Quick Start

HDMRLib supports two related decomposition formulations:

  • HDMR is useful when you want to work explicitly with HDMR-based formulations

  • EMPR provides the same high-level workflow through an alternative decomposition formulation

In both cases, the workflow is the same:

input data → decomposition → components → reconstruction

End-to-end example with HDMR

import numpy as np
from hdmrlib import HDMR

X = np.random.rand(10, 10)

hdmr = HDMR(X, order=2)

X_reconstructed = hdmr.reconstruct()
components = hdmr.components()

This computes an HDMR decomposition of X up to order 2.

  • hdmr.reconstruct() returns a reconstruction based on the computed decomposition

  • hdmr.components() returns the extracted component terms

Understanding the outputs

The components() method returns the component functions produced by the decomposition. These are typically organized by term name, such as lower-order individual terms and interaction terms.

For example, a call such as:

selected = hdmr.components(elements=["g_0", "g_1", "g_2", "g_1,2"])

returns only the requested components.

This is useful when you want to inspect specific lower-order terms or selected interactions rather than the full decomposition output.

Reconstructing lower-order approximations

X_order1 = hdmr.reconstruct(order=1)

This reconstructs X using only terms up to order 1.

Use reconstruct(order=...) when you want to study how much of the data can be approximated using only lower-order structure. This is especially useful when comparing simplified approximations against the full reconstruction.

Running the same workflow with EMPR

import numpy as np
from hdmrlib import EMPR

X = np.random.rand(10, 10)

empr = EMPR(X, order=2)

X_reconstructed = empr.reconstruct()
components = empr.components()

The same workflow applies to EMPR: compute a decomposition, inspect the extracted components, and reconstruct the data from the resulting representation.

Choosing between HDMR and EMPR

As a starting point:

  • use HDMR when you want to work specifically with HDMR-based formulations

  • use EMPR when you want to compare an alternative formulation within the same workflow

Since both follow a consistent interface, it is easy to compare them within the same workflow.