arXiv subjects

Joni Virta

Publications and source records attributed to Joni Virta.

At least 19 recordsLinked to original sources

arXiv2026

Model-based sparse mixed-type PCA

This work presents a new method for principal component analysis (PCA) of a mixed-type data consisting of continuous, binary, integer-valued and positive continuous variables. The data are assumed to come from a probability model, where the parameters of the exponential family distributions are determined by a set of shared Gaussian latent variables. The proposed method, MTPCA, is based on estimating the covariance matrix of these latent mixtures through the method of moments. A way to sparsify the component loadings is presented and aligns with the classical theory of sparse PCA. We propose a strategy for estimating the principal component scores and discuss the choice of the latent dimension. The method's performance is studied with a simulated mixed-type data and we illustrate the model on the Zoo data set consisting of binary animal characteristics.

stat.ME↗

arXiv2026

Data anonymization in the presence of outliers via invariant coordinate selection

Protecting confidential data while preserving utility is particularly challenging when data sets contain outlying observations. Existing latent space anonymization methods, such as spectral anonymization (SA), rely on principal component analysis (PCA) and may therefore be vulnerable to contamination. We investigate anonymization in the presence of outliers and propose ICSA, a robust alternative to SA based on invariant coordinate selection (ICS). By replacing the PCA transformation with ICS, the robustness of the anonymization procedure can be regulated through the choice of scatter matrices. Alongside the methodological development, we derive a theoretical result showing that SA fails under sufficiently influential outliers. To assess the practical implications of this result, we compare the privacy-utility trade-off of ICSA and SA through simulation experiments under varying contamination settings and outlier severities. Our findings indicate that implementations of ICSA based on robust scatter matrices achieve stronger privacy protection than SA, while typically maintaining comparable, and in some cases improved, utility. We further examine the empirical performance of the proposed method using a benchmark clinical data set, where ICSA demonstrates superior overall privacy-utility efficiency relative to SA. These results suggest that explicitly accounting for outliers can materially improve anonymization performance and that robust latent space transformations offer a promising direction for privacy-preserving statistical data release.

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arXiv2026

Evaluation metrics for temporal preservation in synthetic longitudinal patient data

This study introduces a set of metrics for evaluating temporal preservation in synthetic longitudinal patient data, defined as artificially generated data that mimic real patients' repeated measurements over time. The proposed metrics assess how synthetic data reproduces key temporal characteristics, categorized into marginal, covariance, individual-level and measurement structures. We show that strong marginal-level resemblance may conceal distortions in covariance and disruptions in individual-level trajectories. Temporal preservation is influenced by factors such as original data quality, measurement frequency, and preprocessing strategies, including binning, variable encoding and precision. Variables with sparse or highly irregular measurement times provide limited information for learning temporal dependencies, resulting in reduced resemblance between the synthetic and original data. No single metric adequately captures temporal preservation; instead, a multidimensional evaluation across all characteristics provides a more comprehensive assessment of synthetic data quality. Overall, the proposed metrics clarify how and why temporal structures are preserved or degraded, enabling more reliable evaluation and improvement of generative models and supporting the creation of temporally realistic synthetic longitudinal patient data.

cs.LG↗

arXiv2026

Asymptotic testing of covariance separability for matrix elliptical data

We propose a new asymptotic test for the separability of a covariance matrix. The null distribution is valid in wide matrix elliptical model that includes, in particular, both matrix Gaussian and matrix $t$-distribution. The test is fast to compute and makes no assumptions about the component covariance matrices. An alternative, Wald-type version of the test is also proposed. Our simulations reveal that both versions of the test have good power even for heavier-tailed distributions and can compete with the Gaussian likelihood ratio test in the case of normal data.

math.ST↗

arXiv2025

New M-estimator of the leading principal component

We study the minimization of the non-convex and non-differentiable objective function $v \mapsto \mathrm{E} ( \| X - v \| \| X + v \| - \| X \|^2 )$ in $\mathbb{R}^p$. In particular, we show that its minimizers recover the first principal component direction of elliptically symmetric $X$ under specific conditions. The stringency of these conditions is studied in various scenarios, including a diverging number of variables $p$. We establish the consistency and asymptotic normality of the sample minimizer. We propose a Weiszfeld-type algorithm for optimizing the objective and show that it is guaranteed to converge in a finite number of steps. The results are illustrated with two simulations.

