# Predictive Uncertainty Estimators for Sum-Product Networks

## Funding Agency

CNPq grant 304012/2019-0

## Coordinator

Denis Deratani Mauá

## Participants

- Denis Deratani Mauá
- Julissa G. Villanueva, PhD candidate at IME-USP
- Renato Lui Geh, MSc student at IME-USP
- Decio L. Soares, MSc student at IME-USP

## Abstract

Deep models have recently obtained impressive results in a wide range of tasks and domains, from computer vision to image and text processing to diagnosis and automated reasoning. Sum-product networks are special type of neural networks targeted at the representation of high-dimensionality probability distributions. Notably, the structure of a sum-product network (i.e., its graph) encodes a number of probabilistic independence assertions. In addition, each node of the network computes a valid distribution over its part of the variables. Such probabilistic semantics facilitates debugging, allows a wide range of queries and data (including missing and noisy data) to be handled properly and efficiently, and enables efficient structure learning algorithms.

In many applications, it is desirable to have not only a prediction (e.g., the probability of observing a certain object, say an image), but a confidence measure about its prediction. As sum-product networks are learned from data, the probabilities they calculate can be overly confident or too sensitive to hyperparameters on regions where data was scarce, conflicting or too noisy. In this research project, we plan on following two possible approaches to estimating the uncertainty of a sum-product network prediction. The first approach estimates uncertainty by analyzing the effect that small perturbations of the data have on the prediction. The second approach considers the variability of predictions among different networks (learned from the same data).

This document describes a three-year research agenda on producing predictive uncertainty estimators for sum-product networks, to be pursued within the scope of a CNPq productivity scholarship by the applicant and his group.