# Uncertain Bayesian Networks: Learning from Incomplete Data

@article{Hougen2021UncertainBN,
title={Uncertain Bayesian Networks: Learning from Incomplete Data},
author={Conrad D. Hougen and Lance M. Kaplan and F. Cerutti and Alfred O. Hero},
journal={2021 IEEE 31st International Workshop on Machine Learning for Signal Processing (MLSP)},
year={2021},
pages={1-6}
}
• Published 25 October 2021
• Computer Science
• 2021 IEEE 31st International Workshop on Machine Learning for Signal Processing (MLSP)
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the probabilities and quantifying the uncertainty in these estimates. We refer to these cases as uncertain or second-order Bayesian networks. When such data are complete, i.e., all variable values are observed for each instantiation, the conditional probabilities…
1 Citations

## Figures and Tables from this paper

### Evidential Reasoning and Learning: a Survey

• Computer Science
IJCAI
• 2022
This paper focuses on techniques that take the name of evidential reasoning and learning from the process of Bayesian update of given hypotheses based on additional evidence that provide a gentle introduction to the area of investigation, the up-to-date research outcomes, and the open questions still left unanswered.

## References

SHOWING 1-10 OF 12 REFERENCES

### Second-Order Learning and Inference using Incomplete Data for Uncertain Bayesian Networks: A Two Node Example

• Computer Science
2020 IEEE 23rd International Conference on Information Fusion (FUSION)
• 2020
Two methods to compute the covariances for the parameters of Bayesian networks or Markov random fields due to incomplete data for two-node networks are introduced.

### Bayesian Error-Bars for Belief Net Inference

• Computer Science
UAI
• 2001
This paper investigates the distribution of the response the BN will return to any "What is Pr{H/E}?" query, shows that it is asymptotically normal, and derives expressions for its mean and asymPTotic variance.

### Handling Epistemic and Aleatory Uncertainties in Probabilistic Circuits

• Computer Science
Mach. Learn.
• 2022
An algorithm for Bayesian learning from sparse, albeit complete, observations, and for deriving inferences and their confidences keeping track of the dependencies between variables when they are manipulated within the unifying computational formalism provided by probabilistic circuits.

### A differential approach to inference in Bayesian networks

The proposed framework for inference subsumes one of the most influential methods for inference in Bayesian networks, known as the tree-clustering or jointree method, which provides a deeper understanding of this classical method and lifts its desirable characteristics to a much more general setting.

### Bayesian Networks and Decision Graphs

• F. V. Jensen
• Computer Science
Statistics for Engineering and Information Science
• 2001
The book introduces probabilistic graphical models and decision graphs, including Bayesian networks and influence diagrams, and presents a thorough introduction to state-of-the-art solution and analysis algorithms.

### Online and Distributed Bayesian Moment Matching for Parameter Learning in Sum-Product Networks

• Computer Science
AISTATS
• 2016
This work proposes a new Bayesian moment matching (BMM) algorithm that operates naturally in an online fashion and that can be easily distributed and demonstrates the effectiveness and scalability of BMM in comparison to online extensions of gradient descent, exponentiated gradient and expectation maximization on 20 classic benchmarks and 4 large scale datasets.

### On the Relationship between Sum-Product Networks and Bayesian Networks

• Computer Science, Mathematics
ICML
• 2015
This paper proves that every SPN can be converted into a BN in linear time and space in terms of the network size and introduces the notion of {\em normal} SPN and presents a theoretical analysis of the consistency and decomposability properties.