math.ST↗

arXiv2025

Unsupervised linear discrimination using skewness

It is well-known that, in Gaussian two-group separation, the optimally discriminating projection direction can be estimated without any knowledge on the group labels. In this work, we \revision{gather} several such unsupervised estimators based on skewness and derive their limiting distributions. As one of our main results, we show that all affine equivariant estimators of the optimal direction have proportional asymptotic covariance matrices, making their comparison straightforward. Two of our four estimators are novel and two have been proposed already earlier. We use simulations to verify our results and to inspect the finite-sample behaviors of the estimators.

math.ST↗

arXiv2025

Dimension estimation in PCA model using high-dimensional data augmentation

We propose a modified, high-dimensional version of a recent dimension estimation procedure that determines the dimension via the introduction of augmented noise variables into the data. Our asymptotic results show that the proposal is consistent in wide high-dimensional scenarios, and further shed light on why the original method breaks down when the dimension of either the data or the augmentation becomes too large. Simulations are used to demonstrate the superiority of the proposal to competitors both under and outside of the theoretical model.

math.ST↗

arXiv2025

A method for sparse and robust independent component analysis

This work presents sparse invariant coordinate selection, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate selection, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent component analysis, are carefully introduced. Then the proposed new method and its algorithm are derived and presented. This part also includes consistency and breakdown point results for a general case of sparse ICS-like methods. The performance of SICS in identifying sparse independent component loadings is investigated with multiple simulations. The method is illustrated with an example in constructing sparse causal graphs and we also propose a graphical tool for selecting the appropriate sparsity level in SICS.

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arXiv2024

Metric Oja Depth, New Statistical Tool for Estimating the Most Central Objects

The Oja depth (simplicial volume depth) is one of the classical statistical techniques for measuring the central tendency of data in multivariate space. Despite the widespread emergence of object data like images, texts, matrices or graphs, a well-developed and suitable version of Oja depth for object data is lacking. To address this shortcoming, a novel measure of statistical depth, the metric Oja depth applicable to any object data, is proposed. Two competing strategies are used for optimizing metric depth functions, i.e., finding the deepest objects with respect to them. The performance of the metric Oja depth is compared with three other depth functions (half-space, lens, and spatial) in diverse data scenarios. Keywords: Object Data, Metric Oja depth, Statistical depth, Optimization, Metric statistics

stat.ME↗

arXiv2024

Asymptotic utility of spectral anonymization

In the contemporary data landscape characterized by multi-source data collection and third-party sharing, ensuring individual privacy stands as a critical concern. While various anonymization methods exist, their utility preservation and privacy guarantees remain challenging to quantify. In this work, we address this gap by studying the utility and privacy of the spectral anonymization (SA) algorithm, particularly in an asymptotic framework. Unlike conventional anonymization methods that directly modify the original data, SA operates by perturbing the data in a spectral basis and subsequently reverting them to their original basis. Alongside the original version $\mathcal{P}$-SA, employing random permutation transformation, we introduce two novel SA variants: $\mathcal{J}$-spectral anonymization and $\mathcal{O}$-spectral anonymization, which employ sign-change and orthogonal matrix transformations, respectively. We show how well, under some practical assumptions, these SA algorithms preserve the first and second moments of the original data. Our results reveal, in particular, that the asymptotic efficiency of all three SA algorithms in covariance estimation is exactly 50% when compared to the original data. To assess the applicability of these asymptotic results in practice, we conduct a simulation study with finite data and also evaluate the privacy protection offered by these algorithms using distance-based record linkage. Our research reveals that while no method exhibits clear superiority in finite-sample utility, $\mathcal{O}$-SA distinguishes itself for its exceptional privacy preservation, never producing identical records, albeit with increased computational complexity. Conversely, $\mathcal{P}$-SA emerges as a computationally efficient alternative, demonstrating unmatched efficiency in mean estimation.

cs.CR↗

arXiv2024

On the distribution of isometric log-ratio transformations under extra-multinomial count data

