Related papers: A ROAD to Classification in High Dimensional Space
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
The global optimization of classification trees has demonstrated considerable promise, notably in enhancing accuracy, optimizing size, and thereby improving human comprehensibility. While existing optimal classification trees substantially…
Closed-loop optimal control design for high-dimensional nonlinear systems has been a long-standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi-Bellman equation, suffer from the curse of dimensionality.…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
An approach to the classification problem of machine learning, based on building local classification rules, is developed. The local rules are considered as projections of the global classification rules to the event we want to classify. A…
Modern high-dimensional methods often adopt the "bet on sparsity" principle, while in supervised multivariate learning statisticians may face "dense" problems with a large number of nonzero coefficients. This paper proposes a novel…
In this paper, we leverage existing statistical methods to better understand feature learning from data. We tackle this by modifying the model-free variable selection method, Feature Ordering by Conditional Independence (FOCI), which is…
Diffractive deep neural networks have been introduced earlier as an optical machine learning framework that uses task-specific diffractive surfaces designed by deep learning to all-optically perform inference, achieving promising…
While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired…
Clinical research often focuses on complex traits in which many variables play a role in mechanisms driving, or curing, diseases. Clinical prediction is hard when data is high-dimensional, but additional information, like domain knowledge…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
Autonomous vehicles must often contend with conflicting planning requirements, e.g., safety and comfort could be at odds with each other if avoiding a collision calls for slamming the brakes. To resolve such conflicts, assigning importance…
Fair classification is a critical challenge that has gained increasing importance due to international regulations and its growing use in high-stakes decision-making settings. Existing methods often rely on adversarial learning or…
Unsupervised image clustering methods often introduce alternative objectives to indirectly train the model and are subject to faulty predictions and overconfident results. To overcome these challenges, the current research proposes an…
The success of Deep Neural Network (DNN) models significantly depends on the quality of provided annotations. In medical image segmentation, for example, having multiple expert annotations for each data point is common to minimize…
We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…
Conformal inference provides a rigorous statistical framework for uncertainty quantification in machine learning, enabling well-calibrated prediction sets with precise coverage guarantees for any classification model. However, its reliance…
Linear Discriminant Analysis (LDA) is a fundamental method for classification. Its simple linear structure facilitates interpretation, and it is naturally suited to multi-class settings. LDA is also closely connected to several classical…
A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component.…