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Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…
Under the reproducing kernel Hilbert spaces (RKHS), we consider the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate…
Representation learning plays a crucial role in automated feature selection, particularly in the context of high-dimensional data, where non-parametric methods often struggle. In this study, we focus on supervised learning scenarios where…
Activation functions in neural networks are typically selected from a set of empirically validated, commonly used static functions such as ReLU, tanh, or sigmoid. However, by optimizing the shapes of a network's activation functions, we can…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
We present a functional renormalization group (fRG) formalism for interacting fermions on lattices that captures the flow into states with commensurate spin-density wave order. During the flow, the growth of the order parameter is fed back…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
In this paper, we study the functional linear multiplicative model based on the least product relative error criterion. Under some regularization conditions, we establish the consistency and asymptotic normality of the estimator. Further,…
Factorization Machines (FMs) are a supervised learning approach that enhances the linear regression model by incorporating the second-order feature interactions. Despite effectiveness, FM can be hindered by its modelling of all feature…
Identifying the optimal diagnostic test and hardware system instance to infer reliability characteristics using field data is challenging, especially when constrained by fixed budgets and minimal maintenance cycles. Active Learning (AL) has…
Motivation: Alignment-free (AF) distance/similarity functions are a key tool for sequence analysis. Experimental studies on real datasets abound and, to some extent, there are also studies regarding their control of false positive rate…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
Statistical inferences for quadratic functionals of linear regression parameter have found wide applications including signal detection, global testing, inferences of error variance and fraction of variance explained. Classical theory based…
The Functional Linear Model with Functional Response (FLMFR) is one of the most fundamental models to assess the relation between two functional random variables. In this paper, we propose a novel goodness-of-fit test for the FLMFR against…
We analyze a simple one-hidden-layer neural network with ReLU activation functions and fixed biases, with one-dimensional input and output. We study both continuous and discrete versions of the model, and we rigorously prove the convergence…
Random Feature Models (RFMs) have become a powerful tool for approximating multivariate functions and solving partial differential equations efficiently. Sparse Random Feature Expansions (SRFE) improve traditional RFMs by incorporating…
We consider the problem of designing experiments for the estimation of a target in regression analysis if there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed, which minimizes the…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
We propose reproducing activation functions (RAFs) to improve deep learning accuracy for various applications ranging from computer vision to scientific computing. The idea is to employ several basic functions and their learnable linear…
Magnetic Resonance Fingerprinting (MRF) leverages transient-state signal dynamics generated by the tunable acquisition parameters, making the design of an optimal, robust sequence a complex, high-dimensional sequential decision problem,…