A Generalized Argmax Theorem with Applications
The argmax theorem is a useful result for deriving the limiting distribution of estimators in many applications. The conclusion of the argmax theorem states that the argmax of a sequence of stochastic processes converges in distribution to the argmax of a limiting stochastic process. This paper generalizes the argmax theorem to allow the maximization to take place over a sequence of subsets of the domain. If the sequence of subsets converges to a limiting subset, then the conclusion of the argmax theorem continues to hold. We demonstrate the usefulness of this generalization in three applications: estimating a structural break, estimating a parameter on the boundary of the parameter space, and estimating a weakly identified parameter. The generalized argmax theorem simplifies the proofs for existing results and can be used to prove new results in these literatures.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
argmax centroid
We propose a general method to construct centroid approximation for the distribution of maximum points of a random function (a.k.a. argmax distribution), which finds broad applications in machine learning. Our method opt…
Domain AdaptationFew-Shot Image Classificationimage-classificationImage Classification+2Learning Energy Networks with Generalized Fenchel-Young Losses
Energy-based models, a.k.a. energy networks, perform inference by optimizing an energy function, typically parametrized by a neural network. This allows one to capture potentially complex relationships between inputs and…
Imitation LearningGPG: Generalized Policy Gradient Theorem for Transformer-based Policies
We present the Generalized Policy Gradient (GPG) Theorem, specifically designed for Transformer-based policies. Notably, we demonstrate that both standard Policy Gradient Theorem and GRPO emerge as special cases within o…
Continuity of the Distribution Function of the argmax of a Gaussian Process
An increasingly important class of estimators has members whose asymptotic distribution is non-Gaussian, yet characterizable as the argmax of a Gaussian process. This paper presents high-level sufficient conditions under…
Heatmap Regression without Soft-Argmax for Facial Landmark Detection
Facial landmark detection is an important task in computer vision with numerous applications, such as head pose estimation, expression analysis, face swapping, etc. Heatmap regression-based methods have been widely used …
Facial Landmark DetectionStructured PredictionHead Pose EstimationFace Swapping