Programmatic Weak Supervision (PWS) aggregates the source votes of multiple weak supervision sources into probabilistic training labels, which are in turn used to train an end model. With its increasing popularity, it is critical to have some tool for users to understand the influence of each component (\eg, the source vote or training data) in the pipeline and interpret the end model behavior. To achieve this, we build on Influence Function (IF) and propose source-aware IF, which leverages the generation process of the probabilistic labels to decompose the end model's training objective and then calculate the influence associated with each (data, source, class) tuple. These primitive influence score can then be used to estimate the influence of individual component of PWS, such as source vote, supervision source, and training data. On datasets of diverse domains, we demonstrate multiple use cases: (1) interpreting incorrect predictions from multiple angles that reveals insights for debugging the PWS pipeline, (2) identifying mislabeling of sources with a gain of 9\%-37\% over baselines, and (3) improving the end model's generalization performance by removing harmful components in the training objective (13\%-24\% better than ordinary IF).

These authors contributed equally to this work.

Abstract--The accurate labeling of datasets is often both costly and time-consuming. Given an unlabeled dataset, programma tic weak supervision obtains probabilistic predictions for th e labels by leveraging multiple weak labeling functions (LFs) that p ro-vide rough guesses for labels. Weak LFs commonly provide guesses with assorted types and unknown interdependences that can result in unreliable predictions. This paper presents a methodology for programma tic weak supervision that can provide confidence intervals for l abel probabilities and obtain more reliable predictions. In par ticular, the methods proposed use uncertainty sets of distributions that encapsulate the information provided by LFs with unrestric ted behavior and typology. Experiments on multiple benchmark datasets show the improvement of the presented methods over the state-of-the-art and the practicality of the confidence intervals presented. OR many machine learning applications, the accurate labeling of datasets is both costly and time-consuming [1]-[4]. Given an unlabeled dataset, methods for programmatic weak supervision aim to leverage multiple wea k labeling functions (LFs) to provide accurate labels [5], [6 ]. Since common LFs only provide rough guesses for labels, programmatic weak supervision methods use the outputs of multiple LFs to obtain probabilistic predictions for the la bel of each instance [7]-[13]. These predictions can then be use d to create a fully supervised dataset composed by the instanc es corresponding to high-confidence predictions, e.g., a labe l with a large enough predicted probability is regarded as the actu al Manuscript received September 30, 2024; accepted August 4, 2025.

Programmatic Weak Supervision (PWS) aggregates the source votes of multiple weak supervision sources into probabilistic training labels, which are in turn used to train an end model. With its increasing popularity, it is critical to have some tool for users to understand the influence of each component (\eg, the source vote or training data) in the pipeline and interpret the end model behavior. To achieve this, we build on Influence Function (IF) and propose source-aware IF, which leverages the generation process of the probabilistic labels to decompose the end model's training objective and then calculate the influence associated with each (data, source, class) tuple. These primitive influence score can then be used to estimate the influence of individual component of PWS, such as source vote, supervision source, and training data. On datasets of diverse domains, we demonstrate multiple use cases: (1) interpreting incorrect predictions from multiple angles that reveals insights for debugging the PWS pipeline, (2) identifying mislabeling of sources with a gain of 9\%-37\% over baselines, and (3) improving the end model's generalization performance by removing harmful components in the training objective (13\%-24\% better than ordinary IF).

Programmatic Weak Supervision (PWS) aggregates the source votes of multiple weak supervision sources into probabilistic training labels, which are in turn used to train an end model. With its increasing popularity, it is critical to have some tool for users to understand the influence of each component (\eg, the source vote or training data) in the pipeline and interpret the end model behavior. To achieve this, we build on Influence Function (IF) and propose source-aware IF, which leverages the generation process of the probabilistic labels to decompose the end model's training objective and then calculate the influence associated with each (data, source, class) tuple. These primitive influence score can then be used to estimate the influence of individual component of PWS, such as source vote, supervision source, and training data. On datasets of diverse domains, we demonstrate multiple use cases: (1) interpreting incorrect predictions from multiple angles that reveals insights for debugging the PWS pipeline, (2) identifying mislabeling of sources with a gain of 9\%-37\% over baselines, and (3) improving the end model's generalization performance by removing harmful components in the training objective (13\%-24\% better than ordinary IF).

We develop methods for estimating Fr\'echet bounds on (possibly high-dimensional) distribution classes in which some variables are continuous-valued. We establish the statistical correctness of the computed bounds under uncertainty in the marginal constraints and demonstrate the usefulness of our algorithms by evaluating the performance of machine learning (ML) models trained with programmatic weak supervision (PWS). PWS is a framework for principled learning from weak supervision inputs (e.g., crowdsourced labels, knowledge bases, pre-trained models on related tasks, etc), and it has achieved remarkable success in many areas of science and engineering. Unfortunately, it is generally difficult to validate the performance of ML models trained with PWS due to the absence of labeled data. Our algorithms address this issue by estimating sharp lower and upper bounds for performance metrics such as accuracy/recall/precision/F1 score.

Programmatic Weak Supervision (PWS) has emerged as a widespread paradigm to synthesize training labels efficiently. The core component of PWS is the label model, which infers true labels by aggregating the outputs of multiple noisy supervision sources abstracted as labeling functions (LFs). Existing statistical label models typically rely only on the outputs of LF, ignoring the instance features when modeling the underlying generative process. In this paper, we attempt to incorporate the instance features into a statistical label model via the proposed FABLE. In particular, it is built on a mixture of Bayesian label models, each corresponding to a global pattern of correlation, and the coefficients of the mixture components are predicted by a Gaussian Process classifier based on instance features. We adopt an auxiliary variable-based variational inference algorithm to tackle the non-conjugate issue between the Gaussian Process and Bayesian label models. Extensive empirical comparison on eleven benchmark datasets sees FABLE achieving the highest averaged performance across nine baselines.

Labeling training data has become one of the major roadblocks to using machine learning. Among various weak supervision paradigms, programmatic weak supervision (PWS) has achieved remarkable success in easing the manual labeling bottleneck by programmatically synthesizing training labels from multiple potentially noisy supervision sources. This paper presents a comprehensive survey of recent advances in PWS. In particular, we give a brief introduction of the PWS learning paradigm, and review representative approaches for each component within PWS's learning workflow. In addition, we discuss complementary learning paradigms for tackling limited labeled data scenarios and how these related approaches can be used in conjunction with PWS. Finally, we identify several critical challenges that remain under-explored in the area to hopefully inspire future research directions in the field.