The age of Information (AoI) has been introduced to capture the notion of freshness in real-time monitoring applications. However, this metric falls short in many scenarios, especially when quantifying the mismatch between the current and the estimated states. To circumvent this issue, in this paper, we adopt the age of incorrect of information metric (AoII) that considers the quantified mismatch between the source and the knowledge at the destination. We consider for that a problem where a central entity pulls the information from remote sources that evolve according to a Markovian Process. It selects at each time slot which sources should send their updates. As the scheduler does not know the real state of the remote sources, it estimates at each time the value of AoII based on the Markovian sources' parameters. Its goal is to keep the time average of AoII function as small as possible. We develop a scheduling scheme based on Whittle's index policy for that purpose. To that extent, we proceed by using the Lagrangian Relaxation Approach and establish that the dual problem has an optimal threshold policy. Building on that, we compute the expressions of Whittle's indices. Finally, we provide some numerical results to highlight the performance of our derived policy compared to the classical AoI metric.
相關內容
This paper proposes a new technique based on a non-linear Minmax Detector Based (MDB) filter for image restoration. The aim of image enhancement is to reconstruct the true image from the corrupted image. The process of image acquisition frequently leads to degradation and the quality of the digitized image becomes inferior to the original image. Image degradation can be due to the addition of different types of noise in the original image. Image noise can be modelled of many types and impulse noise is one of them. Impulse noise generates pixels with gray value not consistent with their local neighbourhood. It appears as a sprinkle of both light and dark or only light spots in the image. Filtering is a technique for enhancing the image. Linear filter is the filtering in which the value of an output pixel is a linear combination of neighborhood values, which can produce blur in the image. Thus a variety of smoothing techniques have been developed that are non linear. Median filter is the one of the most popular non-linear filter. When considering a small neighborhood it is highly efficient but for large window and in case of high noise it gives rise to more blurring to image. The Centre Weighted Mean (CWM) filter has got a better average performance over the median filter. However the original pixel corrupted and noise reduction is substantial under high noise condition. Hence this technique has also blurring affect on the image. To illustrate the superiority of the proposed approach, the proposed new scheme has been simulated along with the standard ones and various restored performance measures have been compared.
In a sports competition, a team might lose a powerful incentive to exert full effort if its final rank does not depend on the outcome of the matches still to be played. Therefore, the organiser should reduce the probability of such a situation to the extent possible. Our paper provides a classification scheme to identify these weakly (where one team is indifferent) or strongly (where both teams are indifferent) stakeless games. A statistical model is estimated to simulate the UEFA Champions League groups and compare the candidate schedules used in the 2021/22 season according to the competitiveness of the matches played in the last round(s). The option followed in four of the eight groups is found to be optimal under a wide set of parameters. Minimising the number of strongly stakeless matches is verified to be a likely goal in the computer draw of the fixture that remains hidden from the public.
This paper explores Null Island, a fictional place located at 0$^\circ$ latitude and 0$^\circ$ longitude in the WGS84 geographic coordinate system. Null Island is erroneously associated with large amounts of geographic data in a wide variety of location-based services, place databases, social media and web-based maps. While it was originally considered a joke within the geospatial community, this article will demonstrate implications of its existence, both technological and social in nature, promoting Null Island as a fundamental issue of geographic information that requires more widespread awareness. The article summarizes error sources that lead to data being associated with Null Island. We identify four evolutionary phases which help explain how this fictional place evolved and established itself as an entity reaching beyond the geospatial profession to the point of being discovered by the visual arts and the general population. After providing an accurate account of data that can be found at (0, 0), geospatial, technological and social implications of Null Island are discussed. Guidelines to avoid misplacing data to Null Island are provided. Since data will likely continue to appear at this location, our contribution is aimed at both GIScientists and the general population to promote awareness of this error source.
In this paper we propose a methodology to accelerate the resolution of the so-called "Sorted L-One Penalized Estimation" (SLOPE) problem. Our method leverages the concept of "safe screening", well-studied in the literature for \textit{group-separable} sparsity-inducing norms, and aims at identifying the zeros in the solution of SLOPE. More specifically, we derive a set of \(\tfrac{n(n+1)}{2}\) inequalities for each element of the \(n\)-dimensional primal vector and prove that the latter can be safely screened if some subsets of these inequalities are verified. We propose moreover an efficient algorithm to jointly apply the proposed procedure to all the primal variables. Our procedure has a complexity \(\mathcal{O}(n\log n + LT)\) where \(T\leq n\) is a problem-dependent constant and \(L\) is the number of zeros identified by the tests. Numerical experiments confirm that, for a prescribed computational budget, the proposed methodology leads to significant improvements of the solving precision.
In this work, we focus on the high-dimensional trace regression model with a low-rank coefficient matrix. We establish a nearly optimal in-sample prediction risk bound for the rank-constrained least-squares estimator under no assumptions on the design matrix. Lying at the heart of the proof is a covering number bound for the family of projection operators corresponding to the subspaces spanned by the design. By leveraging this complexity result, we perform a power analysis for a permutation test on the existence of a low-rank signal under the high-dimensional trace regression model. We show that the permutation test based on the rank-constrained least-squares estimator achieves non-trivial power with no assumptions on the minimum (restricted) eigenvalue of the covariance matrix of the design. Finally, we use alternating minimization to approximately solve the rank-constrained least-squares problem to evaluate its empirical in-sample prediction risk and power of the resulting permutation test in our numerical study.
