noise matrices are estimated poorly by using the matrix diagonals instead of all the probabilities.

• converge_latent_estimates (bool, optional) – If True, forces numerical consistency of estimates. Each is estimated independently, but they are related mathematically with closed form equivalences. This will iteratively make them mathematically consistent.

Returns

A tuple containing (py, noise_matrix, inv_noise_matrix).

Return type

tuple

cleanlab.count.estimate_noise_matrices(X, labels, clf=LogisticRegression(), *, cv_n_folds=5, thresholds=None, converge_latent_estimates=True, seed=None, clf_kwargs={})[source]#

Estimates the noise_matrix of shape (K, K). This is the fraction of examples in every class, labeled as every other class. The noise_matrix is a conditional probability matrix for P(label=k_s|true_label=k_y).

Under certain conditions, estimates are exact, and in most conditions, estimates are within one percent of the actual noise rates.

Parameters
• X (np.array) – Input feature matrix of shape (N, ...), where N is the number of examples. The classifier that this instance was initialized with, clf, must be able to handle data with this shape.

• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• clf (estimator instance, optional) –

A classifier implementing the sklearn estimator API.

• cv_n_folds (int, default 5) – The number of cross-validation folds used to compute out-of-sample probabilities for each example in X.

• thresholds (array_like, optional) –

An array of shape (K, 1) or (K,) of per-class threshold probabilities, used to determine the cutoff probability necessary to consider an example as a given class label (see Northcutt et al., 2021, Section 3.1, Equation 2).

This is for advanced users only. If not specified, these are computed for you automatically. If an example has a predicted probability greater than this threshold, it is counted as having true_label = k. This is not used for pruning/filtering, only for estimating the noise rates using confident counts.

• converge_latent_estimates (bool, optional) – If True, forces numerical consistency of estimates. Each is estimated independently, but they are related mathematically with closed form equivalences. This will iteratively make them mathematically consistent.

• seed (int, optional) – Set the default state of the random number generator used to split the cross-validated folds. If None, uses np.random current random state.

• clf_kwargs (dict, optional) – Optional keyword arguments to pass into clf’s fit() method.

Returns

A tuple containing (noise_matrix, inv_noise_matrix).

Return type

tuple

cleanlab.count.estimate_py_and_noise_matrices_from_probabilities(labels, pred_probs, *, thresholds=None, converge_latent_estimates=True, py_method='cnt', calibrate=True)[source]#

Computes the confident counts estimate of latent variables py and the noise rates using observed labels and predicted probabilities, pred_probs.

Important: this function assumes that pred_probs are out-of-sample holdout probabilities. This can be done with cross validation. If the probabilities are not computed out-of-sample, overfitting may occur.

This function estimates the noise_matrix of shape (K, K). This is the fraction of examples in every class, labeled as every other class. The noise_matrix is a conditional probability matrix for P(label=k_s|true_label=k_y).

Under certain conditions, estimates are exact, and in most conditions, estimates are within one percent of the actual noise rates.

Parameters
• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• pred_probs (np.array) – An array of shape (N, K) of model-predicted probabilities, P(label=k|x). Each row of this matrix corresponds to an example x and contains the model-predicted probabilities that x belongs to each possible class, for each of the K classes. The columns must be ordered such that these probabilities correspond to class 0, 1, …, K-1. pred_probs should have been computed using 3 (or higher) fold cross-validation.

• thresholds (array_like, optional) –

An array of shape (K, 1) or (K,) of per-class threshold probabilities, used to determine the cutoff probability necessary to consider an example as a given class label (see Northcutt et al., 2021, Section 3.1, Equation 2).

This is for advanced users only. If not specified, these are computed for you automatically. If an example has a predicted probability greater than this threshold, it is counted as having true_label = k. This is not used for pruning/filtering, only for estimating the noise rates using confident counts.

• converge_latent_estimates (bool, optional) – If True, forces numerical consistency of estimates. Each is estimated independently, but they are related mathematically with closed form equivalences. This will iteratively make them mathematically consistent.

• py_method ({"cnt", "eqn", "marginal", "marginal_ps"}, default "cnt") – How to compute the latent prior p(true_label=k). Default is "cnt" as it often works well even when the noise matrices are estimated poorly by using the matrix diagonals instead of all the probabilities.

• calibrate (bool, default True) – Calibrates confident joint estimate P(label=i, true_label=j) such that np.sum(cj) == len(labels) and np.sum(cj, axis = 1) == np.bincount(labels).

Returns

A tuple of (py, noise_matrix, inverse_noise_matrix, confident_joint).

Return type

tuple

cleanlab.count.estimate_py_noise_matrices_and_cv_pred_proba(X, labels, clf=LogisticRegression(), *, cv_n_folds=5, thresholds=None, converge_latent_estimates=False, py_method='cnt', seed=None, clf_kwargs={})[source]#

This function computes the out-of-sample predicted probability P(label=k|x) for every example x in X using cross validation while also computing the confident counts noise rates within each cross-validated subset and returning the average noise rate across all examples.

