Mehryar Mohri
Mehryar Mohri leads the Learning Theory Team in Google Research. The team has extensive expertise in a variety of areas, including learning theory, statistical learning theory, optimization, decision making under uncertainty, reinforcement learning, and theory and algorithms in general.
Authored Publications
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Balancing the Scales: A Theoretical and Algorithmic Framework for Learning from Imbalanced Data
Anqi Mao
Proceedings of the 42nd International Conference on Machine Learning (ICML 2025)
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Class imbalance remains a major challenge in machine learning, especially in multi-class problems with long-tailed distributions. Existing methods, such as data resampling, cost-sensitive techniques, and logistic loss modifications, though popular and often effective, lack solid theoretical foundations. As an example, we demonstrate that cost-sensitive methods are not Bayes-consistent. This paper introduces a novel theoretical framework for analyzing generalization in imbalanced classification. We propose a new class-imbalanced margin loss function for both binary and multi-class settings, prove its strong $H$-consistency, and derive corresponding learning guarantees based on empirical loss and a new notion of class-sensitive Rademacher complexity. Leveraging these theoretical results, we devise novel and general learning algorithms, IMMAX (*Imbalanced Margin Maximization*), which incorporate confidence margins and are applicable to various hypothesis sets. While our focus is theoretical, we also present extensive empirical results demonstrating the effectiveness of our algorithms compared to existing baselines.
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Improved Balanced Classification with Theoretically Grounded Loss Functions
The Thirty-Ninth Annual Conference on Neural Information Processing Systems (NeurIPS 2025)
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The *balanced loss* is a widely adopted objective for multi-class classification under class imbalance. By assigning equal importance to all classes, regardless of their frequency, it promotes fairness and ensures that minority classes are not overlooked. However, directly minimizing the balanced classification loss is typically intractable, which makes the design of effective surrogate losses a central question. This paper introduces and studies two advanced surrogate loss families: Generalized Logit-Adjusted (GLA) loss functions and Generalized Class-Aware weighted (GCA) losses. GLA losses generalize Logit-Adjusted losses, which shift logits based on class priors, to the broader general cross-entropy loss family. GCA loss functions extend the standard class-weighted losses, which scale losses inversely by class frequency, by incorporating class-dependent confidence margins and extending them to the general cross-entropy family. We present a comprehensive theoretical analysis of consistency for both loss families. We show that GLA losses are Bayes-consistent, but only $H$-consistent for unbounded and complete hypothesis sets. Moreover, their $H$-consistency bounds depend inversely on the minimum class probability, scaling at least as $1/\mathsf p _{\min}$. In contrast, GCA losses are $H$-consistent for any hypothesis set that is bounded or complete, with $H$-consistency bounds that scale more favorably as $1/\sqrt{\mathsf p _{\min}}$, offering significantly stronger theoretical guarantees in imbalanced settings. We report the results of experiments demonstrating that, empirically, both the GCA losses with calibrated class-dependent confidence margins and GLA losses can greatly outperform straightforward class-weighted losses as well as the LA losses. GLA generally performs slightly better in common benchmarks, whereas GCA exhibits a slight edge in highly imbalanced settings. Thus, we advocate for both GLA and GCA losses as principled, theoretically sound, and state-of-the-art surrogates for balanced classification under class imbalance.
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Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defer
Anqi Mao
Proceedings of the 42nd International Conference on Machine Learning (ICML 2025)
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The problem of learning to defer with multiple experts consists of optimally assigning input instances to experts, balancing the trade-off between their accuracy and computational cost. This is a critical challenge in natural language generation, but also in other fields such as image processing, and medical diagnostics. Recent studies have proposed surrogate loss functions to optimize deferral, but challenges remain in ensuring their consistency properties. This paper introduces novel surrogate loss functions and efficient algorithms with strong theoretical learning guarantees. We address open questions regarding realizable $H$-consistency, $H$-consistency bounds, and Bayes-consistency for both single-stage (jointly learning predictor and deferral function) and two-stage (learning only the deferral function with a fixed expert) learning scenarios. For single-stage deferral, we introduce a family of new realizable $H$-consistent surrogate losses and further prove $H$-consistency for a selected member. For two-stage deferral, we derive new surrogate losses that achieve realizable $H$-consistency, $H$-consistency bounds, and Bayes-consistency for the two-expert scenario and, under natural assumptions, multiple-expert scenario. Additionally, we provide enhanced theoretical guarantees under low-noise assumptions for both scenarios. Finally, we report the results of experiments using our proposed surrogate losses, comparing their performance against existing baselines.
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Principled Algorithms for Optimizing Generalized Metrics in Binary Classification
Anqi Mao
Proceedings of the 42nd International Conference on Machine Learning (ICML 2025)
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In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary classification loss. However, optimizing these metrics present significant computational and statistical challenges. Existing approaches often rely on the characterization of the Bayes-optimal classifier, and use threshold-based methods that first estimate class probabilities and then seek an optimal threshold. This leads to algorithms that are not tailored to restricted hypothesis sets and lack finite-sample performance guarantees. In this work, we introduce principled algorithms for optimizing generalized metrics, supported by $H$-consistency and finite-sample generalization bounds. Our approach reformulates metric optimization as a generalized cost-sensitive learning problem, enabling the design of novel surrogate loss functions with provable $H$-consistency guarantees. Leveraging this framework, we develop new algorithms, METRO (*Metric Optimization*), with strong theoretical performance guarantees. We report the results of experiments demonstrating the effectiveness of our methods compared to prior baselines.
