The concept of a minimax classifier is well-established in statistical decision theory, but its implementation via neural networks remains challenging, particularly in scenarios with imbalanced training data having a limited number of samples for minority classes. To address this issue, we propose a novel minimax learning algorithm designed to minimize the risk of worst-performing classes. Our algorithm iterates through two steps: a minimization step that trains the model based on a selected target prior, and a maximization step that updates the target prior towards the adversarial prior for the trained model. In the minimization, we introduce a targeted logit-adjustment loss function that efficiently identifies optimal decision boundaries under the target prior. Moreover, based on a new prior-dependent generalization bound that we obtained, we theoretically prove that our loss function has a better generalization capability than existing loss functions. During the maximization, we refine the target prior by shifting it towards the adversarial prior, depending on the worst-performing classes rather than on per-class risk estimates. Our maximization method is particularly robust in the regime of a small number of samples. Additionally, to adapt to overparameterized neural networks, we partition the entire training dataset into two subsets: one for model training during the minimization step and the other for updating the target prior during the maximization step. Our proposed algorithm has a provable convergence property, and empirical results indicate that our algorithm performs better than or is comparable to existing methods. All codes are publicly available at https://github.com/hansung-choi/TLA-linear-ascent.

Vision-language models enable open-world classification of objects without the need for any retraining. While this zero-shot paradigm marks a significant advance, even today's best models exhibit skewed performance when objects are dissimilar from their typical depiction. Real world objects such as pears appear in a variety of forms -- from diced to whole, on a table or in a bowl -- yet standard VLM classifiers map all instances of a class to a \it{single vector based on the class label}. We argue that to represent this rich diversity within a class, zero-shot classification should move beyond a single vector. We propose a method to encode and account for diversity within a class using inferred attributes, still in the zero-shot setting without retraining. We find our method consistently outperforms standard zero-shot classification over a large suite of datasets encompassing hierarchies, diverse object states, and real-world geographic diversity, as well finer-grained datasets where intra-class diversity may be less prevalent. Importantly, our method is inherently interpretable, offering faithful explanations for each inference to facilitate model debugging and enhance transparency. We also find our method scales efficiently to a large number of attributes to account for diversity -- leading to more accurate predictions for atypical instances. Finally, we characterize a principled trade-off between overall and worst class accuracy, which can be tuned via a hyperparameter of our method. We hope this work spurs further research into the promise of zero-shot classification beyond a single class vector for capturing diversity in the world, and building transparent AI systems without compromising performance.

The work in ICML'09 showed that the derivatives of the classical multi-class logistic regression loss function could be re-written in terms of a pre-chosen "base class" and applied the new derivatives in the popular boosting framework. In order to make use of the new derivatives, one must have a strategy to identify/choose the base class at each boosting iteration. The idea of "adaptive base class boost" (ABC-Boost) in ICML'09, adopted a computationally expensive "exhaustive search" strategy for the base class at each iteration. It has been well demonstrated that ABC-Boost, when integrated with trees, can achieve substantial improvements in many multi-class classification tasks. Furthermore, the work in UAI'10 derived the explicit second-order tree split gain formula which typically improved the classification accuracy considerably, compared with using only the fist-order information for tree-splitting, for both multi-class and binary-class classification tasks. In this paper, we develop a unified framework for effectively selecting the base class by introducing a series of ideas to improve the computational efficiency of ABC-Boost. Our framework has parameters $(s,g,w)$. At each boosting iteration, we only search for the "$s$-worst classes" (instead of all classes) to determine the base class. We also allow a "gap" $g$ when conducting the search. That is, we only search for the base class at every $g+1$ iterations. We furthermore allow a "warm up" stage by only starting the search after $w$ boosting iterations. The parameters $s$, $g$, $w$, can be viewed as tunable parameters and certain combinations of $(s,g,w)$ may even lead to better test accuracy than the "exhaustive search" strategy. Overall, our proposed framework provides a robust and reliable scheme for implementing ABC-Boost in practice.