This function estimates the noise_matrix of shape (K, K). This is the fraction of examples in every class, labeled as every other class. The noise_matrix is a conditional probability matrix for P(label=k_s|true_label=k_y).

Under certain conditions, estimates are exact, and in most conditions, estimates are within one percent of the actual noise rates.

Parameters
• X (np.array) – Input feature matrix of shape (N, ...), where N is the number of examples. The classifier that this instance was initialized with, clf, must be able to handle data with this shape.

• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• clf (estimator instance, optional) –

A classifier implementing the sklearn estimator API.

• cv_n_folds (int, default 5) – The number of cross-validation folds used to compute out-of-sample probabilities for each example in X.

• thresholds (array_like, optional) –

An array of shape (K, 1) or (K,) of per-class threshold probabilities, used to determine the cutoff probability necessary to consider an example as a given class label (see Northcutt et al., 2021, Section 3.1, Equation 2).

This is for advanced users only. If not specified, these are computed for you automatically. If an example has a predicted probability greater than this threshold, it is counted as having true_label = k. This is not used for pruning/filtering, only for estimating the noise rates using confident counts.

• converge_latent_estimates (bool, optional) – If True, forces numerical consistency of estimates. Each is estimated independently, but they are related mathematically with closed form equivalences. This will iteratively make them mathematically consistent.

• py_method ({"cnt", "eqn", "marginal", "marginal_ps"}, default "cnt") – How to compute the latent prior p(true_label=k). Default is "cnt" as it often works well even when the noise matrices are estimated poorly by using the matrix diagonals instead of all the probabilities.

• seed (int, optional) – Set the default state of the random number generator used to split the cross-validated folds. If None, uses np.random current random state.

• clf_kwargs (dict, optional) – Optional keyword arguments to pass into clf’s fit() method.

Returns

A tuple of five arrays (py, noise_matrix, inverse_noise_matrix, confident joint, predicted probability matrix).

Return type

tuple

cleanlab.count.get_confident_thresholds(labels: numpy.array, pred_probs: numpy.array) numpy.array[source]#

Returns expected (average) “self-confidence” for each class.

The confident class threshold for a class j is the expected (average) “self-confidence” for class j.

Parameters
• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• pred_probs (np.array) – An array of shape (N, K) of model-predicted probabilities, P(label=k|x). Each row of this matrix corresponds to an example x and contains the model-predicted probabilities that x belongs to each possible class, for each of the K classes. The columns must be ordered such that these probabilities correspond to class 0, 1, …, K-1. pred_probs should have been computed using 3 (or higher) fold cross-validation.

Returns

confident_thresholds – An array of shape (K,).

Return type

np.array

cleanlab.count.num_label_issues(labels, pred_probs, confident_joint=None)[source]#

Estimates the number of label issues in the labels of a dataset.

This method is more accurate than sum(find_label_issues()) because its computed using only the trace of the confident joint, ignoring all off-diagonals (which are used by find_label_issues and are harder to estimate). Here, we sum over only diagonal elements in the joint (which have more data are more constrained, and therefore easier to compute).

TL;DR: use this method to get the most accurate estimate of number of label issues when you don’t need the indices of the label issues.

You can use this method to label issues by using num_label_issues as the cutoff threshold used with ranking/scoring functions from cleanlab.rank with num_label_issues. There are two cases when you should use this approach instead of filter.find_label_issues:

1. As we add more label and data quality scoring functions in cleanlab.rank, this approach will always work.

2. If you have a custom score to rank your data by label quality and you just need to know the cut-off of likely label issues.

Parameters
• labels (np.array) – An array of shape (N,) of noisy labels, i.e. some labels may be erroneous. Elements must be in the set 0, 1, …, K-1, where K is the number of classes.

• pred_probs (np.array) – An array of shape (N, K) of model-predicted probabilities, P(label=k|x). Each row of this matrix corresponds to an example x and contains the model-predicted probabilities that x belongs to each possible class, for each of the K classes. The columns must be ordered such that these probabilities correspond to class 0, 1, …, K-1. pred_probs should have been computed using 3 (or higher) fold cross-validation.

• confident_joint (np.array, optional) – An array of shape (K, K) representing the confident joint, the matrix used for identifying label issues, which estimates a confident subset of the joint distribution of the noisy and true labels, P_{noisy label, true label}. Entry (j, k) in the matrix is the number of examples confidently counted into the pair of (noisy label=j, true label=k) classes. The confident_joint can be computed using count.compute_confident_joint. If not provided, it is computed from the given (noisy) labels and pred_probs.

Returns

An estimate of the number of label issues.

Return type

int