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Imbalanced classification presents a formidable challenge in machine learning, particularly when tabular datasets are plagued by noise and overlapping class boundaries. From a geometric perspective, the core difficulty lies in the…
Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means…
Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…
Most neural network pruning methods, such as filter-level and layer-level prunings, prune the network model along one dimension (depth, width, or resolution) solely to meet a computational budget. However, such a pruning policy often leads…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Reduced rank regression (RRR) is a statistical method for finding a low-dimensional linear mapping between a set of high-dimensional inputs and outputs. In recent years, RRR has found numerous applications in neuroscience, in particular for…
Monocular depth estimation, which plays a key role in understanding 3D scene geometry, is fundamentally an ill-posed problem. Existing methods based on deep convolutional neural networks (DCNNs) have examined this problem by learning…
In this paper, we provide a computable characterization of the geometry of optimal representations in Contrastive Learning (CL) when the classes are imbalanced. When classes are balanced and the representation dimension is greater than the…
Neural multivariate regression underpins a wide range of domains, including control, robotics, and finance, yet the geometry of its learned representations remains poorly characterized. While neural collapse has been shown to benefit…
We propose meta-curvature (MC), a framework to learn curvature information for better generalization and fast model adaptation. MC expands on the model-agnostic meta-learner (MAML) by learning to transform the gradients in the inner…
We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM algorithm, or similar techniques, without provable…
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…
Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well…
This article focuses on solving parametric transmission problems in one and two spatial dimensions. These problems belong to a class of partial differential equations that arise in the modeling of physical systems with heterogeneous…
Among different existing graph self-supervised learning strategies, graph contrastive learning (GCL) has been one of the most prevalent approaches to this problem. Despite the remarkable performance those GCL methods have achieved, existing…
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…
Convolutional neural networks (CNNs) are among the most widely used machine learning models for computer vision tasks, such as image classification. To improve the efficiency of CNNs, many CNNs compressing approaches have been developed.…