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The Column Subset Selection Problem provides a natural framework for unsupervised feature selection. Despite being a hard combinatorial optimization problem, there exist efficient algorithms that provide good approximations. The drawback of…
Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit…
How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the…
In the past few years, large-scale pre-trained vision-language models like CLIP have achieved tremendous success in various fields. Naturally, how to transfer the rich knowledge in such huge pre-trained models to downstream tasks and…
This paper studies linear overparameterized models in economic forecasting and highlights that including noise variables (regressors with no predictive power) regularizes the estimator. We consider a setting where both the outcome variable…
The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…
Unsupervised neural networks, such as restricted Boltzmann machines (RBMs) and deep belief networks (DBNs), are powerful tools for feature selection and pattern recognition tasks. We demonstrate that overfitting occurs in such models just…
3D shape matching is a long-standing problem in computer vision and computer graphics. While deep neural networks were shown to lead to state-of-the-art results in shape matching, existing learning-based approaches are limited in the…
To generalize the model trained in source domains to unseen target domains, domain generalization (DG) has recently attracted lots of attention. Since target domains can not be involved in training, overfitting source domains is inevitable.…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
In real-world applications, commercial off-the-shelf systems are utilized for performing automated facial analysis including face recognition, emotion recognition, and attribute prediction. However, a majority of these commercial systems…
How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…
This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…
While much progress has been made in capturing high-quality facial performances using motion capture markers and shape-from-shading, high-end systems typically also rely on rotoscope curves hand-drawn on the image. These curves are…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
Reward models trained on human preference data have been proven to effectively align Large Language Models (LLMs) with human intent within the framework of reinforcement learning from human feedback (RLHF). However, current reward models…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
Assisted by the availability of data and high performance computing, deep learning techniques have achieved breakthroughs and surpassed human performance empirically in difficult tasks, including object recognition, speech recognition, and…