Estimating network edge probabilities by neighbourhood smoothing

Biometrika ◽  
2017 ◽  
Vol 104 (4) ◽  
pp. 771-783 ◽  
Author(s):  
Yuan Zhang ◽  
Elizaveta Levina ◽  
Ji Zhu
Keyword(s):  
Network Structure ◽  
Efficient Method ◽  
Error Rate ◽  
Adjacency Matrix ◽  
Link Prediction ◽  
Mean Squared Error ◽  
Smoothing Method ◽  
Computationally Efficient ◽  
Squared Error ◽  
The Matrix

Summary The estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighbourhood smoothing method requires little tuning, has a competitive mean squared error rate and outperforms many benchmark methods for link prediction in simulated and real networks.

scholarly journals A hybrid recommender system based-on link prediction for movie baskets analysis

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mohammadsadegh Vahidi Farashah ◽  
Akbar Etebarian ◽  
Reza Azmi ◽  
Reza Ebrahimzadeh Dastjerdi
Keyword(s):  
Recommender System ◽  
Link Prediction ◽  
Mean Squared Error ◽  
Spatial Clustering ◽  
Randomized Algorithm ◽  
Similarity Criterion ◽  
Absolute Error ◽  
Similarity Criteria ◽  
Online Systems ◽  
Squared Error

AbstractOver the past decade, recommendation systems have been one of the most sought after by various researchers. Basket analysis of online systems’ customers and recommending attractive products (movies) to them is very important. Providing an attractive and favorite movie to the customer will increase the sales rate and ultimately improve the system. Various methods have been proposed so far to analyze customer baskets and offer entertaining movies but each of the proposed methods has challenges, such as lack of accuracy and high error of recommendations. In this paper, a link prediction-based method is used to meet the challenges of other methods. The proposed method in this paper consists of four phases: (1) Running the CBRS that in this phase, all users are clustered using Density-based spatial clustering of applications with noise algorithm (DBScan), and classification of new users using Deep Neural Network (DNN) algorithm. (2) Collaborative Recommender System (CRS) Based on Hybrid Similarity Criterion through which similarities are calculated based on a threshold (lambda) between the new user and the users in the selected category. Similarity criteria are determined based on age, gender, and occupation. The collaborative recommender system extracts users who are the most similar to the new user. Then, the higher-rated movie services are suggested to the new user based on the adjacency matrix. (3) Running improved Friendlink algorithm on the dataset to calculate the similarity between users who are connected through the link. (4) This phase is related to the combination of collaborative recommender system’s output and improved Friendlink algorithm. The results show that the Mean Squared Error (MSE) of the proposed model has decreased respectively 8.59%, 8.67%, 8.45% and 8.15% compared to the basic models such as Naive Bayes, multi-attribute decision tree and randomized algorithm. In addition, Mean Absolute Error (MAE) of the proposed method decreased by 4.5% compared to SVD and approximately 4.4% compared to ApproSVD and Root Mean Squared Error (RMSE) of the proposed method decreased by 6.05 % compared to SVD and approximately 6.02 % compared to ApproSVD.

scholarly journals A new modified ridge-type estimator for the beta regression model: simulation and application

2021 ◽  
Vol 7 (1) ◽  
pp. 1035-1057
Author(s):  
Muhammad Nauman Akram ◽  
◽  
Muhammad Amin ◽  
Ahmed Elhassanein ◽  
Muhammad Aman Ullah ◽  
...  
Keyword(s):  
Regression Model ◽  
Mean Squared Error ◽  
Model Simulation ◽  
Beta Regression ◽  
Explanatory Variables ◽  
Squared Error ◽  
The Matrix ◽  
Biased Estimators ◽  
Highly Correlated ◽  
Beta Regression Model

<abstract> <p>The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.</p> </abstract>

Acoustic Echo Cancellation using Computationally Efficient Adaptive Algorithm Techniques

2016 ◽  
Vol 1 (2) ◽  
pp. 57-62
Author(s):  
Mastan Sharif Shaik ◽  
K. Satya Prasad ◽  
Rafi Ahamed Shaik ◽  
D. Venkata Rao
Keyword(s):  
Adaptive Filters ◽  
Mean Squared Error ◽  
Echo Cancellation ◽  
Lms Algorithm ◽  
Acoustic Echo Cancellation ◽  
Computationally Efficient ◽  
Primary Input ◽  
Squared Error ◽  
Acoustic Echo ◽  
The Mean