An important challenge in statistical analysis lies in controlling the estimation bias when handling the ever-increasing data size and model complexity. For example, approximate methods are increasingly used to address the analytical and/or computational challenges when implementing standard estimators, but they often lead to inconsistent estimators. So consistent estimators can be difficult to obtain, especially for complex models and/or in settings where the number of parameters diverges with the sample size. We propose a general simulation-based estimation framework that allows to construct consistent and bias corrected estimators for parameters of increasing dimensions. The key advantage of the proposed framework is that it only requires to compute a simple inconsistent estimator multiple times. The resulting Just Identified iNdirect Inference estimator (JINI) enjoys nice properties, including consistency, asymptotic normality, and finite sample bias correction better than alternative methods. We further provide a simple algorithm to construct the JINI in a computationally efficient manner. Therefore, the JINI is especially useful in settings where standard methods may be challenging to apply, for example, in the presence of misclassification and rounding. We consider comprehensive simulation studies and analyze an alcohol consumption data example to illustrate the excellent performance and usefulness of the method.
A High-dimensional and sparse (HiDS) matrix is frequently encountered in a big data-related application like an e-commerce system or a social network services system. To perform highly accurate representation learning on it is of great significance owing to the great desire of extracting latent knowledge and patterns from it. Latent factor analysis (LFA), which represents an HiDS matrix by learning the low-rank embeddings based on its observed entries only, is one of the most effective and efficient approaches to this issue. However, most existing LFA-based models perform such embeddings on a HiDS matrix directly without exploiting its hidden graph structures, thereby resulting in accuracy loss. To address this issue, this paper proposes a graph-incorporated latent factor analysis (GLFA) model. It adopts two-fold ideas: 1) a graph is constructed for identifying the hidden high-order interaction (HOI) among nodes described by an HiDS matrix, and 2) a recurrent LFA structure is carefully designed with the incorporation of HOI, thereby improving the representa-tion learning ability of a resultant model. Experimental results on three real-world datasets demonstrate that GLFA outperforms six state-of-the-art models in predicting the missing data of an HiDS matrix, which evidently supports its strong representation learning ability to HiDS data.
The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used schemes to compute MEPs numerically. It approximates an MEP by a discrete set of configuration images, where the discretization size determines both computational cost and accuracy of the simulations. In this paper, we consider a discrete MEP to be a stationary state of the NEB method and prove an optimal convergence rate of the discrete MEP with respect to the number of images. Numerical simulations for the transitions of some several proto-typical model systems are performed to support the theory.
The problem of scheduling unrelated machines has been studied since the inception of algorithmic mechanism design~\cite{NR99}. It is a resource allocation problem that entails assigning $m$ tasks to $n$ machines for execution. Machines are regarded as strategic agents who may lie about their execution costs so as to minimize their allocated workload. To address the situation when monetary payment is not an option to compensate the machines' costs, \citeauthor{DBLP:journals/mst/Koutsoupias14} [2014] devised two \textit{truthful} mechanisms, K and P respectively, that achieve an approximation ratio of $\frac{n+1}{2}$ and $n$, for social cost minimization. In addition, no truthful mechanism can achieve an approximation ratio better than $\frac{n+1}{2}$. Hence, mechanism K is optimal. While approximation ratio provides a strong worst-case guarantee, it also limits us to a comprehensive understanding of mechanism performance on various inputs. This paper investigates these two scheduling mechanisms beyond the worst case. We first show that mechanism K achieves a smaller social cost than mechanism P on every input. That is, mechanism K is pointwise better than mechanism P. Next, for each task $j$, when machines' execution costs $t_i^j$ are independent and identically drawn from a task-specific distribution $F^j(t)$, we show that the average-case approximation ratio of mechanism K converges to a constant. This bound is tight for mechanism K. For a better understanding of this distribution dependent constant, on the one hand, we estimate its value by plugging in a few common distributions; on the other, we show that this converging bound improves a known bound \cite{DBLP:conf/aaai/Zhang18} which only captures the single-task setting. Last, we find that the average-case approximation ratio of mechanism P converges to the same constant.
Most of the internet today is composed of digital media that includes videos and images. With pixels becoming the currency in which most transactions happen on the internet, it is becoming increasingly important to have a way of browsing through this ocean of information with relative ease. YouTube has 400 hours of video uploaded every minute and many million images are browsed on Instagram, Facebook, etc. Inspired by recent advances in the field of deep learning and success that it has gained on various problems like image captioning and, machine translation , word2vec , skip thoughts, etc, we present DeepSeek a natural language processing based deep learning model that allows users to enter a description of the kind of images that they want to search, and in response the system retrieves all the images that semantically and contextually relate to the query. Two approaches are described in the following sections.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191