Implementing de-biased estimators using mixed sequences

2020 ◽  
Vol 26 (4) ◽  
pp. 293-301
Author(s):  
Arun Kumar Polala ◽  
Giray Ökten
Keyword(s):  
Principal Component Analysis ◽  
Monte Carlo ◽  
Convergence Rates ◽  
Brownian Bridge ◽  
Principal Component ◽  
Computational Finance ◽  
Low Discrepancy Sequences ◽  
Biased Estimators ◽  
Monte Carlo Implementation ◽  
Better Than

AbstractWe describe an implementation of the de-biased estimator using mixed sequences; these are sequences obtained from pseudorandom and low-discrepancy sequences. We use this implementation to numerically solve some stochastic differential equations from computational finance. The mixed sequences, when combined with Brownian bridge or principal component analysis constructions, offer convergence rates significantly better than the Monte Carlo implementation.

scholarly journals COMPARISON OF FUZZY SUBTRACTIVE CLUSTERING AND FUZZYC-MEANS

Kursor ◽  
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Annisa Eka Haryati ◽  
Sugiyarto Sugiyarto ◽  
Rizki Desi Arindra Putri
Keyword(s):  
Principal Component Analysis ◽  
Fuzzy Clustering ◽  
Principal Component ◽  
Large Data ◽  
Component Analysis ◽  
Subtractive Clustering ◽  
Validity Index ◽  
Fuzzy Clustering Method ◽  
Dependent Variables ◽  
Better Than

Multivariate statistics have related problems with large data dimensions. One method that can be used is principal component analysis (PCA). Principal component analysis (PCA) is a technique used to reduce data dimensions consisting of several dependent variables while maintaining variance in the data. PCA can be used to stabilize measurements in statistical analysis, one of which is cluster analysis. Fuzzy clustering is a method of grouping based on membership values ​​that includes fuzzy sets as a weighting basis for grouping. In this study, the fuzzy clustering method used is Fuzzy Subtractive Clustering (FSC) and Fuzzy C-Means (FCM) with a combination of the Minkowski Chebysev distance. The purpose of this study was to compare the cluster results obtained from the FSC and FCM using the DBI validity index. The results obtained indicate that the results of clustering using FCM are better than the FSC.

A quasi-Monte Carlo implementation of the ziggurat method

2018 ◽  
Vol 24 (2) ◽  
pp. 93-99
Author(s):  
Nguyet Nguyen ◽  
Linlin Xu ◽  
Giray Ökten
Keyword(s):  
Monte Carlo ◽  
Random Variable ◽  
Numerical Results ◽  
Quasi Monte Carlo ◽  
Low Discrepancy Sequences ◽  
Gamma Distributions ◽  
Variable Generation ◽  
Monte Carlo Implementation

Abstract The ziggurat method is a fast random variable generation method introduced by Marsaglia and Tsang in a series of papers. We discuss how the ziggurat method can be implemented for low-discrepancy sequences, and present algorithms and numerical results when the method is used to generate samples from the normal and gamma distributions.

scholarly journals An Incremental Two-Dimensional Principal Component Analysis for Object Recognition

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Weimin Ge ◽  
Mingyue Sun ◽  
Xiaofeng Wang
Keyword(s):  
Principal Component Analysis ◽  
Feature Extraction ◽  
Object Recognition ◽  
Convergence Rates ◽  
Principal Component ◽  
Component Analysis ◽  
Video Stream ◽  
Two Dimensional ◽  
Batch Mode ◽  
Time Requirements

Two-dimensional principal component analysis algorithm (2DPCA) can be performed in the batch mode and can not meet the real-time requirements of the video stream. To overcome these limitations, the incremental learning of the candid covariance-free incremental PCA (CCIPCA) is innovated to the existing 2DPCA, and the called incremental 2DPCA (I2DPCA) is firstly presented to incrementally compute the principal components of a sequence of samples directly on the 2D image matrices without estimating the covariance matrices. Therefore, the I2DPCA can improve the feature extraction speed and reduce the required memory. However, the variations between the column direction, generally neglected, are also useful for the high-accuracy object recognition. Thus, another incremental sequential row-column 2DPCA algorithm (IRC2DPCA), based on the proposed I2DPCA algorithm, is also proposed. The IRC2DPCA can compress the image matrices in the row and column direction, and the feature matrices extracted by the IRC2DPCA are with less dimensions than the I2DPCA. The substantial experimental results show that the IRC2DPCA, compared with the other three algorithms, can improve the convergence rates and the recognition rates, compress the dimensions of the feature matrices, and reduce the feature extraction time and the classification time.

