# Conditional Approximate Normalizing Flows for Joint Multi-Step Probabilistic Forecasting with Application to Electricity Demand

arXiv: https://arxiv.org/abs/2201.02753 · HTML: https://mlsanity.com/paper/2201.02753/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 8 Jan 2022.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Structured Mechanical Models for Robot Learning and Control](https://mlsanity.com/paper/2004.10301/) (2020)
- [Scalable Identification of Partially Observed Systems with Certainty-Equivalent EM](https://mlsanity.com/paper/2006.11615/) (2020)
- [Dynamic Energy Management](https://mlsanity.com/paper/1903.06230/) (2019)

## Built on by (most cited first, 2 of 2)

- [Sample-based Uncertainty Quantification with a Single Deterministic Neural Network](https://mlsanity.com/paper/2209.08418/) (2022)
- [AutoPQ: Automating Quantile estimation from Point forecasts in the context of sustainability](https://mlsanity.com/paper/2412.00419/) (2024)

## Abstract (arXiv)

Some real-world decision-making problems require making probabilistic forecasts over multiple steps at once. However, methods for probabilistic forecasting may fail to capture correlations in the underlying time-series that exist over long time horizons as errors accumulate. One such application is with resource scheduling under uncertainty in a grid environment, which requires forecasting electricity demand that is inherently noisy, but often cyclic. In this paper, we introduce the conditional approximate normalizing flow (CANF) to make probabilistic multi-step time-series forecasts when correlations are present over long time horizons. We first demonstrate our method's efficacy on estimating the density of a toy distribution, finding that CANF improves the KL divergence by one-third compared to that of a Gaussian mixture model while still being amenable to explicit conditioning. We then use a publicly available household electricity consumption dataset to showcase the effectiveness of CANF on joint probabilistic multi-step forecasting. Empirical results show that conditional approximate normalizing flows outperform other methods in terms of multi-step forecast accuracy and lead to up to 10x better scheduling decisions. Our implementation is available at https://github.com/sisl/JointDemandForecasting.