# Tractable Probabilistic Models for Investment Planning

arXiv: https://arxiv.org/abs/2511.13888 · HTML: https://mlsanity.com/paper/2511.13888/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 73 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Tractable Regularization of Probabilistic Circuits](https://mlsanity.com/paper/2106.02264/) (2021)
- [SPFlow: An Easy and Extensible Library for Deep Probabilistic Learning using Sum-Product Networks](https://mlsanity.com/paper/1901.03704/) (2019)
- [Probabilistic Generating Circuits](https://mlsanity.com/paper/2102.09768/) (2021)
- [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024)
- [Capacity Expansion Planning under Uncertainty subject to Expected Energy Not Served Constraints](https://mlsanity.com/paper/2501.17484/) (2025)
- [Robust Transmission Network Expansion Planning under Correlated Uncertainty](https://mlsanity.com/paper/1501.06613/) (2015)
- [Robust Coordinated Transmission and Generation Expansion Planning Considering Ramping Requirements and Construction Periods](https://mlsanity.com/paper/1612.00226/) (2016)
- [Distributionally Robust Transmission Expansion Planning: a Multi-scale Uncertainty Approach](https://mlsanity.com/paper/1810.05212/) (2018)
- [Learning-assisted Stochastic Capacity Expansion Planning: A Bayesian Optimization Approach](https://mlsanity.com/paper/2401.10451/) (2024)
- [Regularized Benders Decomposition for High Performance Capacity Expansion Models](https://mlsanity.com/paper/2403.02559/) (2024)
- [Soft Learning Probabilistic Circuits](https://mlsanity.com/paper/2403.14504/) (2024)

## Abstract (arXiv)

Investment planning in power utilities, such as generation and transmission expansion, requires decisions under substantial uncertainty over decade--long horizons for policies, demand, renewable availability, and outages, while maintaining reliability and computational tractability. Conventional approaches approximate uncertainty using finite scenario sets (modeled as a mixture of Diracs in statistical theory terms), which can become computationally intensive as scenario detail increases and provide limited probabilistic resolution for reliability assessment. We propose an alternative based on tractable probabilistic models, using sum--product networks (SPNs) to represent high--dimensional uncertainty in a compact, analytically tractable form that supports exact probabilistic queries (e.g., likelihoods, marginals, and conditionals). This framework enables the direct embedding of chance constraints into mixed--integer linear programming (MILP) models for investment planning to evaluate reliability events and enforce probabilistic feasibility requirements without enumerating large scenario trees. We demonstrate the approach on a representative planning case study and report reliability--cost trade--offs and computational behavior relative to standard scenario--based formulations.