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We introduce a single-frame diffractive imaging method called randomized probe imaging (RPI). In RPI, a sample is illuminated by a structured probe field containing speckles smaller than the sample's typical feature size. Quantitative…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
Large-scale numerical computations make increasing use of low-precision (LP) floating point formats and mixed precision arithmetic, which can be enhanced by the technique of stochastic rounding (SR), that is, rounding an intermediate…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
Ridge functions have recently emerged as a powerful set of ideas for subspace-based dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces, contrasting…
We propose a solution to the problem of estimating a Riemannian metric associated with a given differentiable manifold. The metric learning problem is based on minimizing the relative volume of a given set of points. We derive the details…
Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…
Alternative expressions for calculating the oblate spheroidal radial functions of both kinds R1ml and R2ml are shown to provide accurate values over very large parameter ranges using 64 bit arithmetic, even where the traditional expressions…
The objective of this paper is to design an embedding method that maps local features describing an image (e.g. SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship…
Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still…
Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…
In recent years, a deep learning framework has been widely used for object pose estimation. While quaternion is a common choice for rotation representation of 6D pose, it cannot represent an uncertainty of the observation. In order to…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…
Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…
Functional magnetic resonance imaging (fMRI) is a powerful tool for investigating human brain function. However, the high cost of data acquisition and the inherent subjectivity of psychiatric rating scales often lead to datasets with small…
The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out…
We introduce a method for computing some pseudo-elliptic integrals in terms of elementary functions. The method is simple and fast in comparison to the algebraic case of the Risch-Trager-Bronstein algorithm. This method can quickly solve…
The massive amounts of data generated by camera sensors motivate data processing inside pixel arrays, i.e., at the extreme-edge. Several critical developments have fueled recent interest in the processing-in-pixel-in-memory paradigm for a…
During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the computer science community. The cornerstone of the framework is the notion of…