Resolving Multi-Modal Regression by Difference-Quotient-Based Clustering:Fast Coarse Conditional-Label Assignment

Prediction intervals for multi-modal regression with tabular variables, text, images, or other input sources are difficult to calibrate when those sources disagree or one is missing. A single global quantile averages these regimes together instead of calibrating to the modality pattern observed at test time. We address this through a modality-aware conformal calibration layer. The layer trains or reuses one predictor per modality, computes a disagreement score from their predictions, and uses that score in split conformal calibration under a strict split protocol. We use the score in two complementary ways. First, a continuous disagreement-scaled method reallocates interval width across examples while preserving the usual marginal split-conformal guarantee. Second, a Mondrian (stratified) method calibrates within groups defined by disagreement or modality availability fixed before calibration, giving group guarantees under joint exchangeability of the calibration and test examples. Across four multi-modal datasets, the disagreement-scaled layer matches or improves the marginal conformal baseline in 59 of 60 paired runs for interval continuous ranked probability score (CRPS) and in 52 of 60 for interval width, while keeping empirical coverage near the 95% target. In stress tests with missing modalities, mask-matched recalibration recovers up to 19.5 percentage points of coverage in the hardest fixed-mask regime. The result is a simple, model-agnostic reliability layer for multi-modal regression systems. A project page is available at https://unco3892.github.io/modality-aware-conformal.

Efficient uncertainty quantification (UQ) is essential for trustworthy large-scale learning. Existing UQ methods for regression tasks mainly operate under the assumption that the conditional label marginal satisfies single-peak parametric models, e.g., Gaussians, where the negative log-likelihood function simplifies to the mean square error. However, such single-peak assumptions fail in regression tasks featuring multi-modal distributions. On the other hand, semi-parametric methods which achieve strong regression performance for multi-modal distributions often lack efficient quantification on their prediction variances. In this work, we extend UQ techniques based on Variational Bayesian Inference (VBI) to two widely used semi-parametric regression models that yield histogram-like reconstructions of the conditional label densities: Quantile Regression (QR) and Classification Restoration (CR). Our approach introduces a unified, distribution-agnostic framework that simultaneously achieves accurate estimation of complex conditional distributions and highly efficient UQ. Theoretically, our method is grounded in novel formulations of QR and CR within the VBI framework, yielding analytic Evidence Lower Bounds (ELBO) to streamline training and a closed-form or analytically approximated predictive density for efficient inference. Empirically, we evaluate our methods on three large-scale regression benchmarks with multi-modal label distributions. Our framework outperforms state-of-the-art multi-modal regression baselines, and even matches predictive performance of computationally expensive ensemble models. Furthermore, by leveraging epistemic uncertainty estimation, our approach enables highly data-efficient active learning strategies.

Multimodal objects can require different partitions under different instructions, as when products in an e-commerce catalog are grouped by color, material, or both. Retrieval-oriented embeddings may not recover these partitions, while generative clustering often relies on intermediate descriptions or iterative decisions. This paper presents CIM-Embed, a framework for learning instruction-conditioned multimodal embeddings for clustering. Supervised contrastive learning uses same-group positives and negatives from other groups, optionally including other tasks; heterogeneous structured batches accommodate tasks with different group counts. At inference, the model maps each object's image, text, and instruction directly to an embedding; HDBSCAN then forms a partition without the ground-truth cluster count. We construct ProductMIC from product metadata in Amazon Reviews 2023, comprising training data and an evaluation benchmark for instruction-conditioned clustering. The benchmark contains 5,373 products and 449 single-attribute and compositional grouping tasks spanning 50 leaf categories excluded from our training. With full-dimensional embeddings and HDBSCAN, direct within-task SupCon training achieves a mean per-task V-measure of 95.01, compared with 53.06 for WeMM 9B, the strongest general-purpose embedding baseline evaluated. Frozen product-trained encoders also improve out-of-domain conditional grouping, while controlled transfer experiments distinguish partition transfer from instruction response. We will release the code and dataset upon acceptance.