Multi-Layer Reconstruction Errors Autoencoding and Density Estimate for Network Anomaly Detection

Anomaly detection is an important method for intrusion detection.In recent years,unsupervised methods have been widely researched because they do not require labeling.For example,a nonlinear autoencoder can use reconstruction errors to attain the discrimination threshold.This method is not effective when the model complexity is high or the data contains noise.The method for detecting the density of compressed features in a hidden layer can be used to reduce the influence of noise on the selection of the threshold because the density of abnormal data in hidden layers is smaller than normal data.However,compressed features may lose some of the high-dimensional distribution information of the original data.In this paper,we present an efficient anomaly detection framework for unsupervised anomaly detection,which includes network data capturing,processing,feature extraction,and anomaly detection.We employ a deep autoencoder to obtain compressed features and multi-layer reconstruction errors,and feeds them the same to the Gaussian mixture model to estimate the density.The proposed approach is trained and tested on multiple current intrusion detection datasets and real network scenes,and performance indicators,namely accuracy,recall,and F1-score,are better than other autoencoder models.

A Weakly-Supervised Crowd Density Estimation Method Based on Two-Stage Linear Feature Calibration

In a crowd density estimation dataset,the annotation of crowd locations is an extremely laborious task,and they are not taken into the evaluation metrics.In this paper,we aim to reduce the annotation cost of crowd datasets,and propose a crowd density estimation method based on weakly-supervised learning,in the absence of crowd position supervision information,which directly reduces the number of crowds by using the number of pedestrians in the image as the supervised information.For this purpose,we design a new training method,which exploits the correlation between global and local image features by incremental learning to train the network.Specifically,we design a parent-child network(PC-Net)focusing on the global and local image respectively,and propose a linear feature calibration structure to train the PC-Net simultaneously,and the child network learns feature transfer factors and feature bias weights,and uses the transfer factors and bias weights to linearly feature calibrate the features extracted from the Parent network,to improve the convergence of the network by using local features hidden in the crowd images.In addition,we use the pyramid vision transformer as the backbone of the PC-Net to extract crowd features at different levels,and design a global-local feature loss function(L2).We combine it with a crowd counting loss(LC)to enhance the sensitivity of the network to crowd features during the training process,which effectively improves the accuracy of crowd density estimation.The experimental results show that the PC-Net significantly reduces the gap between fullysupervised and weakly-supervised crowd density estimation,and outperforms the comparison methods on five datasets of Shanghai Tech Part A,ShanghaiTech Part B,UCF_CC_50,UCF_QNRF and JHU-CROWD++.

Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

Covariate balancing based on kernel density estimates for controlled experiments

Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes.A completely randomised design is usually used to randomly assign treatment levels to experimental units.When covariates of the experimental units are available,the experimental design should achieve covariate balancing among the treatment groups,such that the statistical inference of the treatment effects is not confounded with any possible effects of covariates.However,covariate imbalance often exists,because the experiment is carried out based on a single realisation of the complete randomisation.It is more likely to occur and worsen when the size of the experimental units is small or moderate.In this paper,we introduce a new covariate balancing criterion,which measures the differences between kernel density estimates of the covariates of treatment groups.To achieve covariate balance before the treatments are randomly assigned,we partition the experimental units by minimising the criterion,then randomly assign the treatment levels to the partitioned groups.Through numerical examples,weshow that the proposed partition approach can improve the accuracy of the difference-in-mean estimator and outperforms the complete randomisation and rerandomisation approaches.

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.