Quantitative measurement of complex substances dissolved in an ionic liquid using IR spectroscopy and chemometrics

2017 ◽  
Vol 84 (1) ◽  
Author(s):  
Johannes Kiefer ◽  
Andreas Bösmann ◽  
Peter Wasserscheid
Keyword(s):  
Principal Component Analysis ◽  
Ionic Liquid ◽  
Principal Component Regression ◽  
Principal Component ◽  
Component Analysis ◽  
Least Squares Regression ◽  
Catalytically Active ◽  
Regression Techniques ◽  
Active Substances ◽  
Better Than

AbstractIn the past two decades, ionic liquids have found many applications as solvents for complex solutes. Prominent examples are the dissolution of biomass and carbohydrates as well as catalytically active substances. The chemical analysis of such solutions, however, is still a challenge due to the molecular complexity. In the present work, the use of infrared spectroscopy for quantifying the concentration of different solutes dissolved in an imidazolium-based ionic liquid is investigated. Binary solutions of glucose, cellubiose, and Wilkinson's catalyst in 1-ethyl-3-methylimidazolium acetate are studied as examples. For this purpose, different chemometric approaches (principal component analysis (PCA), partial least-squares regression (PLSR), and principal component regression (PCR)) for analyzing the spectra are tested. Principal component analysis was found to be suitable for classifying the different solutions. Both regression techniques were capable of deriving accurate concentration values. The performance of PLSR was slightly better than that of PCR for the same number of components.

scholarly journals Integral estimation based on Markovian design

2018 ◽  
Vol 50 (3) ◽  
pp. 833-857 ◽  
Author(s):  
Romain Azaïs ◽  
Bernard Delyon ◽  
François Portier
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Convergence Rates ◽  
Finite Sample ◽  
Integration Methods ◽  
Average Value ◽  
Average Temperature ◽  
Integral Estimation ◽  
History Of ◽  
Better Than

AbstractSuppose that a mobile sensor describes a Markovian trajectory in the ambient space and at each time the sensor measures an attribute of interest, e.g. the temperature. Using only the location history of the sensor and the associated measurements, we estimate the average value of the attribute over the space. In contrast to classical probabilistic integration methods, e.g. Monte Carlo, the proposed approach does not require any knowledge of the distribution of the sensor trajectory. We establish probabilistic bounds on the convergence rates of the estimator. These rates are better than the traditional `rootn'-rate, wherenis the sample size, attached to other probabilistic integration methods. For finite sample sizes, we demonstrate the favorable behavior of the procedure through simulations and consider an application to the evaluation of the average temperature of oceans.

scholarly journals Anomaly Detection in Photovoltaic Production Factories via Monte Carlo Pre-Processed Principal Component Analysis

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3951
Author(s):  
Eleonora Arena ◽  
Alessandro Corsini ◽  
Roberto Ferulano ◽  
Dario Alfio Iuvara ◽  
Eric Stefan Miele ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Monte Carlo ◽  
Anomaly Detection ◽  
Principal Component ◽  
Component Analysis ◽  
Operating Conditions ◽  
Production Plant ◽  
Use Case ◽  
Model Errors ◽  
Unseen Data

This paper investigates a use case of robust anomaly detection applied to the scenario of a photovoltaic production factory—namely, Enel Green Power’s 3SUN solar cell production plant in Catania, Italy—by considering a Monte Carlo based pre-processing technique as a valid alternative to other typically used methods. In particular, the proposed method exhibits the following advantages: (i) Outlier replacement, by contrast with traditional methods which are limited to outlier detection only, and (ii) the preservation of temporal locality with respect to the training dataset. After pre-processing, the authors trained an anomaly detection model based on principal component analysis and defined a suitable key performance indicator for each sensor in the production line based on the model errors. In this way, by running the algorithm on unseen data streams, it is possible to isolate anomalous conditions by monitoring the above-mentioned indicators and virtually trigger an alarm when exceeding a reference threshold. The proposed approach was tested on both standard operating conditions and an anomalous scenario. With respect to the considered use case, it successfully anticipated a fault in the equipment with an advance of almost two weeks, but also demonstrated its robustness to false alarms during normal conditions.

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