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We derive the asymptotic risk function of regularized empirical risk minimization (ERM) estimators tuned by $n$-fold cross-validation (CV). The out-of-sample prediction loss of such estimators converges in distribution to the squared-error…

We proved that a trained model in supervised deep learning minimizes the conditional risk for each input (Theorem 2.1). This property provided insights into the behavior of trained models and established a connection between supervised and…

The reasoning-based pose estimation (RPE) benchmark has emerged as a widely adopted evaluation standard for pose-aware multimodal large language models (MLLMs). Despite its significance, we identified critical reproducibility and…

Multiple instance (MI) learning with a convolutional neural network enables end-to-end training in the presence of weak image-level labels. We propose a new method for aggregating predictions from smaller regions of the image into an…

Multiple instance learning (MIL) is a variation of traditional supervised learning problems where data (referred to as bags) are composed of sub-elements (referred to as instances) and only bag labels are available. MIL has a variety of…

Auto-regressive sequence generative models trained by Maximum Likelihood Estimation suffer the exposure bias problem in practical finite sample scenarios. The crux is that the number of training samples for Maximum Likelihood Estimation is…

Collecting labeled data for machine learning models is often expensive and time-consuming. Active learning addresses this challenge by selectively labeling the most informative observations, but when initial labeled data is limited, it…

Noise transition matrix (NTM) estimation is a promising approach for learning with label noise. It can infer clean posterior probabilities, known as Label Distribution (LD), based on noisy ones and reduce the impact of noisy labels.…

The generalization ability of minimizers of the empirical risk in the context of binary classification has been investigated under a wide variety of complexity assumptions for the collection of classifiers over which optimization is…

Learning from positive and unlabeled data (PU learning) is a weakly supervised variant of binary classification in which the learner receives labels only for (some) positively labeled instances, while all other examples remain unlabeled.…

We point out a limitation of the mutual information neural estimation (MINE) where the network fails to learn at the initial training phase, leading to slow convergence in the number of training iterations. To solve this problem, we propose…

Positive-Unlabeled (PU) learning aims to train a binary classifier (positive vs. negative) where only limited positive data and abundant unlabeled data are available. While widely applicable, state-of-the-art PU learning methods…

Recalibrating probabilistic classifiers is vital for enhancing the reliability and accuracy of predictive models. Despite the development of numerous recalibration algorithms, there is still a lack of a comprehensive theory that integrates…

Instruction tuning -- supervised fine-tuning using instruction-response pairs -- is a key step in making pre-trained large language models (LLMs) instructable. Meanwhile, LLMs perform multitask learning during their pre-training, acquiring…

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…

A meta-model is trained on a distribution of similar tasks such that it learns an algorithm that can quickly adapt to a novel task with only a handful of labeled examples. Most of current meta-learning methods assume that the meta-training…

Partial Label Learning (PLL) is a typical weakly supervised learning task, which assumes each training instance is annotated with a set of candidate labels containing the ground-truth label. Recent PLL methods adopt identification-based…

This paper develops robust test procedures for testing the intercept of a simple regression model when it is \textit{apriori} suspected that the slope has a specified value. Defining unrestricted test (UT), restricted test (RT) and pre-test…

The next-token prediction (NTP) objective trains language models to predict a single token at each step, even though many continuations can express the same meaning. For example, in the sentence ``this sticker can be placed here'',…

The emerging neural topic models make topic modeling more easily adaptable and extendable in unsupervised text mining. However, the existing neural topic models is difficult to retain representative information of the documents within the…