AI predictive systems are increasingly embedded in decision making pipelines, shaping high stakes choices once made solely by humans. Yet robust decisions under uncertainty still rely on capabilities that current AI lacks: domain knowledge not captured by data, long horizon context, and reasoning grounded in the physical world. This gap has motivated growing efforts to design collaborative frameworks that combine the complementary strengths of humans and AI. This work advances this vision by identifying the fundamental principles of Human AI collaboration within uncertainty quantification, a key component of reliable decision making. We introduce Human AI Collaborative Uncertainty Quantification, a framework that formalizes how an AI model can refine a human expert's proposed prediction set with two goals: avoiding counterfactual harm, ensuring the AI does not degrade correct human judgments, and complementarity, enabling recovery of correct outcomes the human missed. At the population level, we show that the optimal collaborative prediction set follows an intuitive two threshold structure over a single score function, extending a classical result in conformal prediction. Building on this insight, we develop practical offline and online calibration algorithms with provable distribution free finite sample guarantees. The online method adapts to distribution shifts, including human behavior evolving through interaction with AI, a phenomenon we call Human to AI Adaptation. Experiments across image classification, regression, and text based medical decision making show that collaborative prediction sets consistently outperform either agent alone, achieving higher coverage and smaller set sizes across various conditions.

We present a probabilistic formulation of max-margin matrix factorization and build accordingly a nonparametric Bayesian model which automatically resolves the unknown number of latent factors. Our work demonstrates a successful example that integrates Bayesian nonparametrics and max-margin learning, which are conventionally two separate paradigms and enjoy complementary advantages. We develop an efcient variational algorithm for posterior inference, and our extensive empirical studies on large-scale MovieLens and EachMovie data sets appear to justify the aforementioned dual advantages.

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We present a novel approach to collaborative prediction, using low-norm instead of low-rank factorizations. The approach is inspired by, and has strong connections to, large-margin linear discrimination. We show how to learn low-norm factorizations by solving a semi-definite program, and discuss generalization error bounds for them.

We prove generalization error bounds for predicting entries in a partially observed matrix by fitting the observed entries with a low-rank matrix. In justifying the analysis approach we take to obtain the bounds, we present an example of a class of functions of finite pseudodimension such that the sums of functions from this class have unbounded pseudodimension.

We present a novel approach to collaborative prediction, using low-norm instead of low-rank factorizations. The approach is inspired by, and has strong connections to, large-margin linear discrimination. We show how to learn low-norm factorizations by solving a semi-definite program, and discuss generalization error bounds for them.

We prove generalization error bounds for predicting entries in a partially observed matrix by fitting the observed entries with a low-rank matrix. In justifying the analysis approach we take to obtain the bounds, we present an example of a class of functions of finite pseudodimension such that the sums of functions from this class have unbounded pseudodimension.

We prove generalization error bounds for predicting entries in a partially observed matrix by fitting the observed entries with a low-rank matrix. In justifying the analysis approach we take to obtain the bounds, we present an example of a class of functions of finite pseudodimension such that the sums of functions from this class have unbounded pseudodimension.

We present a novel approach to collaborative prediction, using low-norm instead of low-rank factorizations. The approach is inspired by, and has strong connections to, large-margin linear discrimination. We show how to learn low-norm factorizations by solving a semi-definite program, and discuss generalization error bounds for them.