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Claudio Agostinelli

Publications and source records attributed to Claudio Agostinelli.

35 records · Page 2Linked to original sources
arXiv2021

Robust Multivariate Estimation Based On Statistical Depth Filters

In the classical contamination models, such as the gross-error (Huber and Tukey contamination model or Case-wise Contamination), observations are considered as the units to be identified as outliers or not. This model is very useful when the number of considered variables is moderately small. Alqallaf et al. [2009] shows the limits of this approach for a larger number of variables and introduced the Independent contamination model (Cell-wise Contamination) where now the cells are the units to be identified as outliers or not. One approach to deal, at the same time, with both type of contamination is filter out the contaminated cells from the data set and then apply a robust procedure able to handle case-wise outliers and missing values. Here we develop a general framework to build filters in any dimension based on statistical data depth functions. We show that previous approaches, e.g. Agostinelli et al. [2015a] and Leung et al. [2017], are special cases. We illustrate our method by using the half-space depth.

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arXiv2020

Robust Estimation for Multivariate Wrapped Models

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise inference for standard techniques such as maximum likelihood method. Therefore, there is the need to handle such model inadequacies in the fitting process by a robust technique and an effective down-weighting of observations not following the assumed model. Furthermore, the employ of a robust method could help in situations of hidden and unexpected substructures in the data. Here, it is suggested to build a set of data-dependent weights based on the Pearson residuals and solve the corresponding weighted likelihood estimating equations. In particular, robust estimation is carried out by using a Classification EM algorithm whose M-step is enhanced by the computation of weights based on current parameters' values. The finite sample behavior of the proposed method has been investigated by a Monte Carlo numerical studies and real data examples.

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arXiv2020

Robust Estimation under Linear Mixed Models: The Minimum Density Power Divergence Approach

Many real-life data sets can be analyzed using Linear Mixed Models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measures the discrepancy between two probability density functions, has been successfully used to build robust estimators with high stability associated with minimal loss in efficiency. Here, we develop the minimum DPD estimator (MDPDE) for independent but non identically distributed observations in LMMs. We prove the theoretical properties, including consistency and asymptotic normality. The influence function and sensitivity measures are studied to explore the robustness properties. As a data based choice of the MDPDE tuning parameter $α$ is very important, we propose two candidates as "optimal" choices, where optimality is in the sense of choosing the strongest downweighting that is necessary for the particular data set. We conduct a simulation study comparing the proposed MDPDE, for different values of $α$, with the S-estimators, M-estimators and the classical maximum likelihood estimator, considering different levels of contamination. Finally, we illustrate the performance of our proposal on a real-data example.

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arXiv2019

Network depth: identifying median and contours in complex networks

Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be considered as the `centre' of a complex network. In fact, this problem corresponds to finding the median of a complex network. The median is a non-parametric and robust estimator of the location parameter of a probability distribution. In this work, we present the most natural generalisation of the concept of median to the realm of complex networks, discussing its advantages for defining the centre of the system and percentiles around that centre. To this aim, we introduce a new statistical data depth and we apply it to networks embedded in a geometric space induced by different metrics. The application of our framework to empirical networks allows us to identify median nodes which are socially or biologically relevant.

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arXiv2018

Estimation of Multivariate Wrapped Models for Data in Torus

Multivariate circular observations, i.e. points on a torus are nowadays very common. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, statistical inference based on this model is quite complicated since each contribution in the log likelihood involve an infinite sum of indices in Z^p where p is the dimension of the problem. To overcome this, two estimates procedures based on Expectation Maximization and Classification Expectation Maximization algorithms are proposed that worked well in moderate dimension size. The performance of the introduced methods are studied by Monte Carlo simulation and illustrated on three real data sets.

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arXiv2018

Weighted likelihood mixture modeling and model based clustering

A weighted likelihood approach for robust fitting of a mixture of multivariate Gaussian components is developed in this work. Two approaches have been proposed that are driven by a suitable modification of the standard EM and CEM algorithms, respectively. In both techniques, the M-step is enhanced by the computation of weights aimed at downweighting outliers. The weights are based on Pearson residuals stemming from robust Mahalanobis-type distances. Formal rules for robust clustering and outlier detection can be also defined based on the fitted mixture model. The behavior of the proposed methodologies has been investigated by some numerical studies and real data examples in terms of both fitting and classification accuracy and outlier detection.

