Related papers: Multivariate Rational Approximation via Low-Rank T…
Optimal resource allocation (RA) in massive carrier aggregation scenarios is a challenging combinatorial optimization problem whose dimension is proportional to the number of users, component carriers (CCs), and OFDMA resource blocks per…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
Low-Rank Adaptation (LoRA) has become a widely adopted parameter-efficient fine-tuning method for large language models, with its effectiveness largely influenced by the allocation of ranks and scaling factors, as well as initialization.…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…
We call matrix algorithms superfast if they use much fewer flops and memory cells than the input matrix has entries. Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one…
We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process…
We study the approximation of the value function of deterministic optimal control problems with fixed initial state, motivated by \(N\)-body systems. In this setting, the action functional consists of local kinetic and potential terms,…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
In this paper, we present a rigorous framework for rational minimax approximation of matrix-valued functions that generalizes classical scalar approximation theory. Given sampled data $\{(x_\ell, {F}(x_\ell))\}_{\ell=1}^m$ where…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…
A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarchy of triangulations and piecewise polynomial approximations…
We propose Quantum-informed Tensor Adaptation (QuanTA), a novel, easy-to-implement, fine-tuning method with no inference overhead for large-scale pre-trained language models. By leveraging quantum-inspired methods derived from quantum…
Long-form speech recognition is an application area of increasing research focus. ASR models based on multi-head attention (MHA) are ill-suited to long-form ASR because of their quadratic complexity in sequence length. We build on recent…
This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
The Pandora's Box problem and its extensions capture optimization problems with stochastic input where the algorithm can obtain instantiations of input random variables at some cost. To our knowledge, all previous work on this class of…
Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data analysis, has been successfully used in several applications, such as in collaborative filtering to design recommender systems or in computer vision to…