Related papers: Localization and dimension free estimates for maxi…
A new dimension reduction methodology for change-point detection in functional means is developed in this paper. The major advantage and novelty of the proposed method is its efficiency in selecting basis functions that capture the change,…
This paper introduces a version of the argmax continuous mapping theorem that applies to M-estimation problems in which the objective functions converge to a limiting process with multiple maximizers. The concept of the smallest maximizer…
We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on $L^p$ spaces for all $1<p<\infty$ and…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
We study measurable spaces equipped with a $\sigma$-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version -- a kind of fiber space that describes locally their directions -- defined by…
Density function describes the density of states in the state space of a dynamic system or a Markov Decision Process (MDP). Its evolution follows the Liouville equation. We show that the density function is the dual of the value function in…
The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…
Randomized value functions offer a promising approach towards the challenge of efficient exploration in complex environments with high dimensional state and action spaces. Unlike traditional point estimate methods, randomized value…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
In contrast to taking the dual approach for finding a global minimum solution of a double well potential function, in Part II of the paper, we characterize a local minimizer, local maximizer, and global minimizer directly from the primal…
This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the…
We establish inequalities for assessing the distance between the distribution of a (possibly multidimensional) functional of a Poisson random measure and that of a Gaussian element. Our bounds only involve add-one cost operators at the…
Let $(X,d,\mu)$ be a doubling metric measure space. We consider the behaviour of the fractional maximal function $M^\alpha$ for $0\leq \alpha<Q$, where $Q$ is the doubling dimension, acting on functions of bounded mean oscillation (BMO) and…
We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method:…
Let $D\in\mathbb{N}$, $q\in[2,\infty)$ and $(\mathbb{R}^D,|\cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, the authors establish the Fefferman-Stein decomposition of Triebel-Lizorkin…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…