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Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
Correlation remains to be one of the most widely used statistical tools for assessing the strength of relationships between data series. This paper presents a novel compositional correlation method for detecting linear and nonlinear…
Thesis is devoted to the application of cumulant analysis in the estimation of impulse response functions for continuous time-invariant linear systems, including systems with inner noises. The main assumption of the work is the second-order…
We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods…
We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…
Core-periphery detection is a key task in exploratory network analysis where one aims to find a core, a set of nodes well-connected internally and with the periphery, and a periphery, a set of nodes connected only (or mostly) with the core.…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
This paper formulates a general cross validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as Trend Filtering and Dyadic CART. The resulting cross validated versions are…
We propose the Linearly Adaptive Cross Entropy Loss function. This is a novel measure derived from the information theory. In comparison to the standard cross entropy loss function, the proposed one has an additional term that depends on…
Incorporating sparsity priors in learning tasks can give rise to simple, and interpretable models for complex high dimensional data. Sparse models have found widespread use in structure discovery, recovering data from corruptions, and a…
A large body of research into semantic textual similarity has focused on constructing state-of-the-art embeddings using sophisticated modelling, careful choice of learning signals and many clever tricks. By contrast, little attention has…
We study the multi-target detection problem of recovering a target signal from a noisy measurement that contains multiple copies of the signal at unknown locations. Motivated by the structure reconstruction problem in cryo-electron…
The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required…
This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…
We introduce a novel unbiased, cross-correlation estimator for the one-point statistics of cosmological random fields. One-point statistics are a useful tool for analysis of highly non-Gaussian density fields, while cross-correlations…
We propose an estimation approach to analyse correlated functional data which are observed on unequal grids or even sparsely. The model we use is a functional linear mixed model, a functional analogue of the linear mixed model. Estimation…
We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measurements per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear…
Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables…
It is usual to rely on the quasi-likelihood methods for deriving statistical methods applied to clustered multinomial data with no underlying distribution. Even though extensive literature can be encountered for these kind of data sets,…
Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration…