Available Distributions

LightGBMLSS is built upon PyTorch and Pyro, enabling users to harness a diverse set of distributional families and to leverage automatic differentiation capabilities. This greatly expands the options for probabilistic modeling and uncertainty estimation and allows users to tackle complex regression tasks.

LightGBMLSS currently supports the following univariate distributions.

Distribution Usage Type Support Number of Parameters
Beta Beta() Continuous
(Univariate)
\(y \in (0, 1)\) 2
Cauchy Cauchy() Continuous
(Univariate)
\(y \in (-\infty,\infty)\) 2
Expectile Expectile() Continuous
(Univariate)
\(y \in (-\infty,\infty)\) Number of expectiles
Gamma Gamma() Continuous
(Univariate)
\(y \in (0, \infty)\) 2
Gaussian Gaussian() Continuous
(Univariate)
\(y \in (-\infty,\infty)\) 2
Gumbel Gumbel() Continuous
(Univariate)
\(y \in (-\infty,\infty)\) 2
Laplace Laplace() Continuous
(Univariate)
\(y \in (-\infty,\infty)\) 2
LogNormal LogNormal() Continuous
(Univariate)
\(y \in (0,\infty)\) 2
Mixture Mixture(CompDist(), M) Continuous & Discrete Count
(Univariate)
\(y \in (-\infty,\infty)\)

\(y \in [0, \infty)\)

\(y \in [0, 1]\)

\(y \in (0, 1, 2, 3, \ldots)\)
CompDist + M
Negative Binomial NegativeBinomial() Discrete Count
(Univariate)
\(y \in (0, 1, 2, 3, \ldots)\) 2
Poisson Poisson() Discrete Count
(Univariate)
\(y \in (0, 1, 2, 3, \ldots)\) 1
Spline Flow SplineFlow() Continuous & Discrete Count
(Univariate)
\(y \in (-\infty,\infty)\)

\(y \in [0, \infty)\)

\(y \in [0, 1]\)

\(y \in (0, 1, 2, 3, \ldots)\)
2xcount_bins + (count_bins-1) (order=quadratic)

3xcount_bins + (count_bins-1) (order=linear)
Student-T StudentT() Continuous
(Univariate)
\(y \in (-\infty,\infty)\) 3
Weibull Weibull() Continuous
(Univariate)
\(y \in [0, \infty)\) 2
Zero-Adjusted Beta ZABeta() Discrete-Continuous
(Univariate)
\(y \in [0, 1)\) 3
Zero-Adjusted Gamma ZAGamma() Discrete-Continuous
(Univariate)
\(y \in [0, \infty)\) 3
Zero-Adjusted LogNormal ZALN() Discrete-Continuous
(Univariate)
\(y \in [0, \infty)\) 3
Zero-Inflated Negative Binomial ZINB() Discrete-Count
(Univariate)
\(y \in [0, 1, 2, 3, \ldots)\) 3
Zero-Inflated Poisson ZIPoisson() Discrete-Count
(Univariate)
\(y \in [0, 1, 2, 3, \ldots)\) 2