Learning from Label Proportions: Bootstrapping Supervised Learners via Belief Propagation (2310.08056v4)

Abstract: Learning from Label Proportions (LLP) is a learning problem where only aggregate level labels are available for groups of instances, called bags, during training, and the aim is to get the best performance at the instance-level on the test data. This setting arises in domains like advertising and medicine due to privacy considerations. We propose a novel algorithmic framework for this problem that iteratively performs two main steps. For the first step (Pseudo Labeling) in every iteration, we define a Gibbs distribution over binary instance labels that incorporates a) covariate information through the constraint that instances with similar covariates should have similar labels and b) the bag level aggregated label. We then use Belief Propagation (BP) to marginalize the Gibbs distribution to obtain pseudo labels. In the second step (Embedding Refinement), we use the pseudo labels to provide supervision for a learner that yields a better embedding. Further, we iterate on the two steps again by using the second step's embeddings as new covariates for the next iteration. In the final iteration, a classifier is trained using the pseudo labels. Our algorithm displays strong gains against several SOTA baselines (up to 15%) for the LLP Binary Classification problem on various dataset types - tabular and Image. We achieve these improvements with minimal computational overhead above standard supervised learning due to Belief Propagation, for large bag sizes, even for a million samples.

• The paper introduces a novel BP-based framework that generates pseudo-labels from bag-level aggregate constraints for effective instance-level prediction.
• The paper employs an iterative two-step algorithm that refines feature embeddings with an aggregate embedding loss to enhance classifier accuracy.
• The paper demonstrates that integrating belief propagation in a weakly supervised context achieves significant performance gains while addressing privacy constraints.

Analyzing Learning from Label Proportions Through a Belief Propagation Methodology

The paper "Learning from Label Proportions: Bootstrapping Supervised Learners via Belief Propagation" presents an innovative approach that leverages Belief Propagation (BP) for the problem of Learning from Label Proportions (LLP). This approach is particularly relevant in contexts requiring privacy, where only aggregate-level labels for groups of instances (or 'bags') are provided during training. The challenge lies in predicting instance-level labels from these group-based proportions.

Algorithmic Framework

The proposed solution is structured around an iterative two-step algorithm. In the first step, a Gibbs distribution is constructed over binary instance labels incorporating both covariate information and bag-level aggregate constraints. Belief Propagation is then employed to derive pseudo-labels from this distribution. In the subsequent step, these pseudo-labels are used to refine the feature embeddings. This embedding refinement allows for improved representation of each instance's feature data, which in turn assists in the training of a final classifier.

Performance Evaluation

The framework demonstrates significant empirical strength, showcasing improvements in LLP binary classification tasks across various datasets, including tabular and image data. The authors report improvements of up to 15% over state-of-the-art (SOTA) benchmarks, reinforcing the potential of their algorithm. Notably, the computational overhead of incorporating BP in this context is minimal, even when dealing with large datasets and substantial bag sizes.

Technical Contributions

1. Novel Use of BP: The authors leverage BP to form pseudo-labels by considering bag constraints and covariate similarity, drawing a parallel to parity recovery problems in coding theory.
2. Aggregate Embedding Loss: A novel loss formulation that integrates bag-level supervision with instance-level predictions ensures coherence between pseudo-labels and bag constraints. This dual-oriented approach effectively bridges the gap between aggregate-level supervision and individual instance learning.
3. Iterative Optimization: By iterating over BP-derived pseudo-labels and refined embeddings, the method progressively improves instance-level predictor performance.

Empirical Insights

Across the board, the methodology appears robust, achieving notable gains for large bag settings where supervision signals are inherently weak. This is crucial given the LLP context where individual labels are not individually available. The facilitated embedding refinement process crucially supports enhanced learning dynamics, particularly in datasets with varied structural characteristics (e.g., image data requiring interpretive feature embeddings).

Implications and Future Research

The findings suggest that well-constructed pseudo-labels can substantially boost learning performance in LLP settings, provided they are synergistically integrated with effective feature embeddings. The paper opens avenues for further exploration of BP in other weakly supervised contexts or integrating additional unlabeled data into the learning model. Future work could also extend the framework to explore other forms of label noise or leverage alternative embedding techniques to enhance covariate representation.

Despite its promise, the methodology's reliance on BP hints at computational challenges in extremely large-scale datasets or more complex label structures. Addressing these limitations could significantly widen the application scope.

In conclusion, this paper adds a valuable dimension to LLP methodologies by blending traditional machine learning principles with innovative probabilistic inference techniques, establishing a robust foundation for future developments in privacy-conscious learning scenarios.