def compute_py_inv_noise_matrix(ps, noise_matrix):
'''Compute py := P(y=k), and the inverse noise matrix.
Parameters
----------
ps : np.array (shape (K, 1))
The fraction (prior probability) of each observed, noisy class label, P(s = k)
noise_matrix : np.array of shape (K, K), K = number of classes
A conditional probablity matrix of the form P(s=k_s|y=k_y) containing
the fraction of examples in every class, labeled as every other class.
Assumes columns of noise_matrix sum to 1.'''
# Number of classes
K = len(ps)
# 'py' is p(y=k) = noise_matrix^(-1) * p(s=k)
# because in *vector computation*: P(s=k|y=k) * p(y=k) = P(s=k)
# The pseudoinverse is used when noise_matrix is not invertible.
py = np.linalg.inv(noise_matrix).dot(ps)
# No class should have probability 0 so we use .001
# Make sure valid probabilites that sum to 1.0
py = clip_values(py, low=0.001, high=1.0, new_sum = 1.0)
# All the work is done in this function (below)
return py, compute_inv_noise_matrix(py, noise_matrix, ps)
def estimate_latent(
confident_joint,
s,
py_method='cnt',
converge_latent_estimates=False,
):
'''Computes the latent prior p(y), the noise matrix P(s|y) and the
inverse noise matrix P(y|s) from the `confident_joint` count(s, y). The
`confident_joint` estimated by `compute_confident_joint`
by counting confident examples.
Parameters
----------
s : np.array
A discrete vector of labels, s, which may contain mislabeling. "s" denotes
the noisy label instead of \tilde(y), for ASCII encoding reasons.
confident_joint : np.array (shape (K, K), type int)
A K,K integer matrix of count(s=k, y=k). Estimatesa a confident subset of
the joint disribution of the noisy and true labels P_{s,y}.
Each entry in the matrix contains the number of examples confidently
counted into every pair (s=j, y=k) classes.
py_method : str (Options: ["cnt", "eqn", "marginal", "marginal_ps"])
How to compute the latent prior p(y=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.
converge_latent_estimates : bool
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).'''
# Number of classes
K = len(np.unique(s))
# 'ps' is p(s=k)
ps = value_counts(s) / float(len(s))
# Ensure labels are of type np.array()
s = np.asarray(s)
# Number of training examples confidently counted from each noisy class
s_count = confident_joint.sum(axis=1).astype(float)
# Number of training examples confidently counted into each true class
y_count = confident_joint.sum(axis=0).astype(float)
# Confident Counts Estimator for p(s=k_s|y=k_y) ~ |s=k_s and y=k_y| / |y=k_y|
noise_matrix = confident_joint / y_count
# Confident Counts Estimator for p(y=k_y|s=k_s) ~ |y=k_y and s=k_s| / |s=k_s|
inv_noise_matrix = confident_joint.T / s_count
# Compute the prior p(y), the latent (uncorrupted) class distribution.
py = compute_py(ps, noise_matrix, inv_noise_matrix, py_method, y_count)
# Clip noise rates to be valid probabilities.
noise_matrix = clip_noise_rates(noise_matrix)
inv_noise_matrix = clip_noise_rates(inv_noise_matrix)
# Make latent estimates mathematically agree in their algebraic relations.
if converge_latent_estimates:
py, noise_matrix, inv_noise_matrix = converge_estimates(
ps, py, noise_matrix, inv_noise_matrix)
# Again clip py and noise rates into proper range [0,1)
py = clip_values(py, low=1e-5, high=1.0, new_sum=1.0)
noise_matrix = clip_noise_rates(noise_matrix)
inv_noise_matrix = clip_noise_rates(inv_noise_matrix)
return py, noise_matrix, inv_noise_matrix
def compute_py(ps, noise_matrix, inverse_noise_matrix, py_method = 'cnt', y_count = None):
'''Compute py := P(y=k) from ps := P(s=k), noise_matrix, and inverse noise matrix.
This method is ** ROBUST ** when py_method = 'cnt'
It may work well even when the noise matrices are estimated
poorly by using the diagonals of the matrices
instead of all the probabilities in the entire matrix.
Parameters
----------
ps : np.array (shape (K, ) or (1, K))
The fraction (prior probability) of each observed, noisy class label, P(s = k).
noise_matrix : np.array of shape (K, K), K = number of classes
A conditional probablity matrix of the form P(s=k_s|y=k_y) containing
the fraction of examples in every class, labeled as every other class.
Assumes columns of noise_matrix sum to 1.
inverse_noise_matrix : np.array of shape (K, K), K = number of classes
A conditional probablity matrix of the form P(y=k_y|s=k_s) representing
the estimated fraction observed examples in each class k_s, that are
mislabeled examples from every other class k_y. If None, the
inverse_noise_matrix will be computed from psx and s.
Assumes columns of inverse_noise_matrix sum to 1.
py_method : str (Options: ["cnt", "eqn", "marginal", "marginal_ps"])
How to compute the latent prior p(y=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.
y_count : np.array (shape (K, ) or (1, K))
The marginal counts of the confident joint (like cj.sum(axis = 0))
Output
------
py : np.array (shape (K, ) or (1, K))
The fraction (prior probability) of each observed, noisy class label, P(y = k).'''
if len(np.shape(ps)) > 2 or (len(np.shape(ps)) == 2 and np.shape(ps)[0] != 1):
w = 'Input parameter np.array ps has shape ' + str(np.shape(ps))
w += ', but shape should be (K, ) or (1, K)'
warnings.warn(w)
if py_method == 'marginal' and y_count is None:
err = 'py_method == "marginal" requires y_count, but y_count is None.'
err += ' Provide parameter y_count.'
raise ValueError(err)
if py_method == 'cnt':
# Computing py this way avoids dividing by zero noise rates.
# More robust bc error est_p(y|s) / est_p(s|y) ~ p(y|s) / p(s|y)
py = inverse_noise_matrix.diagonal() / noise_matrix.diagonal() * ps
# Equivalently,
# py = (y_count / s_count) * ps
elif py_method == 'eqn':
py = np.linalg.inv(noise_matrix).dot(ps)
elif py_method == 'marginal':
py = y_count / float(sum(y_count))
elif py_method == 'marginal_ps':
py = np.dot(inverse_noise_matrix, ps)
else:
err = 'py_method {}'.format(py_method)
err += ' should be in [cnt, eqn, marginal, marginal_ps]'
raise ValueError(err)
# Clip py (0,1), .s.t. no class should have prob 0, hence 1e-5
py = clip_values(py, low=1e-5, high=1.0, new_sum = 1.0)
return py