African Lion Population Estimates in Tanzania’s Ruaha National Park

Tanzania is considered a country with the largest number of African lions (Panthera leo). However, the continued absence of ecological population estimates and understanding of the associated factors influencing lion distribution hinders the development of conservation planning. This is particularly true in the Ruaha-Rungwa landscape, where it was estimated that more than 10% of the global lion population currently resides. By using a call-back survey method, we aimed to provide population estimates (population size and density) of African lions in the Ruaha National Park, between wet (March 2019) and dry (October 2019) seasons. We also assessed the key factors that influenced the distribution of the observed lions towards call-back stations. Ferreira & Funston’s (2010) formula was used to calculate population size and in turn used to estimate density in the sampled area, while the Generalized Linear Model (GLMM) with zero-inflated Poisson error distribution was used to determine factors that influence the distribution of the observed lions to call-back stations. The population size we calculated for the sampled area of 3137.2 km2 revealed 286 lions (95% CI, 236 - 335) during the wet season, and 196 lions (95% CI, 192 - 200) during the dry season. The density of lions was 9.1/100 km2 during the wet season, and 6.3/100 km2 during the dry season. Distance to water source had a significant negative effect on the distribution of the observed lions to the call-back stations, while habitat had a marginal effect. Our findings show that, although lion population estimates were larger during the wet season than the dry season, the season had no effect on the distribution of the observed lions to call-back stations. We suggest that the proximity to water sources is important in study design. Further, we suggest that density and population size are useful indices in identifying conservation area priorities and lion coexistence strategies.

STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE:EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY

In this paper we study a fractional stochastic heat equation on Rd （d 〉 1） with additive noise /t u（t, x） = Dα/δ u（t, x）＋ b（u（t, x） ） ＋ WH （t, x） where D α/δ is a nonlocal fractional differential operator and W H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d = 1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.

Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation

In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.

Deep density estimation via invertible block-triangular mapping

In this work,we develop an invertible transport map,called KRnet,for density estimation by coupling the Knothe–Rosenblatt(KR)rearrangement and the flow-based generative model,which generalizes the real-valued non-volume preserving(real NVP)model(arX-iv:1605.08803v3).The triangular structure of the KR rearrangement breaks the symmetry of the real NVP in terms of the exchange of information between dimensions,which not only accelerates the training process but also improves the accuracy significantly.We have also introduced several new layers into the generative model to improve both robustness and effectiveness,including a reformulated affine coupling layer,a rotation layer and a component-wise nonlinear invertible layer.The KRnet can be used for both density estimation and sample generation especially when the dimensionality is relatively high.Numerical experiments have been presented to demonstrate the performance of KRnet.

A new approach on seismic mortality estimations based on average population density

This study examines a new methodology to predict the final seismic mortality from earthquakes in China. Most studies established the association between mortality estimation and seismic intensity without considering the population density. In China, however, the data are not always available, especially when it comes to the very urgent relief situation in the disaster. And the popu- lation density varies greatly from region to region. This motivates the development of empirical models that use historical death data to provide the path to analyze the death tolls for earthquakes. The present paper employs the average population density to predict the final death tolls in earthquakes using a case-based reasoning model from realistic perspective. To validate the forecasting results, historical data from 18 large-scale earthquakes occurred in China are used to estimate the seismic morality of each case. And a typical earthquake case occurred in the northwest of Sichuan Province is employed to demonstrate the estimation of final death toll. The strength of this paper is that it provides scientific methods with overall forecast errors lower than 20 %, and opens the door for conducting final death forecasts with a qualitative and quantitative approach. Limitations and future research are also analyzed and discussed in the conclusion.

Improved Logistic Regression Algorithm Based on Kernel Density Estimation for Multi-Classification with Non-Equilibrium Samples

Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classification problem,such as problem with non-equilibrium samples.Many scholars have proposed some methods,such as neural network,least square support vector machine,AdaBoost meta-algorithm,etc.These methods essentially belong to machine learning categories.In this work,based on the probability theory and statistical principle,we propose an improved logistic regression algorithm based on kernel density estimation for solving nonlinear multi-classification.We have compared our approach with other methods using non-equilibrium samples,the results show that our approach guarantees sample integrity and achieves superior classification.

Diversity Sampling Based Kernel Density Estimation for Background Modeling

A novel diversity-sampling based nonparametric multi-modal background model is proposed. Using the samples having more popular and various intensity values in the training sequence, a nonparametric model is built for background subtraction. According to the related intensifies, different weights are given to the distinct samples in kernel density estimation. This avoids repeated computation using all samples, and makes computation more efficient in the evaluation phase. Experimental results show the validity of the diversity- sampling scheme and robustness of the proposed model in moving objects segmentation. The proposed algorithm can be used in outdoor surveillance systems.

A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA

A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.

