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The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM…
Functional data such as curves and surfaces have become more and more common with modern technological advancements. The use of functional predictors remains challenging due to its inherent infinite-dimensionality. The common practice is to…
Functional quadratic regression models postulate a polynomial relationship between a scalar response rather than a linear one. As in functional linear regression, vertical and specially high-leverage outliers may affect the classical…
This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and…
Feature engineering, a crucial step of machine learning, aims to extract useful features from raw data to improve data quality. In recent years, great efforts have been devoted to Automated Feature Engineering (AutoFE) to replace expensive…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
We propose a function-on-function linear regression model for time-dependent curve data that is consistently estimated by imposing factor structures on the regressors. An integral operator based on cross-covariances identifies two…
Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…
Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…
Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly…
In federated learning (FL), accommodating clients' varied computational capacities poses a challenge, often limiting the participation of those with constrained resources in global model training. To address this issue, the concept of model…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…
Lensless cameras based on thin diffusers offer a compact alternative to conventional refractive imaging but rely on computational reconstruction, since the diffuser's point spread function (PSF) globally multiplexes every scene point across…
In this paper a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of periodic functions exhibiting structured frequency support. These functions…
Several applications of slicing require a program to be sliced with respect to more than one slicing criterion. Program specialization, parallelization and cohesion measurement are examples of such applications. These applications can…
We propose a new method for dimension reduction in regression using the first two inverse moments. We develop corresponding weighted chi-squared tests for the dimension of the regression. The proposed method considers linear combinations of…
Although the sparse multinomial logistic regression (SMLR) has provided a useful tool for sparse classification, it suffers from inefficacy in dealing with high dimensional features and manually set initial regressor values. This has…
The common methods of spectral analysis for multivariate ($n$-dimensional) time series, like discrete Frourier transform (FT) or Wavelet transform, are based on Fourier series to decompose discrete data into a set of trigonometric model…
We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with…