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This paper presents an overview and comparative study of the state of the art in State-Order Reduction (SOR) and Scheduling Dimension Reduction (SDR) for Linear Parameter-Varying (LPV) State-Space (SS) models, comparing and benchmarking…
Self-supervised learning (SSL), especially contrastive methods, has raised attraction recently as it learns effective transferable representations without semantic annotations. A common practice for self-supervised pre-training is to use as…
Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g.,…
This manuscript is superseded by Constantine, Dow, and Wang's "Active Subspaces in Theory and Practice: Applications to Kriging Surfaces" [SIAM J. of Sci. Comput., 36 (2014), pp. A1500-A1524]. Many multivariate functions encountered in…
We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated…
Weakly-supervised semantic segmentation (WSS) ensures high-quality segmentation with limited data and excels when employed as input seed masks for large-scale vision models such as Segment Anything. However, WSS faces challenges related to…
Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…
We study the problem of robust estimation of the mean vector of a sub-Gaussian distribution. We introduce an estimator based on spectral dimension reduction (SDR) and establish a finite sample upper bound on its error that is…
Among existing Neural Architecture Search methods, DARTS is known for its efficiency and simplicity. This approach applies continuous relaxation of network representation to construct a weight-sharing supernet and enables the identification…
A space-time adaptive decision feedback (DF) receiver using recurrent neural networks (RNN) is proposed for joint equalization and interference suppression in direct-sequence code-division-multiple-access (DS-CDMA) systems equipped with…
This paper investigates a new approach to estimate the gradient of the conditional probability given the covariates in the binary classification framework. The proposed approach consists in fitting a localized nearest-neighbor logistic…
In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate, which can provide sharp estimates for the error reduction per iteration. We also study the…
This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…
Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li…
Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
Mapping is crucial in robotics for localization and downstream decision-making. As robots are deployed in ever-broader settings, the maps they rely on continue to increase in size. However, storing these maps indefinitely (cold storage),…
Robust subspace recovery (RSR) is a fundamental problem in robust representation learning. Here we focus on a recently proposed RSR method termed Dual Principal Component Pursuit (DPCP) approach, which aims to recover a basis of the…
In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image…