# Learning Influence Functions from Incomplete Observations

arXiv: https://arxiv.org/abs/1611.02305 · HTML: https://mlsanity.com/paper/1611.02305/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2016.

## Built on by (most cited first, 7 of 7)

- [Network Inference and Influence Maximization from Samples](https://mlsanity.com/paper/2106.03403/) (2021)
- [USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problems](https://mlsanity.com/paper/2107.07508/) (2021)
- [Learnability of Competitive Threshold Models](https://mlsanity.com/paper/2205.03750/) (2022)
- [Online Influence Maximization under the Independent Cascade Model with Node-Level Feedback](https://mlsanity.com/paper/2109.06077/) (2021)
- [Social-Inverse: Inverse Decision-making of Social Contagion Management with Task Migrations](https://mlsanity.com/paper/2209.10493/) (2022)
- [Learning Set Functions with Implicit Differentiation](https://mlsanity.com/paper/2412.11239/) (2024)
- [Efficient PAC Learnability of Dynamical Systems Over Multilayer Networks](https://mlsanity.com/paper/2405.06884/) (2024)

## Abstract (arXiv)

We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missing observations. Proper PAC learnability under the Discrete-Time Linear Threshold (DLT) and Discrete-Time Independent Cascade (DIC) models is established by reducing incomplete observations to complete observations in a modified graph. Our improper PAC learnability result applies for the DLT and DIC models as well as the Continuous-Time Independent Cascade (CIC) model. It is based on a parametrization in terms of reachability features, and also gives rise to an efficient and practical heuristic. Experiments on synthetic and real-world datasets demonstrate the ability of our method to compensate even for a fairly large fraction of missing observations.