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We present new efficient algorithms for high-dimensional calibration via reduction to the TreeSwap algorithm of Dagan et al.
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We present new efficient algorithms for high-dimensional calibration via reduction to the TreeSwap algorithm of Dagan et al.
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Enhanced $H$-Consistency Bounds
Anqi Mao
Proceedings of the 36th International Conference on Algorithmic Learning Theory (ALT 2025)
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Recent research has introduced a key notion of $H$-consistency bounds for surrogate losses. These bounds offer finite-sample guarantees, quantifying the relationship between the zero-one estimation error (or other target loss) and the surrogate loss estimation error for a specific hypothesis set. However, previous bounds were derived under the condition that a lower bound of the surrogate loss conditional regret is given as a convex function of the target conditional regret, without non-constant factors depending on the predictor or input instance. Can we derive finer and more favorable $H$-consistency bounds? In this work, we relax this condition and present a general framework for establishing *enhanced $H$-consistency bounds* based on more general inequalities relating conditional regrets. Our theorems not only subsume existing results as special cases but also enable the derivation of more favorable bounds in various scenarios. These include standard multi-class classification, binary and multi-class classification under Tsybakov noise conditions, and bipartite ranking.
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Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention
Anqi Mao
The Thirty-Seventh International Conference on Artificial Intelligence and Statistics (AISTATS 2024)
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Learning with abstention is a key scenario where the learner can abstain from making a prediction at some cost. In this paper, we analyze the score-based formulation of learning with abstention in the multi-class classification setting. We introduce new families of surrogate losses for the abstention loss function, which include the state-of-the-art surrogate losses in the single-stage setting and a novel family of loss functions in the two-stage setting. We prove strong non-asymptotic and hypothesis set-specific consistency guarantees for these surrogate losses, which upper-bound the estimation error of the abstention loss function in terms of the estimation error of the surrogate loss. Our bounds can help compare different score-based surrogates and guide the design of novel abstention algorithms by minimizing the proposed surrogate losses. We experimentally evaluate our new algorithms on CIFAR-10, CIFAR-100, and SVHN datasets and the practical significance of our new surrogate losses and two-stage abstention algorithms. Our results also show that the relative performance of the state-of-the-art score-based surrogate losses can vary across datasets.
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Multi-Label Learning with Stronger Consistency Guarantees
Anqi Mao
The Thirty-Eighth Annual Conference on Neural Information Processing Systems (NeurIPS 2024)
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We present a detailed study of surrogate losses and algorithms for multi-label learning, supported by $H$-consistency bounds. We first show that, for the simplest form of multi-label loss (the popular Hamming loss), the well-known consistent binary relevance surrogate suffers from a sub-optimal dependency on the number of labels in terms of $H$-consistency bounds, when using smooth losses such as logistic losses. Furthermore, this loss function fails to account for label correlations. To address these drawbacks, we introduce a novel surrogate loss, *multi-label logistic loss*, that accounts for label correlations and benefits from label-independent $H$-consistency bounds. We then broaden our analysis to cover a more extensive family of multi-label losses, including all common ones and a new extension defined based on linear-fractional functions with respect to the confusion matrix. We also extend our multi-label logistic losses to more comprehensive multi-label comp-sum losses, adapting comp-sum losses from standard classification to the multi-label learning. We prove that this family of surrogate losses benefits from $H$-consistency bounds, and thus Bayes-consistency, across any general multi-label loss. Our work thus proposes a unified surrogate loss framework benefiting from strong consistency guarantees for any multi-label loss, significantly expanding upon previous work which only established Bayes-consistency and for specific loss functions. Additionally, we adapt constrained losses from standard classification to multi-label constrained losses in a similar way, which also benefit from $H$-consistency bounds and thus Bayes-consistency for any multi-label loss. We further describe efficient gradient computation algorithms for minimizing the multi-label logistic loss.
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Regression with Multi-Expert Deferral
Anqi Mao
Proceedings of the 41st International Conference on Machine Learning (ICML 2024)
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Learning to defer with multiple experts is a framework where the learner can choose to defer the prediction to several experts. While this problem has received significant attention in classification contexts, it presents unique challenges in regression due to the infinite and continuous nature of the label space. In this work, we introduce a novel framework of *regression with deferral*, which involves deferring the prediction to multiple experts. We present a comprehensive analysis for both the single-stage scenario, where there is simultaneous learning of predictor and deferral functions, and the two-stage scenario, which involves a pre-trained predictor with a learned deferral function. We introduce new surrogate loss functions for both scenarios and prove that they are supported by $H$-consistency bounds. These bounds provide consistency guarantees that are stronger than Bayes consistency, as they are non-asymptotic and hypothesis set-specific. Our framework is versatile, applying to multiple experts, accommodating any bounded regression losses, addressing both instance-dependent and label-dependent costs, and supporting both single-stage and two-stage methods. Our single-stage formulation subsumes as a special case the recent *regression with abstention* (Cheng et al., 2023) framework, where only a single expert is considered, specifically for the squared loss and a label-independent cost. Minimizing our proposed loss functions directly leads to novel algorithms for regression with deferral. We report the results of extensive experiments showing the effectiveness of our proposed algorithms.
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