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Add support for mixture distributions
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Alexander März committed Aug 25, 2023
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2 changes: 1 addition & 1 deletion docs/dgbm.md
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Expand Up @@ -44,7 +44,7 @@ Within the original distributional regression framework, the functions $f_{k}(\c

Mixture densities or mixture distributions offer an extension to the notion of traditional univariate distributions by allowing the observed data to be thought of as arising from multiple underlying processes. In its essence, a mixture distribution is a weighted combination of several component distributions, where each component contributes to the overall mixture distribution, with the weights indicating the importance of each component. For instance, if you imagine the observed data distribution having multiple modes, a mixture of Gaussians could be employed to capture each mode with a separate Gaussian distribution.

<img align="center" width="400" src="mixture.png">
<img align="middle" width="400" src="mixture.png">

For each component of the mixture, there would be a set of parameters that depend on covariates, and additional mixing coefficients which are also modeled as a function of covariates. This is particularly useful when a single parametric distribution cannot adequately capture the underlying data generating process. A mixture distribution can be represented as follows:

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3 changes: 2 additions & 1 deletion docs/index.md
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Expand Up @@ -5,8 +5,9 @@ We introduce a comprehensive framework that models and predicts the full conditi

## Features
- Estimation of all distributional parameters. <br/>
- Multi-target regression allows modelling of multivariate responses and their dependencies. <br/>
- Normalizing Flows allow modelling of complex and multi-modal distributions. <br/>
- Mixture-Densities can model a diverse range of data characteristics. <br/>
- Multi-target regression allows modelling of multivariate responses and their dependencies. <br/>
- Zero-Adjusted and Zero-Inflated Distributions for modelling excess of zeros in the data. <br/>
- Automatic derivation of Gradients and Hessian of all distributional parameters using [PyTorch](https://pytorch.org/docs/stable/autograd.html). <br/>
- Automated hyper-parameter search, including pruning, is done via [Optuna](https://optuna.org/). <br/>
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