Citation maturity time varies for different articles. However, the impact of all articles is measured in a fixed window. Clustering their citation trajectories helps understand the knowledge diffusion process and reveals that not all articles gain immediate success after publication. Moreover, clustering trajectories is necessary for paper impact recommendation algorithms. It is a challenging problem because citation time series exhibit significant variability due to non linear and non stationary characteristics. Prior works propose a set of arbitrary thresholds and a fixed rule based approach. All methods are primarily parameter dependent. Consequently, it leads to inconsistencies while defining similar trajectories and ambiguities regarding their specific number. Most studies only capture extreme trajectories. Thus, a generalised clustering framework is required. This paper proposes a feature based multiple k means cluster ensemble framework. 1,95,783 and 41,732 well cited articles from the Microsoft Academic Graph data are considered for clustering short term (10 year) and long term (30 year) trajectories, respectively. It has linear run time. Four distinct trajectories are obtained Early Rise Rapid Decline (2.2%), Early Rise Slow Decline (45%), Delayed Rise No Decline (53%), and Delayed Rise Slow Decline (0.8%). Individual trajectory differences for two different spans are studied. Most papers exhibit Early Rise Slow Decline and Delayed Rise No Decline patterns. The growth and decay times, cumulative citation distribution, and peak characteristics of individual trajectories are redefined empirically. A detailed comparative study reveals our proposed methodology can detect all distinct trajectory classes.
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In recent decades, the use of optical detection systems for meteor studies has increased dramatically, resulting in huge amounts of data being analyzed. Automated meteor detection tools are essential for studying the continuous meteoroid incoming flux, recovering fresh meteorites, and achieving a better understanding of our Solar System. Concerning meteor detection, distinguishing false positives between meteor and non-meteor images has traditionally been performed by hand, which is significantly time-consuming. To address this issue, we developed a fully automated pipeline that uses Convolutional Neural Networks (CNNs) to classify candidate meteor detections. Our new method is able to detect meteors even in images that contain static elements such as clouds, the Moon, and buildings. To accurately locate the meteor within each frame, we employ the Gradient-weighted Class Activation Mapping (Grad-CAM) technique. This method facilitates the identification of the region of interest by multiplying the activations from the last convolutional layer with the average of the gradients across the feature map of that layer. By combining these findings with the activation map derived from the first convolutional layer, we effectively pinpoint the most probable pixel location of the meteor. We trained and evaluated our model on a large dataset collected by the Spanish Meteor Network (SPMN) and achieved a precision of 98\%. Our new methodology presented here has the potential to reduce the workload of meteor scientists and station operators and improve the accuracy of meteor tracking and classification.
Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately assessed. Conversely, the Bayesian neural networks (BNNs) naturally offer predictive uncertainty by applying Bayes' theorem. However, their computational requirements pose significant challenges. Moreover, both frequentist NNs and BNNs suffer from overfitting issues when dealing with noisy and sparse data, which render their predictions unwieldy away from the available data space. To address both these problems simultaneously, we leverage insights from a hierarchical setting in which the parameter priors are conditional on hyperparameters to construct a BNN by applying a semi-analytical framework known as nonlinear sparse Bayesian learning (NSBL). We call our network sparse Bayesian neural network (SBNN) which aims to address the practical and computational issues associated with BNNs. Simultaneously, imposing a sparsity-inducing prior encourages the automatic pruning of redundant parameters based on the automatic relevance determination (ARD) concept. This process involves removing redundant parameters by optimally selecting the precision of the parameters prior probability density functions (pdfs), resulting in a tractable treatment for overfitting. To demonstrate the benefits of the SBNN algorithm, the study presents an illustrative regression problem and compares the results of a BNN using standard Bayesian inference, hierarchical Bayesian inference, and a BNN equipped with the proposed algorithm. Subsequently, we demonstrate the importance of considering the full parameter posterior by comparing the results with those obtained using the Laplace approximation with and without NSBL.
We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. Though the described Bayesian computational framework is general, we look at a specific application to the susceptible-infectious-removed (SIR) model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations. The SIR model consists of three states, namely, the three compartments, and two parameters which control the coupling among the states. The deterministic SIR model with time-invariant parameters has shown to be overly simplistic for modelling the complex long-term dynamics of diseases transmission. Recognizing that certain model parameters will naturally vary in time due to seasonal trends, non-pharmaceutical interventions, and other random effects, the estimation procedure must systematically permit these time-varying effects to be captured, without unduly introducing artificial dynamics into the system. To this end, we leverage the robustness of the Markov Chain Monte Carlo (MCMC) algorithm for the estimation of time-invariant parameters alongside nonlinear filters for the joint estimation of the system state and time-varying parameters. We demonstrate performance of the framework by first considering a series of examples using synthetic data, followed by an exposition on public health data collected in the province of Ontario.
Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper, we introduce a framework for answering this question both intuitively and quantitatively. The underlying structure of the framework is a race between quantum and classical computers, where their relative strengths determine when each wins. While classical computers operate faster, quantum computers can sometimes run more efficient algorithms. Whether the speed advantage or the algorithmic advantage dominates determines whether a problem will benefit from quantum computing or not. Our analysis reveals that many problems, particularly those of small to moderate size that can be important for typical businesses, will not benefit from quantum computing. Conversely, larger problems or those with particularly big algorithmic gains will benefit from near-term quantum computing. Since very large algorithmic gains are rare in practice and theorized to be rare even in principle, our analysis suggests that the benefits from quantum computing will flow either to users of these rare cases, or practitioners processing very large data.
This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of weighting procedures and in their flexibility with respect to the effective bootstrap sample size. In addition to the standard multinomial bootstrap and the m-out-of-n bootstrap, our results apply to a large class of randomly weighted sums involving negatively orthant dependent (NOD) weights, including the Bayesian bootstrap, jackknife, resampling without replacement, simple random sampling with over-replacement, independent weights, and multivariate Gaussian weighting schemes. Weights are permitted to be non-identically distributed and possibly even negative. Our proof technique is based on extending a proof of the i.i.d. strong uniform law of large numbers to employ strong laws for randomly weighted sums; in particular, we exploit a recent Marcinkiewicz--Zygmund strong law for NOD weighted sums.
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article, the Modulated Fourier Expansion is analytically derived for a linear partial differential equation with a multifrequency highly oscillatory potential. The solution of the equation is expressed as a convergent Neumann series within the appropriate Sobolev space. The proposed approach enables, firstly, to derive a general formula for the error associated with the approximation of the solution by MFE, and secondly, to determine the coefficients for this expansion -- without the need to solve numerically the system of differential equations to find the coefficients of MFE. Numerical experiments illustrate the theoretical investigations.
Randomized Controlled Trials (RCTs) may suffer from limited scope. In particular, samples may be unrepresentative: some RCTs over- or under- sample individuals with certain characteristics compared to the target population, for which one wants conclusions on treatment effectiveness. Re-weighting trial individuals to match the target population can improve the treatment effect estimation. In this work, we establish the exact expressions of the bias and variance of such reweighting procedures -- also called Inverse Propensity of Sampling Weighting (IPSW) -- in presence of categorical covariates for any sample size. Such results allow us to compare the theoretical performance of different versions of IPSW estimates. Besides, our results show how the performance (bias, variance, and quadratic risk) of IPSW estimates depends on the two sample sizes (RCT and target population). A by-product of our work is the proof of consistency of IPSW estimates. Results also reveal that IPSW performances are improved when the trial probability to be treated is estimated (rather than using its oracle counterpart). In addition, we study choice of variables: how including covariates that are not necessary for identifiability of the causal effect may impact the asymptotic variance. Including covariates that are shifted between the two samples but not treatment effect modifiers increases the variance while non-shifted but treatment effect modifiers do not. We illustrate all the takeaways in a didactic example, and on a semi-synthetic simulation inspired from critical care medicine.
Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and unitary, but are rather augmented with probabilistic byproducts. Yet, the main algorithmic use of MBQC so far has been to completely counteract this probabilistic nature in order to simulate unitary computations expressed in the circuit model. In this work, we propose designing MBQC algorithms that embrace this inherent randomness and treat the random byproducts in MBQC as a resource for computation. As a natural application where randomness can be beneficial, we consider generative modeling, a task in machine learning centered around generating complex probability distributions. To address this task, we propose a variational MBQC algorithm equipped with control parameters that allow to directly adjust the degree of randomness to be admitted in the computation. Our numerical findings indicate that this additional randomness can lead to significant gains in learning performance in certain generative modeling tasks. These results highlight the potential advantages in exploiting the inherent randomness of MBQC and motivate further research into MBQC-based algorithms.
We propose an approach to 3D reconstruction via inverse procedural modeling and investigate two variants of this approach. The first option consists in the fitting set of input parameters using a genetic algorithm. We demonstrate the results of our work on tree models, complex objects, with the reconstruction of which most existing methods cannot handle. The second option allows us to significantly improve the precision by using gradients within memetic algorithm, differentiable rendering and also differentiable procedural generators. In our work we see 2 main contributions. First, we propose a method to join differentiable rendering and inverse procedural modeling. This gives us an opportunity to reconstruct 3D model more accurately than existing approaches when a small number of input images are available (even for single image). Second, we join both differentiable and non-differentiable procedural generators in a single framework which allow us to apply inverse procedural modeling to fairly complex generators: when gradient is available, reconstructions is precise, when gradient is not available, reconstruction is approximate, but always high quality without visual artifacts.
In recent years, object detection has experienced impressive progress. Despite these improvements, there is still a significant gap in the performance between the detection of small and large objects. We analyze the current state-of-the-art model, Mask-RCNN, on a challenging dataset, MS COCO. We show that the overlap between small ground-truth objects and the predicted anchors is much lower than the expected IoU threshold. We conjecture this is due to two factors; (1) only a few images are containing small objects, and (2) small objects do not appear enough even within each image containing them. We thus propose to oversample those images with small objects and augment each of those images by copy-pasting small objects many times. It allows us to trade off the quality of the detector on large objects with that on small objects. We evaluate different pasting augmentation strategies, and ultimately, we achieve 9.7\% relative improvement on the instance segmentation and 7.1\% on the object detection of small objects, compared to the current state of the art method on MS COCO.
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