Related papers: Multivariate Functional Regression via Nested Redu…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
Heterogeneous data are now ubiquitous in many applications in which correctly identifying the subgroups from a heterogeneous population is critical. Although there is an increasing body of literature on subgroup detection, existing methods…
Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these…
Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…
Recurrent Neural Networks (RNNs) are frequently used to model aspects of brain function and structure. In this work, we trained small fully-connected RNNs to perform temporal and flow control tasks with time-varying stimuli. Our results…
How to better utilize sequential information has been extensively studied in the setting of recommender systems. To this end, architectural inductive biases such as Markov-Chains, Recurrent models, Convolutional networks and many others…
Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data…
For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data.…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
This paper proposes a partition-based functional ridge regression framework to address multicollinearity, overfitting, and interpretability in high-dimensional functional linear models. The coefficient function vector \(…
Multivariate random effects with unstructured variance-covariance matrices of large dimensions, $q$, can be a major challenge to estimate. In this paper, we introduce a new implementation of a reduced-rank approach to fit large dimensional…
The normalized radial basis function neural network emerges in the statistical modeling of natural laws that relate components of multivariate data. The modeling is based on the kernel estimator of the joint probability density function…
The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important areas such as control, recommender systems, matrix completion…
Low-rank adaptation (LoRA) approximates the update of a pretrained weight matrix using the product of two low-rank matrices. However, standard LoRA follows an explicit-rank paradigm, where increasing model capacity requires adding more rows…
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…
Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on…
Recurrent neural networks (RNNs), including long short-term memory (LSTM) RNNs, have produced state-of-the-art results on a variety of speech recognition tasks. However, these models are often too large in size for deployment on mobile…
The low-rank tensor approximation is very promising for the compression of deep neural networks. We propose a new simple and efficient iterative approach, which alternates low-rank factorization with a smart rank selection and fine-tuning.…
We study the low rank regression problem $\my = M\mx + \epsilon$, where $\mx$ and $\my$ are $d_1$ and $d_2$ dimensional vectors respectively. We consider the extreme high-dimensional setting where the number of observations $n$ is less than…
Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…