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arXiv2018

A Weighted Likelihood Approach Based on Statistical Data Depths

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model with that of the sample in a given point. Observations are considered regular when the ratio of these two depths is close to one, whereas, when the ratio is large the corresponding score contribution may be downweigthed. Details and examples are provided for the robust estimation of the parameters in the multivariate normal model. Because of the form of the weights, we expect that, there will be no downweighting under the true model leading to highly efficient estimators. Robustness is illustrated using two real data sets.

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arXiv2018

Robust estimation in single index models when the errors have a unimodal density with unknown nuisance parameter

In this paper, we propose a robust profile estimation method for the parametric and nonparametric components of a single index model when the errors have a strongly unimodal density with unknown nuisance parameter. Under regularity conditions, we derive consistency results for the link function estimators as well as consistency and asymptotic distribution results for the single index parameter estimators. Under a log--Gamma model, the sensitivity to anomalous observations is studied by means of the empirical influence curve. We also discuss a robust $K-$fold procedure to select the smoothing parameters involved. A numerical study is conducted to evaluate the small sample performance of the robust proposal with that of their classical relatives, both for errors following a log--Gamma model and for contaminated schemes. The numerical experiment shows the good robustness properties of the proposed estimators and the advantages of considering a robust approach instead of the classical one.

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arXiv2017

Convolutional neural networks for structured omics: OmicsCNN and the OmicsConv layer

Convolutional Neural Networks (CNNs) are a popular deep learning architecture widely applied in different domains, in particular in classifying over images, for which the concept of convolution with a filter comes naturally. Unfortunately, the requirement of a distance (or, at least, of a neighbourhood function) in the input feature space has so far prevented its direct use on data types such as omics data. However, a number of omics data are metrizable, i.e., they can be endowed with a metric structure, enabling to adopt a convolutional based deep learning framework, e.g., for prediction. We propose a generalized solution for CNNs on omics data, implemented through a dedicated Keras layer. In particular, for metagenomics data, a metric can be derived from the patristic distance on the phylogenetic tree. For transcriptomics data, we combine Gene Ontology semantic similarity and gene co-expression to define a distance; the function is defined through a multilayer network where 3 layers are defined by the GO mutual semantic similarity while the fourth one by gene co-expression. As a general tool, feature distance on omics data is enabled by OmicsConv, a novel Keras layer, obtaining OmicsCNN, a dedicated deep learning framework. Here we demonstrate OmicsCNN on gut microbiota sequencing data, for Inflammatory Bowel Disease (IBD) 16S data, first on synthetic data and then a metagenomics collection of gut microbiota of 222 IBD patients.

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arXiv2017

Robust Estimation in High Dimensional Generalized Linear Models

Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust procedures are presented in the literature but they need a robust initial estimate in order to be computed. This is especially important for robust procedures with non convex loss function such as redescending M-estimators. Subsampling techniques are often used to determine a robust initial estimate; however when the number of unknown parameters is large the number of subsamples needed in order to have a high probability of having one subsample free of outliers become infeasible. Furthermore the subsampling procedure provides a non deterministic starting point. Based on ideas in Pena and Yohai (1999), we introduce a deterministic robust initial estimate for M-estimators based on transformations Valdora and Yohai (2014) for which we also develop an iteratively reweighted least squares algorithm. The new methods are studied by Monte Carlo experiments.

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arXiv2017

Phylogenetic Convolutional Neural Networks in Metagenomics

Background: Convolutional Neural Networks can be effectively used only when data are endowed with an intrinsic concept of neighbourhood in the input space, as is the case of pixels in images. We introduce here Ph-CNN, a novel deep learning architecture for the classification of metagenomics data based on the Convolutional Neural Networks, with the patristic distance defined on the phylogenetic tree being used as the proximity measure. The patristic distance between variables is used together with a sparsified version of MultiDimensional Scaling to embed the phylogenetic tree in a Euclidean space. Results: Ph-CNN is tested with a domain adaptation approach on synthetic data and on a metagenomics collection of gut microbiota of 38 healthy subjects and 222 Inflammatory Bowel Disease patients, divided in 6 subclasses. Classification performance is promising when compared to classical algorithms like Support Vector Machines and Random Forest and a baseline fully connected neural network, e.g. the Multi-Layer Perceptron. Conclusion: Ph-CNN represents a novel deep learning approach for the classification of metagenomics data. Operatively, the algorithm has been implemented as a custom Keras layer taking care of passing to the following convolutional layer not only the data but also the ranked list of neighbourhood of each sample, thus mimicking the case of image data, transparently to the user. Keywords: Metagenomics; Deep learning; Convolutional Neural Networks; Phylogenetic trees

