Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly used for LPC, alternate between clustering and linear regression but lack global optimality. While effective for separable clusters, they struggle in non-separable settings where clusters overlap in feature space. In an alternative constrained optimization paradigm, previous works formulated LPC as a Mixed-Integer Program (MIP), ensuring global optimality regardless of separability but at the cost of poor scalability. This work builds on the constrained optimization paradigm to introduce two novel approaches that improve the efficiency of global optimization for LPC. By leveraging key theoretical properties of separability, we derive near-optimal approximations with provable error bounds, significantly reducing the MIP formulation’s complexity and improving scalability. Additionally, we can further approximate LPC as a Quadratic Pseudo-Boolean Optimization (QPBO) problem, achieving additional computational gains in the special case of two clusters. Comparative analyses on synthetic and real-world datasets demonstrate that our methods consistently achieve near-optimal solutions with substantially lower regression errors than greedy optimization while exhibiting superior scalability over existing MIP formulations.

Multimodal conversational recommendation has recently emerged as a promising paradigm for delivering personalized experiences through natural dialogue enriched by visual and contextual grounding. Yet, currently available multimodal conversational recommendation datasets remain limited: existing resources either simulate conversations, omit user history, or fail to collect sufficiently detailed feedback, all of which constrain the types of research and evaluation they support.

Dense Passage Retrieval (DPR) typically relies on Euclidean or cosine distance to measure query-passage relevance in embedding space, which is effective when embeddings lie on a linear manifold.However, our experiments across DPR benchmarks suggest that embeddings often lie on lower-dimensional, non-linear manifolds, especially in out-of-distribution (OOD) settings, where cosine and Euclidean distance fail to capture semantic similarity.To address this limitation, we propose a manifold-aware distance metric for DPR (MA-DPR) that models the intrinsic manifold structure of passages using a nearest neighbor graph and measures query-passage distance based on their shortest path in this graph.We show that MA-DPR outperforms Euclidean and cosine distances by up to 26% on OOD passage retrieval with comparable in-distribution performance across various embedding models while incurring a minimal increase in query inference time.Empirical evidence suggests that manifold-aware distance allows DPR to leverage context from related neighboring passages, making it effective even in the absence of direct semantic overlap.MA-DPR can be applied to a wide range of dense embedding and retrieval tasks, offering potential benefits across a wide spectrum of domains.