gmm#

diffsptk.GMM#: alias of GaussianMixtureModeling

class diffsptk.GaussianMixtureModeling(order: int, n_mixture: int, *, n_iter: int = 100, eps: float = 1e-05, weight_floor: float = 1e-05, var_floor: float = 1e-06, var_type: str = 'diag', block_size: list[int] | tuple[int, ...] | ndarray | None = None, ubm: tuple[Tensor, Tensor, Tensor] | None = None, alpha: float = 0, batch_size: int | None = None, verbose: bool | int = False, device: device | None = None, dtype: dtype | None = None)[source]#

See this page for details. Note that the forward method is not differentiable.

Parameters:

orderint >= 0: The order of the vector, \(M\).
n_mixtureint >= 1: The number of mixture components, \(K\).
n_iterint >= 1: The number of iterations.
epsfloat >= 0: The convergence threshold.
weight_floorfloat >= 0: The floor value for mixture weights.
var_floorfloat >= 0: The floor value for variance.
var_type[‘diag’, ‘full’]: The type of covariance matrix.
block_sizelist[int]: The block size of covariance matrix.
ubmtuple of Tensors [shape=((K,), (K, M+1), (K, M+1, M+1))]: The GMM parameters of a universal background model.
alphafloat in [0, 1]: The smoothing parameter.
batch_sizeint >= 1 or None: The batch size.
verbosebool: If 1, shows the likelihood at each iteration; if 2, shows progress bars.
devicetorch.device or None: The device of this module.
dtypetorch.dtype or None: The data type of this module.

References

[1]

J-L. Gauvain et al., “Maximum a posteriori estimation for multivariate Gaussian mixture observations of Markov chains,” IEEE Transactions on Speech and Audio Processing, vol. 2, no. 2, pp. 291-298, 1994.

forward(x: Tensor | DataLoader, return_posterior: bool = False) → tuple[tuple[Tensor, Tensor, Tensor], Tensor] | tuple[tuple[Tensor, Tensor, Tensor], Tensor, Tensor][source]#

Train Gaussian mixture models.

Parameters:

xTensor [shape=(T, M+1)] or DataLoader: The input vectors or a DataLoader that yields the input vectors.
return_posteriorbool: If True, return the posterior probabilities.

Returns:

paramstuple of Tensors [shape=((K,), (K, M+1), (K, M+1, M+1))]: The estimated GMM parameters.
posteriorTensor [shape=(T, K)] (optional): The posterior probabilities.
log_likelihoodTensor [scalar]: The total log-likelihood.

Examples

>>> import diffsptk
>>> import torch
>>> gmm = diffsptk.GMM(1, 2)
>>> x = torch.tensor([
...     [-0.5, 0.3], [0.0, 0.7], [0.2, -0.1], [3.4, 2.0], [-2.8, 1.0],
...     [2.9, -3.0], [2.2, -2.5], [1.5, -1.6], [1.8, 0.5], [1.3, 0.0],
... ])
>>> gmm.warmup(x)
>>> params, log_likelihood = gmm(x)
>>> w, mu, sigma = params
>>> w
tensor([0.5471, 0.4529])
>>> mu
tensor([[-0.1507,  0.4112],
        [ 2.3901, -1.0930]])
>>> print(sigma)
tensor([[[2.1197, 0.0000],
         [0.0000, 0.1536]],

        [[0.5578, -0.0000],
         [-0.0000, 3.6378]]])
>>> log_likelihood
tensor(-32.5925)

set_params(params: tuple[Tensor | None, Tensor | None, Tensor | None]) → None[source]#

Set model parameters.

Parameters:

paramstuple of Tensors [shape=((K,), (K, M+1), (K, M+1, M+1))]: The GMM parameters.

transform(x: Tensor) → tuple[Tensor | None, Tensor, Tensor][source]#

Transform the input vectors based on a single mixture sequence.

Parameters:

xTensor [shape=(T, N+1)]: The input vectors.

Returns:

yTensor [shape=(T, M-N)]: The output vectors.
indicesTensor [shape=(T,)]: The selected mixture indices.
log_probTensor [shape=(T,)]: The log probabilities.

warmup(x: Tensor | DataLoader, **lbg_params) → None[source]#

Initialize the model parameters by K-means clustering.

Parameters:

xTensor [shape=(T, M+1)] or DataLoader: The training data.
lbg_paramsadditional keyword arguments: The parameters for the Linde-Buzo-Gray algorithm.