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Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) have a wide range of applications and have attracted a tremendous amount of attention in the last two decades as canonical examples of statistical problems in…
In the new perspective of spatial quantization, this article systematically studies the advantages of reconfigurable reflectarray (RRA) designed with closely spaced elements in terms of sidelobe level (SLL), scanning accuracy and scan loss,…
How to improve discriminative feature learning is central in classification. Existing works address this problem by explicitly increasing inter-class separability and intra-class similarity, whether by constructing positive and negative…
We present the first provable method for identifying symmetric linear dynamical systems (LDS) with accuracy guarantees that are independent of the systems' state dimension or effective memory. Our approach builds upon recent work that…
The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…
Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by…
Source-Free Domain Adaptation (SFDA) aims to solve the domain adaptation problem by transferring the knowledge learned from a pre-trained source model to an unseen target domain. Most existing methods assign pseudo-labels to the target data…
We revisit Deep Linear Discriminant Analysis (Deep LDA) from a likelihood-based perspective. While classical LDA is a simple Gaussian model with linear decision boundaries, attaching an LDA head to a neural encoder raises the question of…
Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…
This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable…
The Minimum Covariance Determinant (MCD) approach robustly estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension…
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is…
We consider the problem of finding tuned regularized parameter estimators for linear models. We start by showing that three known optimal linear estimators belong to a wider class of estimators that can be formulated as a solution to a…
We present the first algorithm to efficiently compute certifiably optimal solutions to range-aided simultaneous localization and mapping (RA-SLAM) problems. Robotic navigation systems increasingly incorporate point-to-point ranging sensors,…
This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
Simultaneous Localization and Mapping (SLAM) using 3D LiDAR has emerged as a cornerstone for autonomous navigation in robotics. While feature-based SLAM systems have achieved impressive results by leveraging edge and planar structures, they…
We introduce Reward-Guided Speculative Decoding (RSD), a novel framework aimed at improving the efficiency of inference in large language models (LLMs). RSD synergistically combines a lightweight draft model with a more powerful target…
Classical linear discriminant analysis (LDA) is based on squared Frobenious norm and hence is sensitive to outliers and noise. To improve the robustness of LDA, in this paper, we introduce capped l_{2,1}-norm of a matrix, which employs…
In recent years many sparse linear discriminant analysis methods have been proposed for high-dimensional classification and variable selection. However, most of these proposals focus on binary classification and they are not directly…