zuko.flows.polynomial

Polynomial flows.

Classes

BPF	Creates a Bernstein polynomial flow (BPF).
SOSPF	Creates a sum-of-squares polynomial flow (SOSPF).

Descriptions

class zuko.flows.polynomial.BPF(features, context=0, degree=16, **kwargs)

Creates a Bernstein polynomial flow (BPF).

Warning

The Bernstein polynomial is bounded to the interval \([-5, 5]\). Any feature outside of this domain is not transformed. It is recommended to standardize features (zero mean, unit variance) before training.

See also

zuko.transforms.BoundedBernsteinTransform

References

Deep transformation models: Tackling complex regression problems with neural network based transformation models (Sick et al., 2020)

https://arxiv.org/abs/2004.00464

Short-Term Density Forecasting of Low-Voltage Load using Bernstein-Polynomial Normalizing Flows (Arpogaus et al., 2022)

https://arxiv.org/abs/2204.13939

Parameters:

• features (int) – The number of features.

• context (int) – The number of context features.

• degree (int) – The degree \(M\) of the Bernstein polynomial.

• kwargs – Keyword arguments passed to zuko.flows.autoregressive.MAF.

class zuko.flows.polynomial.SOSPF(features, context=0, degree=4, polynomials=3, slope=0.001, **kwargs)

Creates a sum-of-squares polynomial flow (SOSPF).

Warning

Invertibility is only guaranteed for features within the interval \([-10, 10]\). It is recommended to standardize features (zero mean, unit variance) before training.

See also

zuko.transforms.SOSPolynomialTransform

References

Sum-of-Squares Polynomial Flow (Jaini et al., 2019)

https://arxiv.org/abs/1905.02325

Parameters:

• features (int) – The number of features.

• context (int) – The number of context features.

• degree (int) – The degree \(L\) of polynomials.

• polynomials (int) – The number of polynomials \(K\).

• slope (float) – The minimum slope of the polynomial transformation(s).

• kwargs – Keyword arguments passed to zuko.flows.autoregressive.MAF.