Several sign based LMS adaptive filters, which are computationally free having multiplier free weight update loops, are proposed for acoustic echo cancellation. The adaptive filters essentially minimizes the mean- squared error between a primary input, which is the echo, and a reference input, which is either echo that is correlated in some way with the echo in the primary input. The results show that the performance of the signed regressor. LMS algorithm is superior than conventional LMS algorithm, the performance of signed LMS and sign- sign LMS based realizations are comparable to that of the LMS based filtering techniques in terms of Average Attenuation and computational complexity.

scholarly journals Acoustic Echo Cancellation using Computationally Efficient Adaptive Algorithm Techniques

2016 ◽  
Vol 1 (2) ◽  
pp. 57-62
Author(s):  
Mastan Sharif Shaik ◽  
K. Satya Prasad ◽  
Rafi Ahamed Shaik ◽  
D. Venkata Rao
Keyword(s):  
Adaptive Filters ◽  
Mean Squared Error ◽  
Echo Cancellation ◽  
Lms Algorithm ◽  
Acoustic Echo Cancellation ◽  
Computationally Efficient ◽  
Primary Input ◽  
Squared Error ◽  
Acoustic Echo ◽  
The Mean

Several sign based LMS adaptive filters, which are computationally free having multiplier free weight update loops, are proposed for acoustic echo cancellation. The adaptive filters essentially minimizes the mean-squared error between a primary input, which is the echo, and a reference input, which is either echo that is correlated in some way with the echo in the primary input. The results show that the performance of the signed regressor. LMS algorithm is superior than conventional LMS algorithm, the performance of signed LMS and sign-sign LMS based realizations are comparable to that of the LMS based filtering techniques in terms of Average Attenuation and computational complexity.

scholarly journals A Hybrid Recommender System Based-on Link Prediction for Movie Baskets Analysis

2020 ◽  
Author(s):  
Mohammadsadegh Vahidi Farashah ◽  
Akbar Etebarian ◽  
Reza Azmi ◽  
Reza Ebrahimzadeh Dastjerdi
Keyword(s):  
Decision Tree ◽  
Link Prediction ◽  
Mean Squared Error ◽  
Randomized Algorithm ◽  
Similarity Criteria ◽  
Squared Error ◽  
Proposed Model ◽  
The Mean ◽  
Hybrid Recommender System ◽  
Hybrid Recommender

Abstract The proposed method in this paper consists of three steps: initial clustering of all users and assigning new user to appropriate clusters, assigning appropriate weights to users' characteristics, and identifying new user’s adjacent users using hybrid similarity criteria and adjacency matrix of adjacent users’ rating to the movie services and calculating new user’s rating to each movie considering adjacent users’ rating and the similarity level of each adjacent user to the new user. The results show that the mean squared error of the proposed model has decreased respectively 8.59%, 8.67%, 8.45% and 8.15% compared to the basic models such as Naive Bayes, multi-attribute decision tree and randomized algorithm. Also, MAE of the proposed method decreased by 4.5% compared to SVD and approximately 4.4% compared to ApproSVD and RMSE of the proposed method decreased by 6.05% compared to SVD and approximately 6.02% compared to ApproSVD.

scholarly journals The Structure of Oxide Film on the Porous Silicon Surface

2020 ◽  
Vol 65 (1) ◽  
pp. 75
Author(s):  
O. I. Zavalistyi ◽  
O. V. Makarenko ◽  
V. A. Odarych ◽  
A. L. Yampolskyi
Keyword(s):  
Refractive Index ◽  
Surface Layer ◽  
Porous Silicon ◽  
Structural Changes ◽  
Mean Squared Error ◽  
Single Layer ◽  
Prolonged Stay ◽  
Near Surface ◽  
Squared Error ◽  
The Matrix

A prolonged stay of porous silicon in the air environment gives rise to structural changes in its surface layer, and the standard single-layer model is not sufficiently accurate to describe them. In this work, the structure of the near-surface layer in porous silicon is studied using the polygonal ellipsometry method. A combined approach is proposed to analyze the angular ellipsometry data for the parameters ф and Δ. It consists in the application of the multilayer medium model and the matrix method, while simulating the propagation of optical radiation in this medium in order to obtain the theoretical angular dependences of tan ф and cosΔ. In this method, the dependence of the sought optical profile on the specimen depth is an additional condition imposed on the multilayer model. Evolutionary numerical methods are used for finding the global minimum of the mean squared error (MSE) between the corresponding theoretical and experimental dependences, and the parameters of an optical profile are determined. A model in which the inner non-oxidized layer of porous silicon is homogeneous, whereas the refractive index in the outer oxidized layer has a linear profile, is analyzed. It is shown that the linear and two-step models for the refractive index of an oxidized film provided the best agreement with the experimental ellipsometric functions. The adequacy of the theoretical model is also confirmed by determining the color coordinates of the specimen.