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arXiv2017

Weighted likelihood estimation of multivariate location and scatter

A novel approach to obtain weighted likelihood estimates of multivariate location and scatter is discussed. A weighting scheme is proposed that is based on the distribution of the Mahalanobis distances rather than the distribution of the data at the assumed model. This strategy allows to avoid the curse of dimensionality affecting non-parametric density estimation, that is involved in the construction of the weights through the Pearson residuals Markatou et al (1998). Then, weighted likelihood based outlier detection rules and robust dimensionality reduction techniques are developed. The effectiveness of the methodology is illustrated through some numerical studies and real data examples.

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arXiv2016

Local Half-Region Depth for Functional Data

Data depth proves successful in the analysis of multivariate data sets, in particular deriving an overall center and assigning ranks to the observed units. Two key features are: the directions of the ordering, from the center towards the outside, and the recognition of a unique center irrespective of the distribution being unimodal or multimodal. This behaviour is a consequence of the monotonicity of the ranks that decrease along any ray from the deepest point. Recently, a wider framework allowing identification of partial centers was suggested in Agostinelli and Romanazzi [2011]. The corresponding generalized depth functions, called local depth functions are able to record local fluctuations and can be used in mode detection, identification of components in mixture models and in cluster analysis. Functional data [Ramsay and Silverman, 2006] are become common nowadays. Recently, Lopez-Pintado and Romo [2011] has proposed the half-region depth suited for functional data and for high dimensional data. Here, following their work we propose a local version of this data depth, we study its theoretical properties and illustrate its behaviour with examples based on real data sets.

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arXiv2015

Robust estimators of accelerated failure time regression with generalized log-gamma errors

The generalized log-gamma (GLG) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology. In this paper, we propose estimators which are simultaneously highly robust and highly efficient for the parameters of a GLG distribution in the presence of censoring. We also introduced estimators with the same properties for accelerated failure time models with censored observations and error distribution belonging to the GLG family. We prove that the proposed estimators are asymptotically fully efficient and examine the maximum mean square error using Monte Carlo simulations. The simulations confirm that the proposed estimators are highly robust and highly efficient for finite sample size. Finally, we illustrate the good behavior of the proposed estimators with two real datasets.

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arXiv2014

Composite Robust Estimators for Linear Mixed Models

The Classical Tukey-Huber Contamination Model (CCM) is a usual framework to describe the mechanism of outliers generation in robust statistics. In a data set with $n$ observations and $p$ variables, under the CCM, an outlier is a unit, even if only one or few values are corrupted. Classical robust procedures were designed to cope with this setting and the impact of observations were limited whenever necessary. Recently, a different mechanism of outliers generation, namely Independent Contamination Model (ICM), was introduced. In this new setting each cell of the data matrix might be corrupted or not with a probability independent on the status of the other cells. ICM poses new challenge to robust statistics since the percentage of contaminated rows dramatically increase with $p$, often reaching more than $50\%$. When this situation appears, classical affine equivariant robust procedures do not work since their breakdown point is $50\%$. For this contamination model we propose a new type of robust methods namely composite robust procedures which are inspired on the idea of composite likelihood, where low dimension likelihood, very often the likelihood of pairs, are aggregate together in order to obtain an approximation of the full likelihood which is more tractable. Our composite robust procedures are build over pairs of observations in order to gain robustness in the independent contamination model. We propose composite S and $τ$-estimators for linear mixed models. Composite $τ$-estimators are proved to have an high breakdown point both in the CCM and ICM. A Monte Carlo study shows that our estimators compare favorably with respect to classical S-estimators under the CCM and outperform them under the ICM. One example based on a real data set illustrates the new robust procedure.

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arXiv2014

Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination

Multivariate location and scatter matrix estimation is a cornerstone in multivariate data analysis. We consider this problem when the data may contain independent cellwise and casewise outliers. Flat data sets with a large number of variables and a relatively small number of cases are common place in modern statistical applications. In these cases global down-weighting of an entire case, as performed by traditional robust procedures, may lead to poor results. We highlight the need for a new generation of robust estimators that can efficiently deal with cellwise outliers and at the same time show good performance under casewise outliers.

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