Density Estimation Using Gumbel Kernel Estimator

In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of the probability density function (pdf). When the density functions have limited bounded support on [0, ∞) and they are liberated of boundary bias, always non-negative and obtain the optimal rate of convergence for the mean integrated squared error (MISE). The bias, variance and the optimal bandwidth of the proposed estimators are investigated on theoretical grounds as well as on simulation basis. Further, the applicability of the proposed estimator is compared to Weibull kernel estimator, where performance of newly proposed kernel is outstanding.

Wavelet-Based Density Estimation in Presence of Additive Noise under Various Dependence Structures

We study the following model: . The aim is to estimate the distribution of X when only are observed. In the classical model, the distribution of is assumed to be known, and this is often considered as an important drawback of this simple model. Indeed, in most practical applications, the distribution of the errors cannot be perfectly known. In this paper, the author will construct wavelet estimators and analyze their asymptotic mean integrated squared error for additive noise models under certain dependent conditions, the strong mixing case, the β-mixing case and the ρ-mixing case. Under mild conditions on the family of wavelets, the estimator is shown to be -consistent and fast rates of convergence have been established.

A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).

Optimization Strategy of Commercial Space in Xianyukou Hutong Based on Kernel Density and Space Syntax

Beijing Xianyukou Hutong(hutong refers to historical and cultural block in Chinese)occupies an important geographical location with unique urban fabric,and after years of renewal and protection,the commercial space of Xianyukou Street and has gained some recognition.This article Xianyukou takes commercial hutong in Beijing as an example,spatial analysis was carried out using methods like GIS kernel density method,space syntax after site investigation and research.Based on the street space problems found,this paper then puts forward strategies to improve and upgrade Xianyukou Street’s commercial space and improve businesses in Xianyukou Street and other similar hutong.

NONLINEAR WAVELET SMOOTHING OF ERROR DENSITY IN A SEMIPARAM ETRIC REGRESSION MODEL

In this paper,a sem iparam etric regression m odel in w hich errors are i.i.d random variables from an unknow n density f(·) is considered.Based on Hallet al.(1995),a nonlinear w avelet estim ation of f(·) withoutrestrictions ofcontinuity everyw here on f(·) is given,and the convergence rate ofthe estim ators in L2 is obtained.

2011-2020年我国医学生分布的区域差异及动态演进

目的研究我国医学生分布的集聚水平、空间分布特征和时空演变趋势,为宏观调控医学高等院校区域均衡发展提供依据。方法运用集聚度、空间自相关模型和核密度估计法分析医学生空间分布情况和发展趋势。结果2011—2020年,我国医学生集聚水平在观察末期升至7.478,涨幅15.43%,呈现“东高西低、南高北低”的空间分布格局。各省份间呈空间正相关性,形成稳定的“高高集聚、低低集聚”的空间分布特征。医学生分布的绝对差异在中部地区趋于缓和,在东、西部地区持续扩大,总体呈多极化演化特征。结论我国医学生分布的集聚水平稳步上升且存在不均衡现象,已形成稳定的聚集区域并存在低流动性。建议构建区域医学高等教育协同发展机制,以促进医学院校资源的优质均衡发展。

Active Kriging-Based Adaptive Importance Sampling for Reliability and Sensitivity Analyses of Stator Blade Regulator

The reliability and sensitivity analyses of stator blade regulator usually involve complex characteristics like highnonlinearity,multi-failure regions,and small failure probability,which brings in unacceptable computing efficiency and accuracy of the current analysismethods.In this case,by fitting the implicit limit state function(LSF)with active Kriging(AK)model and reducing candidate sample poolwith adaptive importance sampling(AIS),a novel AK-AIS method is proposed.Herein,theAKmodel andMarkov chainMonte Carlo(MCMC)are first established to identify the most probable failure region(s)(MPFRs),and the adaptive kernel density estimation(AKDE)importance sampling function is constructed to select the candidate samples.With the best samples sequentially attained in the reduced candidate samples and employed to update the Kriging-fitted LSF,the failure probability and sensitivity indices are acquired at a lower cost.The proposed method is verified by twomulti-failure numerical examples,and then applied to the reliability and sensitivity analyses of a typical stator blade regulator.Withmethods comparison,the proposed AK-AIS is proven to hold the computing advantages on accuracy and efficiency in complex reliability and sensitivity analysis problems.