Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition

To generate accurate and reliable predictions, modern AI systems need to combine data from multiple modalities, such as text, images, audio, spreadsheets, and time series. Multi-modal data introduces new opportunities and challenges for disentangling uncertainty: it is commonly assumed in the machine learning community that epistemic uncertainty can be reduced by collecting more data, while aleatoric uncertainty is irreducible. However, this assumption is challenged in modern AI systems when information is obtained from different modalities. This paper introduces an innovative data acquisition framework where uncertainty disentanglement leads to actionable decisions, allowing sampling in two directions: sample size and data modality. The main hypothesis is that aleatoric uncertainty decreases as the number of modalities increases, while epistemic uncertainty decreases by collecting more observations. We provide proof-of-concept implementations on two multi-modal datasets to showcase our data acquisition framework, which combines ideas from active learning, active feature acquisition and uncertainty quantification.

Soft Learning Probabilistic Circuits

Probabilistic Circuits (PCs) are prominent tractable probabilistic models, allowing for a range of exact inferences. This paper focuses on the main algorithm for training PCs, LearnSPN, a gold standard due to its efficiency, performance, and ease of use, in particular for tabular data. We show that LearnSPN is a greedy likelihood maximizer under mild assumptions. While inferences in PCs may use the entire circuit structure for processing queries, LearnSPN applies a hard method for learning them, propagating at each sum node a data point through one and only one of the children/edges as in a hard clustering process. We propose a new learning procedure named SoftLearn, that induces a PC using a soft clustering process. We investigate the effect of this learning-inference compatibility in PCs. Our experiments show that SoftLearn outperforms LearnSPN in many situations, yielding better likelihoods and arguably better samples. We also analyze comparable tractable models to highlight the differences between soft/hard learning and model querying.

Probabilistic Circuits with Constraints via Convex Optimization

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and marginal probabilities) while achieving state-of-the-art performance in some domains. The proposed approach takes both a PC and constraints as inputs, and outputs a new PC that satisfies the constraints. This is done efficiently via convex optimization without the need to retrain the entire model. Empirical evaluations indicate that the combination of constraints and PCs can have multiple use cases, including the improvement of model performance under scarce or incomplete data, as well as the enforcement of machine learning fairness measures into the model without compromising model fitness. We believe that these ideas will open possibilities for multiple other applications involving the combination of logics and deep probabilistic models.