scholarly journals Optimal Binning of Peri-Event Time Histograms Using Akaike Information Criterion

2020 ◽  
Author(s):  
Ali Ghazizadeh ◽  
Frederic Ambroggi
Keyword(s):  
Firing Rate ◽  
Akaike Information Criterion ◽  
Mean Squared Error ◽  
Temporal Dynamics ◽  
Real Data ◽  
Information Criterion ◽  
Neuronal Firing ◽  
Computationally Efficient ◽  
Event Time ◽  
Squared Error

AbstractPeri-event time histograms (PETH) are widely used to study correlations between experimental events and neuronal firing. The accuracy of firing rate estimate using a PETH depends on the choice of binsize. We show that the optimal binsize for a PETH depends on factors such as the number of trials and the temporal dynamics of the firing rate. These factors argue against the use of a one-size-fits-all binsize when making PETHs for an inhomogeneous population of neurons. Here we propose a binsize selection method by adapting the Akaike Information Criterion (AIC). Simulations show that optimal binsizes estimated by AIC closely match the optimal binsizes using mean squared error (MSE). Furthermore, using real data, we find that optimal binning improves detection of responses and their dynamics. Together our analysis strongly supports optimal binning of PETHs and proposes a computationally efficient method for this optimization based on AIC approach to model selection.

scholarly journals Implementasi Metode Penghalusan Ekponensial Tunggal Dalam Prediksi Penjualan Buku

2021 ◽  
Vol 9 (2) ◽  
pp. 1
Author(s):  
Heri Setyawan ◽  
Sri Hariyati Fitriasih ◽  
Retno Tri Vulandari
Keyword(s):  
Mean Squared Error ◽  
Exponential Smoothing ◽  
Smoothing Method ◽  
Squared Error ◽  
Double Exponential ◽  
Double Exponential Smoothing ◽  
Product Sales ◽  
Exponential Smoothing Method ◽  
The Relationship ◽  
Single Exponential

The prediction of the quantity of product sales in the future is intended to control the amount of existing product stock, so that product shortages or excess stock can be minimized. When the quantity of sales can be predicted accurately, the fulfillment of consumer demand can be sought on time and the cooperation of the store with the relationship is maintained well so that the store can avoid losing both sales and consumers. The purpose of this study is to compare the effectiveness of the use of the Single Exponential Smoothing method and methods Double Exponential Smoothing with a smoothing parameter value a = 0.5 for forecasting sales by comparing the error values in the two methods using the Mean Squared Error (MSE) method, the MSE results of the Single Exponential Smoothing method is 4967.75 while the MSE Double Exponential Smoothing is 5113.03. Thus, the Single Exponential Smoothing method is more accurate than Double Exponential Smoothing in calculating book sales forecasting because it has a low MSE value.

The transition model test for serial dependence in mixed-effects models for binary data

2015 ◽  
Vol 26 (4) ◽  
pp. 1756-1773 ◽  
Author(s):  
Nina Breinegaard ◽  
Sophia Rabe-Hesketh ◽  
Anders Skrondal
Keyword(s):  
Model Test ◽  
Mixed Models ◽  
Binary Data ◽  
Mean Squared Error ◽  
Transition Model ◽  
Serial Dependence ◽  
Computationally Efficient ◽  
Consistent Estimation ◽  
Squared Error ◽  
Standard Software

Generalized linear mixed models for longitudinal data assume that responses at different occasions are conditionally independent, given the random effects and covariates. Although this assumption is pivotal for consistent estimation, violation due to serial dependence is hard to assess by model elaboration. We therefore propose a targeted diagnostic test for serial dependence, called the transition model test (TMT), that is straightforward and computationally efficient to implement in standard software. The TMT is shown to have larger power than general misspecification tests. We also propose the targeted root mean squared error of approximation (TRSMEA) as a measure of the population misfit due to serial dependence.

scholarly journals An Improved Computationally Efficient Method for Finding the Drazin Inverse

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Haifa Bin Jebreen ◽  
Yurilev Chalco-Cano
Keyword(s):  
Efficient Method ◽  
Matrix Theory ◽  
Iterative Scheme ◽  
Drazin Inverse ◽  
Stability And Convergence ◽  
Computationally Efficient ◽  
Initial Matrix ◽  
The Matrix ◽  
The Stability

Drazin inverse is one of the most significant inverses in the matrix theory, where its computation is an intensive and useful task. The objective of this work is to propose a computationally effective iterative scheme for finding the Drazin inverse. The convergence is investigated analytically by applying a suitable initial matrix. The theoretical discussions are upheld by several experiments showing the stability and convergence of the proposed method.

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