Related papers: Quantile tomography: using quantiles with multivar…
Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…
Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…
Quantum many-body systems are characterized by patterns of correlations that define highly-non trivial manifolds when interpreted as data structures. Physical properties of phases and phase transitions are typically retrieved via simple…
Quantile regression has demonstrated promising utility in longitudinal data analysis. Existing work is primarily focused on modeling cross-sectional outcomes, while outcome trajectories often carry more substantive information in practice.…
The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden…
This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…
Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
A statistical estimation model with qualitative input provides a mechanism to fuse human intuition in the form of qualitative information into a statistical model. We investigate the statistical properties of this model and devise a…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
Angle halving, or alternatively the reverse operation of angle doubling, is a useful tool when studying directional distributions. It is especially useful on the circle where, in particular, it yields an identification between the wrapped…
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
Recent developments in computer vision have enabled the availability of segmented images across various domains, such as medicine, where segmented radiography images play an important role in diagnosis-making. As prediction problems are…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its…
The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel and is the centerpiece of…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian…