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We study the properties of time sequences extracted from a self-organized critical system, within the framework of the mathematical multifractal analysis. To this end, we propose a fixed-mass algorithm, well suited to deal with highly…
Recent work introduced loss functions which measure the error of a prediction based on multiple simultaneous observations or outcomes. In this paper, we explore the theoretical and practical questions that arise when using such…
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;…
Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this…
As an important and challenging problem in computer vision, learning based optical flow estimation aims to discover the intrinsic correspondence structure between two adjacent video frames through statistical learning. Therefore, a key…
A phenomenon of racial segregation in U.S. cities is a multifaceted area of study. A recent advancement in this field is the development of a methodology that transforms census population count-by-race data into a grid of monoracial cells.…
We study various box-size scaling techniques to obtain the multifractal properties, in terms of the singularity spectrum f(alpha), of the critical eigenstates at the metal-insulator transition within the 3-D Anderson model of localisation.…
Self-similarity is widely considered the reference framework for modeling the scaling properties of real-world data. However, most theoretical studies and their practical use have remained univariate. Operator Fractional Brownian Motion…
This paper concerns an application of the orthogonality sampling method (OSM) for a real-time identification of small objects from two-dimensional Fresnel experimental dataset in transverse electric polarization. First, we apply the OSM…
We introduce a low dimensional function of the site frequency spectrum that is tailor-made for distinguishing coalescent models with multiple mergers from Kingman coalescent models with population growth, and use this function to construct…
Multifractal analysis aims to characterize signals, functions, images or fields, via the fluctuations of their local regularity along time or space, hence capturing crucial features of their temporal/spatial dynamics. Multifractal analysis…
Multi-task learning (MTL) has been widely adopted for its ability to simultaneously learn multiple tasks. While existing gradient manipulation methods often yield more balanced solutions than simple scalarization-based approaches, they…
A method for segmenting water bodies in optical and synthetic aperture radar (SAR) satellite images is proposed. It makes use of the textural features of the different regions in the image for segmentation. The method consists in a…
Understanding and predicting Origin-Destination (OD) flows is crucial for urban planning and transportation management. Traditional OD prediction models, while effective within single cities, often face limitations when applied across…
Image ordinal estimation is to predict the ordinal label of a given image, which can be categorized as an ordinal regression problem. Recent methods formulate an ordinal regression problem as a series of binary classification problems. Such…
In a previous work \cite{She} we constructed measures on symbolic spaces which satisfy an extended multifractal formalism (in the sense that Olsen's functions $b$ and $B$ differ and that their Legendre transforms have the expected…
Analysis of biological rhythm data often involves performing least squares trigonometric regression, which models the oscillations of a response over time as a sum of sinusoidal components. When the response is not normally distributed, an…
This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of…
Online reinforcement learning (RL) methods are often data-inefficient or unreliable, making them difficult to train on real robotic hardware, especially quadruped robots. Learning robotic tasks from pre-collected data is a promising…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…