Incomplete multi-view multi-label learning is fundamentally an information integration problem under simultaneous view and label incompleteness. We introduce Permutation-Consistent Variational Encoding framework (PCVE) with an information bottleneck strategy, which learns variational representations capable of aggregating shared semantics across views while remaining robust to incompleteness. PCVE formulates a principled objective that maximizes a variational evidence lower bound to retain task-relevant information, and introduces a permutation-consistent regularization to encourage distributional consistency among representations that encode the same target semantics from different views. This regularization acts as an information alignment mechanism that suppresses view-private redundancy and mitigates over-alignment, thereby improving both sufficiency and consistency of the learned representations. To address missing labels, PCVE further incorporates a masked multi-label learning objective that leverages available supervision while modeling label dependencies. Extensive experiments across diverse benchmarks and missing ratios demonstrate consistent gains over state-of-the-art methods in multi-label classification, while enabling reliable inference of missing views without explicit imputation. Analyses corroborate that the proposed information-theoretic formulation improves cross-view semantic cohesion and preserves discriminative capacity, underscoring the effectiveness and generality of PCVE for incomplete multi-view multi-label learning.
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