ikpls 1.0.0

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Fast CPU, GPU, and TPU Python implementations of Improved Kernel PLS Algorithm #1 and Algorithm #2 by Dayal and MacGregor [1]. Improved Kernel PLS has been shown to be both fast [2] and numerically stable [3]. The CPU implementations are made using NumPy [4] and subclass BaseEstimator from scikit-learn [5], allowing integration into scikit-learn’s ecosystem of machine learning algorithms and pipelines. For example, the CPU implementations can be used with scikit-learn’s cross_validate. The GPU and TPU implementations are made using Google’s JAX [6]. While allowing CPU, GPU, and TPU execution, automatic differentiation is also supported by JAX. This implies that the JAX implementations can be used together with deep learning approaches as the PLS fit is differentiable.

The documentation is available at https://ikpls.readthedocs.io/en/latest/, and examples can be found at https://github.com/Sm00thix/IKPLS/tree/main/examples.

[1]

Dayal, B. S., & MacGregor, J. F. (1997). Improved PLS algorithms. Journal of Chemometrics: A Journal of the Chemometrics Society, 11(1), 73-85.

[2]

Alin, A. (2009). Comparison of PLS algorithms when the number of objects is much larger than the number of variables. Statistical papers, 50, 711-720.

[3]

Andersson, M. (2009). A comparison of nine PLS1 algorithms. Journal of Chemometrics: A Journal of the Chemometrics Society, 23(10), 518-529.

[4]

NumPy.

[5]

scikit-learn.

[6]

JAX.

Extremely Fast Cross-Validation

In addition to the aforementioned implementations, this package contains a novel, fast cross-validation implementations of both IKPLS algorithms. The fast cross-validation algorithm benefits both IKPLS Algorithms but especially Algorithm #2. The fast cross-validation algorithm is mathematically equivalent with the classical cross-validation algorithm, but it is much faster if the training split size is larger than the validation split size. The fast cross-validation algorithm is correct for any preprocessing that is not dependent on dataset statistics. An exception to this rule is the built-in support for (column-wise) centering of the X and Y input matrices. This centering can be enabled by setting the center parameter to True.

Pre-requisites

The JAX implementations support running on both CPU, GPU, and TPU. To use the GPU or TPU, follow the instructions from the JAX Installation Guide.

To ensure that JAX implementations use Float64, set the environment variable JAX_ENABLE_X64=True as per the Current Gotchas.

Installation

• Install the package for Python3 using the following command:

  $ pip3 install ikpls
• Now you can import the NumPy and JAX implementations with:

  from ikpls.numpy_ikpls import PLS as NpPLS

  from ikpls.jax_ikpls_alg_1 import PLS as JAXPLS_Alg_1

  from ikpls.jax_ikpls_alg_2 import PLS as JAXPLS_Alg_2

  from ikpls.fast_cross_validation.numpy_ikpls import PLS as NpPLS_FastCV

Quick Start

Use the ikpls package for PLS modelling

import numpy as np

from ikpls.numpy_ikpls import PLS

N = 100  # Number of samples.
K = 50  # Number of features.
M = 10  # Number of targets.
A = 20  # Number of latent variables (PLS components).

X = np.random.uniform(size=(N, K)).astype(np.float64)
Y = np.random.uniform(size=(N, M)).astype(np.float64)

# The other PLS algorithms and implementations, except for NpPLS_FastCV, have the same interface for fit() and predict().
np_ikpls_alg_1 = PLS(algorithm=1)
np_ikpls_alg_1.fit(X, Y, A)

y_pred = np_ikpls_alg_1.predict(X) # Has shape (A, N, M) = (20, 100, 10). Contains a prediction for all possible number of components up to and including A.
y_pred_20_components = np_ikpls_alg_1.predict(X, n_components=20) # Has shape (N, M) = (100, 10).
(y_pred_20_components == y_pred[19]).all() # True

# The internal model parameters can be accessed as follows:
np_ikpls_alg_1.B  # Regression coefficients tensor of shape (A, K, M) = (20, 50, 10).
np_ikpls_alg_1.W  # X weights matrix of shape (K, A) = (50, 20).
np_ikpls_alg_1.P  # X loadings matrix of shape (K, A) = (50, 20).
np_ikpls_alg_1.Q  # Y loadings matrix of shape (M, A) = (10, 20).
np_ikpls_alg_1.R  # X rotations matrix of shape (K, A) = (50, 20).
np_ikpls_alg_1.T  # X scores matrix of shape (N, A) = (100, 20). This is only computed for IKPLS Algorithm #1.

Examples

In examples you will find:

• Fit and Predict with NumPy.

• Fit and Predict with JAX.

• Cross-validate with NumPy.

• Cross-validate with NumPy and fast cross-validation.

• Cross-validate with JAX.

• Compute the gradient of a preprocessing convolution filter with respect to the RMSE between the target value and the value predicted by PLS after fitting with JAX.