Robust Filters for Intensive Care Monitoring: Beyond the Running Median

Current alarm systems on intensive care units create a very high rate of false positive alarms because most of them simply compare the physiological measurements to fixed thresholds. An improvement can be expected when the actual measurements are replaced by smoothed estimates of the underlying signal. However, classical filtering procedures are not appropriate for signal extraction as standard assumptions, like stationarity, do no hold here: the measured time series often show long periods without change, but also upward or downward trends, sudden shifts and numerous large measurement artefacts. Alternative approaches are needed to extract the relevant information from the data, i.e. the underlying signal of the monitored variables and the relevant patterns of change, like abrupt shifts and trends. This article reviews recent research on filter based online signal extraction methods which are designed for application in intensive care. --

BSA - exact algorithm computing LTS estimate

The main result of this paper is a new exact algorithm computing the estimate given by the Least Trimmed Squares (LTS). The algorithm works under very weak assumptions. To prove that, we study the respective objective function using basic techniques of analysis and linear algebra.Comment: 18 pages, 1 figur

Outlier Detection Using Nonconvex Penalized Regression

This paper studies the outlier detection problem from the point of view of penalized regressions. Our regression model adds one mean shift parameter for each of the $n$ data points. We then apply a regularization favoring a sparse vector of mean shift parameters. The usual $L_1$ penalty yields a convex criterion, but we find that it fails to deliver a robust estimator. The $L_1$ penalty corresponds to soft thresholding. We introduce a thresholding (denoted by $\Theta$) based iterative procedure for outlier detection ($\Theta$-IPOD). A version based on hard thresholding correctly identifies outliers on some hard test problems. We find that $\Theta$-IPOD is much faster than iteratively reweighted least squares for large data because each iteration costs at most $O(np)$ (and sometimes much less) avoiding an $O(np^2)$ least squares estimate. We describe the connection between $\Theta$-IPOD and $M$-estimators. Our proposed method has one tuning parameter with which to both identify outliers and estimate regression coefficients. A data-dependent choice can be made based on BIC. The tuned $\Theta$-IPOD shows outstanding performance in identifying outliers in various situations in comparison to other existing approaches. This methodology extends to high-dimensional modeling with $p\gg n$, if both the coefficient vector and the outlier pattern are sparse

The Factors of Growth of Small Family Businesses: A Robust Estimation of the Behavioral Consistency in the Panel Data Models

The paper quantifies the role of factors associated with the growth (or decline) of micro and small businesses in European economies. The growth is related to employment and value added in enterprises as well as to ten institutional variables. We test the data for consistency of behavioural patterns in various countries and gradually remove outlying observations, quite a unique a pproach in the panel data analysis, that can lead to erroneous conclusions when using the classical estimators. In the first part of this paper we outline a highly robust method of estimation based on fixed effects and least trimmed squares (LTS). In its second part we apply this method on the panel data of 28 countries in 2002-2008 testing for the hypothesis that micro and small businesses in Europe use different strategies for their growth. We run a series of econometric tests where we regress employment and total net production in micro and small businesses on three economic factors: gross capital returns, labour cost gaps in small relative to large enterprises and the GDP per capita. In addition, we also test the role of 10 institutional factors in the growth of familty businesses.Family business, robust estimator, LTS, fixed effects

ROBUST REGRESSION IN MONTHLY BUSINESS SURVEY

There are many sample surveys of populations that contain outliers (extreme values). This is especially true in business, agricultural, household and medicine surveys. Outliers can have a large distorting influence on classical statistical methods that are optimal under the assumption of normality or linearity. As a result, the presence of extreme observations may adversely affect estimation, especially when it is carried out at a low level of aggregation. To deal with this problem, several alternative techniques of estimation, less sensitive to outliers, have been proposed in the statistical literature. In this paper we attempt to apply and assess some robust regression methods (LTS, M estimation, S-estimation, MM-estimation) in the business survey conducted within the framework of official statistics

Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify PCA against outliers. A least-trimmed squares estimator of a low-rank bilinear factor analysis model is shown closely related to that obtained from an $\ell_0$-(pseudo)norm-regularized criterion encouraging sparsity in a matrix explicitly modeling the outliers. This connection suggests robust PCA schemes based on convex relaxation, which lead naturally to a family of robust estimators encompassing Huber's optimal M-class as a special case. Outliers are identified by tuning a regularization parameter, which amounts to controlling sparsity of the outlier matrix along the whole robustification path of (group) least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its neat ties to robust statistics, the developed outlier-aware PCA framework is versatile to accommodate novel and scalable algorithms to: i) track the low-rank signal subspace robustly, as new data are acquired in real time; and ii) determine principal components robustly in (possibly) infinite-dimensional feature spaces. Synthetic and real data tests corroborate the effectiveness of the proposed robust PCA schemes, when used to identify aberrant responses in personality assessment surveys, as well as unveil communities in social networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin

The least trimmed squares. Part III: Asymptotic normality

summary:Asymptotic normality of the least trimmed squares estimator is proved under general conditions. At the end of paper a discussion of applicability of the estimator (including the discussion of algorithm for its evaluation) is offered

Robust detail-preserving signal extraction

We discuss robust filtering procedures for signal extraction from noisy time series. Particular attention is paid to the preservation of relevant signal details like abrupt shifts. moving averages and running medians are widely used but have shortcomings when large spikes (outliers) or trends occur. Modifications like modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Better solutions can be based on robust regression techniques, which even work in real time because of increased computational power and faster algorithms. Reviewing previous work we present filters for robust signal extraction and discuss their merits for preserving trends, abrupt shifts and local extremes as well as for the removal of outliers. --

Robust multivariate methods in Chemometrics

This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the chapter builds up to the construction (and use) of robust alternatives for some methods for multivariate analysis frequently used in chemometrics, such as principal component analysis and partial least squares. The chapter then provides an insight into how these robust methods can be used or extended to classification. To conclude, the issue of validation of the results is being addressed: it is shown how uncertainty statements associated with robust estimates, can be obtained.Comment: This article is an update of: P. Filzmoser, S. Serneels, R. Maronna, P.J. Van Espen, 3.24 - Robust Multivariate Methods in Chemometrics, in Comprehensive Chemometrics, 1st Edition, edited by Steven D. Brown, Rom\'a Tauler, Beata Walczak, Elsevier, 2009, https://doi.org/10.1016/B978-044452701-1.00113-