# Creating Probabilistic Forecasts from Arbitrary Deterministic Forecasts using Conditional Invertible Neural Networks

arXiv: https://arxiv.org/abs/2302.01800 · HTML: https://mlsanity.com/paper/2302.01800/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 3 Feb 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Deep Generative Quantile-Copula Models for Probabilistic Forecasting](https://mlsanity.com/paper/1907.10697/) (2019)
- [A deep generative model for probabilistic energy forecasting in power systems: normalizing flows](https://mlsanity.com/paper/2106.09370/) (2021)
- [Probabilistic Forecasting of Sensory Data with Generative Adversarial Networks - ForGAN](https://mlsanity.com/paper/1903.12549/) (2019)
- [Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows](https://mlsanity.com/paper/2205.13826/) (2022)
- [Scenario Forecasting of Residential Load Profiles](https://mlsanity.com/paper/1906.07373/) (2019)
- [pyWATTS: Python Workflow Automation Tool for Time Series](https://mlsanity.com/paper/2106.10157/) (2021)
- [Short-Term Density Forecasting of Low-Voltage Load using Bernstein-Polynomial Normalizing Flows](https://mlsanity.com/paper/2204.13939/) (2022)
- [Probabilistic Forecasting using Deep Generative Models](https://mlsanity.com/paper/1909.11865/) (2019)

## Abstract (arXiv)

In various applications, probabilistic forecasts are required to quantify the inherent uncertainty associated with the forecast. However, numerous modern forecasting methods are still designed to create deterministic forecasts. Transforming these deterministic forecasts into probabilistic forecasts is often challenging and based on numerous assumptions that may not hold in real-world situations. Therefore, the present article proposes a novel approach for creating probabilistic forecasts from arbitrary deterministic forecasts. In order to implement this approach, we use a conditional Invertible Neural Network (cINN). More specifically, we apply a cINN to learn the underlying distribution of the data and then combine the uncertainty from this distribution with an arbitrary deterministic forecast to generate accurate probabilistic forecasts. Our approach enables the simple creation of probabilistic forecasts without complicated statistical loss functions or further assumptions. Besides showing the mathematical validity of our approach, we empirically show that our approach noticeably outperforms traditional methods for including uncertainty in deterministic forecasts and generally outperforms state-of-the-art probabilistic forecasting benchmarks.