Related papers: Relative Resolution: An Analysis with the Kullback…
Estimating the Kullback-Leibler (KL) divergence between two distributions given samples from them is well-studied in machine learning and information theory. Motivated by considerations of multi-group fairness, we seek KL divergence…
This paper proposes a simple, accurate, and robust approach to single image nonparametric blind Super-Resolution (SR). This task is formulated as a functional to be minimized with respect to both an intermediate super-resolved image and a…
The deepening penetration of renewable resources into power systems entails great difficulties that have not been surmounted satisfactorily. An issue that merits special attention is the short-term planning of power systems under net load…
In this paper we document the results of the study which led to the ripple correction and absolute calibration algorithms applied to the high resolution spectra processed with the NEWSIPS software for the Final Archive of the IUE Project.…
We present in this work a new methodology to design kernels on data which is structured with smaller components, such as text, images or sequences. This methodology is a template procedure which can be applied on most kernels on measures…
We consider the well-known max-(relative) entropy problem $\Theta$(y) = infQ$\ll$P DKL(Q P ) with Kullback-Leibler divergence on a domain $\Omega$ $\subset$ R d , and with ''moment'' constraints h dQ = y, y $\in$ R m . We show that when m…
We present a new method for reconstructing two-dimensional mass maps of galaxy clusters from the image distortion of background galaxies. In contrast to most previous approaches, which directly convert locally averaged image ellipticities…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
We study concentration inequalities for the Kullback--Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes…
Understanding universal aspects of many-body systems is one of the central themes in modern physics. Recently, the stabilizer R\'{e}nyi entropy (SRE) has emerged as a computationally tractable measure of nonstabilizerness, a crucial…
The purpose of this paper is to present new classes of function systems as part of multiresolution analyses. Our approach is representation theoretic, and it makes use of generalized multiresolution function systems (MRSs). It further…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
Real-world Super-Resolution (Real-SR) methods focus on dealing with diverse real-world images and have attracted increasing attention in recent years. The key idea is to use a complex and high-order degradation model to mimic real-world…
Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models…
Real-world image restoration is hampered by diverse degradations stemming from varying capture conditions, capture devices and post-processing pipelines. Existing works make improvements through simulating those degradations and leveraging…
The measure-theoretic definition of Kullback-Leibler relative-entropy (KL-entropy) plays a basic role in the definitions of classical information measures. Entropy, mutual information and conditional forms of entropy can be expressed in…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field…
The min-entropy is a widely used metric to quantify the randomness of generated random numbers, which measures the difficulty of guessing the most likely output. It is difficult to accurately estimate the min-entropy of a non-independent…
Limited by the context window size of Large Language Models(LLMs), handling various tasks with input tokens exceeding the upper limit has been challenging, whether it is a simple direct retrieval task or a complex multi-hop reasoning task.…