Online Direct Density-Ratio Estimation Applied to Inlier-Based Outlier Detection

2015 ◽  
Vol 27 (9) ◽  
pp. 1899-1914
Author(s):  
Marthinus Christoffel du Plessis ◽  
Hiroaki Shiino ◽  
Masashi Sugiyama
Keyword(s):  
Outlier Detection ◽  
Density Estimation ◽  
Density Ratio ◽  
Learning Problems ◽  
Conditional Density ◽  
Ratio Estimation ◽  
Data Set ◽  
Step Procedure ◽  
Training Samples ◽  
Probability Densities

Many machine learning problems, such as nonstationarity adaptation, outlier detection, dimensionality reduction, and conditional density estimation, can be effectively solved by using the ratio of probability densities. Since the naive two-step procedure of first estimating the probability densities and then taking their ratio performs poorly, methods to directly estimate the density ratio from two sets of samples without density estimation have been extensively studied recently. However, these methods are batch algorithms that use the whole data set to estimate the density ratio, and they are inefficient in the online setup, where training samples are provided sequentially and solutions are updated incrementally without storing previous samples. In this letter, we propose two online density-ratio estimators based on the adaptive regularization of weight vectors. Through experiments on inlier-based outlier detection, we demonstrate the usefulness of the proposed methods.

Inlier-Based Outlier Detection via Direct Density Ratio Estimation

2008 ◽  
Author(s):  
Shohei Hido ◽  
Yuta Tsuboi ◽  
Hisashi Kashima ◽  
Masashi Sugiyama ◽  
Takafumi Kanamori
Keyword(s):  
Outlier Detection ◽  
Density Ratio ◽  
Ratio Estimation

Statistical outlier detection using direct density ratio estimation

2010 ◽  
Vol 26 (2) ◽  
pp. 309-336 ◽  
Author(s):  
Shohei Hido ◽  
Yuta Tsuboi ◽  
Hisashi Kashima ◽  
Masashi Sugiyama ◽  
Takafumi Kanamori
Keyword(s):  
Outlier Detection ◽  
Density Ratio ◽  
Ratio Estimation

Least-Squares Independent Component Analysis

2011 ◽  
Vol 23 (1) ◽  
pp. 284-301 ◽  
Author(s):  
Taiji Suzuki ◽  
Masashi Sugiyama
Keyword(s):  
Independent Component Analysis ◽  
Least Squares ◽  
Density Estimation ◽  
Regularization Parameter ◽  
Density Ratio ◽  
Estimation Method ◽  
Component Analysis ◽  
Independent Component ◽  
Probability Densities ◽  
Hyperparameter Selection

Accurately evaluating statistical independence among random variables is a key element of independent component analysis (ICA). In this letter, we employ a squared-loss variant of mutual information as an independence measure and give its estimation method. Our basic idea is to estimate the ratio of probability densities directly without going through density estimation, thereby avoiding the difficult task of density estimation. In this density ratio approach, a natural cross-validation procedure is available for hyperparameter selection. Thus, all tuning parameters such as the kernel width or the regularization parameter can be objectively optimized. This is an advantage over recently developed kernel-based independence measures and is a highly useful property in unsupervised learning problems such as ICA. Based on this novel independence measure, we develop an ICA algorithm, named least-squares independent component analysis.

scholarly journals Outlier Detection Transilience-Probabilistic Model for Wind Tunnels Based on Sensor Data

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2532
Author(s):  
Encarna Quesada ◽  
Juan J. Cuadrado-Gallego ◽  
Miguel Ángel Patricio ◽  
Luis Usero
Keyword(s):  
Anomaly Detection ◽  
Outlier Detection ◽  
Research Work ◽  
Industrial Sector ◽  
Sensor Data ◽  
Correct Selection ◽  
Wind Tunnels ◽  
Data Set ◽  
First Case ◽  
Anomaly Analysis

Anomaly Detection research is focused on the development and application of methods that allow for the identification of data that are different enough—compared with the rest of the data set that is being analyzed—and considered anomalies (or, as they are more commonly called, outliers). These values mainly originate from two sources: they may be errors introduced during the collection or handling of the data, or they can be correct, but very different from the rest of the values. It is essential to correctly identify each type as, in the first case, they must be removed from the data set but, in the second case, they must be carefully analyzed and taken into account. The correct selection and use of the model to be applied to a specific problem is fundamental for the success of the anomaly detection study and, in many cases, the use of only one model cannot provide sufficient results, which can be only reached by using a mixture model resulting from the integration of existing and/or ad hoc-developed models. This is the kind of model that is developed and applied to solve the problem presented in this paper. This study deals with the definition and application of an anomaly detection model that combines statistical models and a new method defined by the authors, the Local Transilience Outlier Identification Method, in order to improve the identification of outliers in the sensor-obtained values of variables that affect the operations of wind tunnels. The correct detection of outliers for the variables involved in wind tunnel operations is very important for the industrial ventilation systems industry, especially for vertical wind tunnels, which are used as training facilities for indoor skydiving, as the incorrect performance of such devices may put human lives at risk. In consequence, the use of the presented model for outlier detection may have a high impact in this industrial sector. In this research work, a proof-of-concept is carried out using data from a real installation, in order to test the proposed anomaly analysis method and its application to control the correct performance of wind tunnels.

scholarly journals Multivariate Tail Probabilities: Predicting Regional Pertussis Cases in Washington State

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 675
Author(s):  
Xuze Zhang ◽  
Saumyadipta Pyne ◽  
Benjamin Kedem
Keyword(s):  
Disease Modeling ◽  
Empirical Distribution ◽  
Density Ratio ◽  
Washington State ◽  
Ratio Model ◽  
Multiple Sources ◽  
Tail Probabilities ◽  
Data Set ◽  
Density Ratio Model ◽  
Regional Prediction

In disease modeling, a key statistical problem is the estimation of lower and upper tail probabilities of health events from given data sets of small size and limited range. Assuming such constraints, we describe a computational framework for the systematic fusion of observations from multiple sources to compute tail probabilities that could not be obtained otherwise due to a lack of lower or upper tail data. The estimation of multivariate lower and upper tail probabilities from a given small reference data set that lacks complete information about such tail data is addressed in terms of pertussis case count data. Fusion of data from multiple sources in conjunction with the density ratio model is used to give probability estimates that are non-obtainable from the empirical distribution. Based on a density ratio model with variable tilts, we first present a univariate fit and, subsequently, improve it with a multivariate extension. In the multivariate analysis, we selected the best model in terms of the Akaike Information Criterion (AIC). Regional prediction, in Washington state, of the number of pertussis cases is approached by providing joint probabilities using fused data from several relatively small samples following the selected density ratio model. The model is validated by a graphical goodness-of-fit plot comparing the estimated reference distribution obtained from the fused data with that of the empirical distribution obtained from the reference sample only.

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