Shared Canonical Component Removal Beyond Expert Views

Detailed Research Summary: Shared Canonical Component Removal Beyond Expert Views (SCCR)

This research introduces a novel audit framework, Shared Canonical Component Removal (SCCR), designed to quantify and selectively remove redundant information from raw model embeddings that is already adequately captured by an expert-derived view. The core objective is to determine the predictive signal residing in the raw input that extends beyond what the expert view provides, thereby isolating complementary domain knowledge.

Core Framework and Methodology

The SCCR framework operates on a dual-branch architecture:

1. Raw Embedding: The raw input is mapped to a raw embedding (r).

2. Expert Embedding: A specified expert view is mapped to an expert embedding (psi).

The central audit problem is to identify the complementary predictive signal within r that explains the performance gap between a model trained on psi and one trained directly on r. SCCR addresses this by selectively filtering linear directions in the raw embedding space that are strongly shared with the expert embedding, based on a correlation threshold (tau).

The SCCR operator is defined as a selective residualization operator based on regularized Canonical Correlation Analysis (CCA). It identifies and removes only those canonical directions whose canonical correlation meets or exceeds tau. This approach is distinct from concept erasure techniques, which discard information indiscriminately, as SCCR preserves lower correlation directions that may encode subtle, domain-specific signals not fully explained by the expert view.

Key Contributions and Theoretical Foundations

The paper presents three primary contributions:

1. Audit Framework: A robust framework utilizing an expert view as a reference to test the sufficiency of domain-specified information for prediction and to rigorously measure the complementary predictive signal beyond that view, validated through synthetic and clinical experiments across diverse tasks (CAD detection, antidepressant dropout prediction, skin lesion classification).

2. SCCR Operator: The development of SCCR, a selective residualization operator based on regularized CCA. This operator is designed to retain residual predictive signal by selectively pruning strongly shared linear directions while preserving weaker correlations that might encode valuable domain knowledge.

3. Frozen Calibration for Deterministic Inference: A theoretical proof establishing the stability of the frozen SCCR operator under specific calibration error conditions (i.e., when calibration covariance blocks converge to their population counterparts). This ensures that the resulting dual-branch model maintains black-box performance while achieving a reduction in redundancy with the expert view, leading to deterministic inference at test time.

Theoretical Analysis and Experimental Validation

The theoretical underpinning of SCCR is detailed through several analytical sections:

• Pitfalls and Benefits: The work analyzes existing residualization techniques, demonstrating the specific advantage of SCCR in its selective removal strategy.

• Theoretical Properties: Formal proofs establish the stability of the frozen operator, linking convergence properties to deterministic inference.

• Synthetic Data Experiments: These experiments provide crucial insight into signal retention. In an image classification task where labels depend on both a primary factor (A) and an interaction between two factors (F1 and F2), SCCR was shown to retain predictive information beyond the expert predictor by setting the threshold appropriately (gamma < tau < rho). Specifically, when four raw factors are considered, if S is fully shared with the expert view and A is strongly shared, SCCR successfully removes S and A while preserving the complementary factors F1 and F2.

Empirical Results Across Diverse Datasets

The framework's utility has been validated across several high-stakes domains:

• Skin Lesion Classification: Experiments on skin lesion classification utilize dual-encoder architectures (ImageNet-initialized EfficientNetV2-S encoder) and test various removal thresholds. For instance, at a threshold of tau = 0.40, SCCR demonstrated predictive performance metrics (e.g., linear AUROC of 0.613) that were competitive or superior to baseline models, confirming the retention of residual signal when tau is tuned correctly.

• Coronary Artery Disease (CAD) Detection: Audits on coronary angiograms showed a shift in prediction reliance from mask-based to image-based methods. Crucially, residual audits indicated no significant gain beyond corresponding expert embeddings at low thresholds, suggesting that the most salient features are well-captured by the expert view.

• Antidepressant Treatment Dropout Prediction: Across held-out hospitals, SCCR demonstrated retention of predictive value beyond the psychiatric view while simultaneously reducing linear recovery of included codes. This suggests it successfully isolates complementary signals related to patient outcomes not captured in standard clinical views.

Comparison with Baselines and Practical Considerations

SCCR was benchmarked against several established baselines, including end-to-end OLS, regularized LEACE-style removal (R-LEACE), D-CCA, JIVE, and AJIVE. The analysis confirmed that SCCR achieves its intended suppression–retention pattern by removing only the two most strongly shared canonical directions.

Furthermore, the study compared SCCR against matched top- q methods and found that SCCR and matched top- q have identical fitted maps, suggesting equivalence in mapping capability under certain conditions. The study also addressed the accessibility of true domain features (e.g., Crust) within the expert code, concluding that for removal to be meaningful, these features must be accessible in the expert embedding.

Conclusion and Impact Statement

The SCCR framework offers a principled method for auditing black-box models by quantifying the predictive signal that lies outside a predefined expert view. It moves beyond simple concept erasure by selectively filtering shared linear structure based on correlation strength (tau). While the method requires careful domain oversight for deployment in high-stakes settings, its ability to retain complementary signals—even when other techniques fail—makes it a significant advancement in interpretability and model refinement. The final parameter tau can be optimally determined by finding the minimum threshold where prediction quality matches that of training solely on raw data.

1. SCCR Audit Framework Integration: Implement an audit framework where the expert view serves as a reference for examining the raw input to quantify predictive signal beyond domain expertise, specifically by using SCCR to selectively remove only those directions strongly shared between learned raw and expert embeddings. This allows the AI system to determine what complementary signal in zr explain[s] the performance gap between an expert-view model and a raw black-box model.

2. Deterministic Inference via Frozen Operator: Utilize the frozen SCCR operator, which is computed from empirical second moments on a calibration set, for deterministic inference. This ensures that the residual map is deterministic and consistent with the training distribution at test time, allowing for reliable prediction without needing to re-estimate complex operators during deployment.

3. Feature-Specific Signal Retention: The system can be designed to retain specific weakly shared factors while suppressing others by tuning the threshold τ in SCCR. For instance, as shown in Table 3, SCCR removes only the top two raw canonical directions when α < τ < ρ, allowing for the audit objective of removing S [the fully shared component] and preserving both F1, F2.

4. Robustness Against Calibration Error: The system's stability under calibration perturbations is guaranteed by Theorem B.1, which shows that if the calibration covariance blocks converge to population counterparts, then gb(z) → g(z) for every fixed z ∈ Rdr, ensuring that the audit prediction remains stable even if training statistics vary slightly across datasets.

5. Comparative Audit Diagnostics: The AI system can perform comparative diagnostics by evaluating different residualization techniques (SCCR, OLS, LEACE) and decomposition methods (JIVE, D-CCA). This allows researchers to examine what complementary signal in zr explain[s] the performance gap and compare how different methods handle the trade-off between redundancy and complementary evidence.

In clinical practice, experts often begin by converting raw inputs into a set of expert features before making a decision. While black-box models trained on raw input can outperform models trained on expert views, it remains unclear what predictive signal the raw model exploits beyond what the expert view captures. We introduce an audit framework to quantify this gap using Shared Canonical Component Removal (SCCR). Unlike standard residualization or concept erasure, SCCR selectively removes only those directions strongly shared between learned raw and expert embeddings. Evaluations on synthetic data, coronary artery disease (CAD) detection, antidepressant treatment dropout prediction, and skin lesion classification using SkinCon annotations show that SCCR identifies the ways in which expert views are insufficient and recovers residual predictive signal while minimizing redundancy with the expert view.