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Transformers have improved the state-of-the-art across numerous tasks in sequence modeling. Besides the quadratic computational and memory complexity w.r.t the sequence length, the self-attention mechanism only processes information at the…

Linear discriminant analysis (LDA) is a fundamental method for feature extraction and dimensionality reduction. Despite having many variants, classical LDA has its own importance, as it is a keystone in human knowledge about statistical…

Spatial resolution in optical microscopy has traditionally been treated as a fixed parameter of the optical system. Here, we present an approach to enhance transverse resolution in beam-scanned optical coherence tomography (OCT) beyond its…

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright…

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of…

Multi-view learning (MVL) is a strategy for fusing data from different sources or subsets. Canonical correlation analysis (CCA) is very important in MVL, whose main idea is to map data from different views onto a common space with maximum…

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever…

Canonical correlation analysis is a statistical technique that is used to find relations between two sets of variables. An important extension in pattern analysis is to consider more than two sets of variables. This problem can be expressed…

Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling methodology for fusion and inference from multiple and massive…

We study the problem of estimating the frequencies of several complex sinusoids with constant amplitude (CA) (also called constant modulus) from multichannel signals of their superposition. To exploit the CA property for frequency…

LINC-NIRVANA (LN) is a high resolution, near infrared imager that uses a multiple field-of-view, layer-oriented, multi-conjugate AO system, consisting of four multi-pyramid wavefront sensors (two for each arm of the Large Binocular…

Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area…

We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…

We investigate the identifiability of nonlinear Canonical Correlation Analysis (CCA) in a multi-view setup, where each view is generated by an unknown nonlinear map applied to a linear mixture of shared latents and view-private noise.…

We propose Deep Multiset Canonical Correlation Analysis (dMCCA) as an extension to representation learning using CCA when the underlying signal is observed across multiple (more than two) modalities. We use deep learning framework to learn…

To do dimensionality reduction on the datasets with outliers, the $\ell_1$-norm principal component analysis (L1-PCA) as a typical robust alternative of the conventional PCA has enjoyed great popularity over the past years. In this work, we…

The ubiquitous presence of shot noise sets a fundamental limit to the measurement precision in classical metrology. Recent advances in quantum devices and novel quantum algorithms utilizing interference effects are opening new routes for…

Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical…

Transformers have revolutionized Computer Vision (CV) through self-attention mechanisms. However, their complexity makes latent token representations difficult to interpret. We introduce ULTra, a framework for interpreting Transformer…

The significance of the broken ray transform (BRT) is due to its occurrence in a number of modalities spanning optical, x-ray, and nuclear imaging. When data are indexed by the scatter location, the BRT is both linear and shift invariant.…