Compositional data arise when count observations are normalised into proportions adding up to unity. To allow use of standard statistical methods, compositional proportions can be mapped from the simplex into the Euclidean space through the isometric log-ratio (ilr) transformation. When the counts follow a multinomial distribution with fixed class-specific probabilities, the distribution of the ensuing ilr coordinates has been shown to be asymptotically multivariate normal. We here derive an asymptotic normal approximation to the distribution of the ilr coordinates when the counts show overdispersion under the Dirichlet-multinomial mixture model. Using a simulation study, we then investigate the practical applicability of the approximation against the empirical distribution of the ilr coordinates under varying levels of extra-multinomial variation and the total count. The approximation works well, except with a small total count or high amount of overdispersion. These empirical results remain even under population-level heterogeneity in the total count. Our work is motivated by microbiome data, which often exhibit considerable extra-multinomial variation and are increasingly treated as compositional through scaling taxon-specific counts into proportions. We conclude that if the analysis of empirical data relies on normality of the ilr coordinates, it may be advisable to choose a taxonomic level where counts are less sparse so that the distribution of taxon-specific class probabilities remains unimodal.

stat.ME↗

arXiv2023

Measure of shape for object data

Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The object shape is easy to compute and interpret, owing to its intuitive interpretation as interpolation between two extreme forms of symmetry. As one major part of this work, we apply object shape in various metric spaces and show that it manages to unify several pre-existing, classical forms of symmetry. We also propose a new visualization tool called the peeling plot, which allows using the object shape for outlier detection and principal component analysis of object data.

math.ST↗

arXiv2023

Structure-preserving non-linear PCA for matrices

We propose MNPCA, a novel non-linear generalization of (2D)$^2${PCA}, a classical linear method for the simultaneous dimension reduction of both rows and columns of a set of matrix-valued data. MNPCA is based on optimizing over separate non-linear mappings on the left and right singular spaces of the observations, essentially amounting to the decoupling of the two sides of the matrices. We develop a comprehensive theoretical framework for MNPCA by viewing it as an eigenproblem in reproducing kernel Hilbert spaces. We study the resulting estimators on both population and sample levels, deriving their convergence rates and formulating a coordinate representation to allow the method to be used in practice. Simulations and a real data example demonstrate MNPCA's good performance over its competitors.

math.ST↗

arXiv2023

Methods for generating and evaluating synthetic longitudinal patient data: a systematic review

The rapid growth in data availability has facilitated research and development, yet not all industries have benefited equally due to legal and privacy constraints. The healthcare sector faces significant challenges in utilizing patient data because of concerns about data security and confidentiality. To address this, various privacy-preserving methods, including synthetic data generation, have been proposed. Synthetic data replicate existing data as closely as possible, acting as a proxy for sensitive information. While patient data are often longitudinal, this aspect remains underrepresented in existing reviews of synthetic data generation in healthcare. This paper maps and describes methods for generating and evaluating synthetic longitudinal patient data in real-life settings through a systematic literature review, conducted following the PRISMA guidelines and incorporating data from five databases up to May 2024. Thirty-nine methods were identified, with four addressing all challenges of longitudinal data generation, though none included privacy-preserving mechanisms. Resemblance was evaluated in most studies, utility in the majority, and privacy in just over half. Only a small fraction of studies assessed all three aspects. Our findings highlight the need for further research in this area.

stat.ME↗

arXiv2023

Spatial depth for data in metric spaces

We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution, allowing quantifying their centrality/outlyingness. This depth measure is shown to have highly interpretable geometric properties, making it appealing in object data analysis where standard descriptive statistics are difficult to compute. The proposed measure reduces to the classical spatial depth in a Euclidean space. In addition to studying its theoretical properties, to provide intuition on the concept, we explicitly compute metric spatial depths in several different metric spaces. Finally, we showcase the practical usefulness of the metric spatial depth in outlier detection, non-convex depth region estimation and classification.

math.ST↗

arXiv2022

Large-Sample Properties of Non-Stationary Source Separation for Gaussian Signals

Non-stationary source separation is a well-established branch of blind source separation with many different methods. However, for none of these methods large-sample results are available. To bridge this gap, we develop large-sample theory for NSS-JD, a popular method of non-stationary source separation based on the joint diagonalization of block-wise covariance matrices. We work under an instantaneous linear mixing model for independent Gaussian non-stationary source signals together with a very general set of assumptions: besides boundedness conditions, the only assumptions we make are that the sources exhibit finite dependency and that their variance functions differ sufficiently to be asymptotically separable. The consistency of the unmixing estimator and its convergence to a limiting Gaussian distribution at the standard square root rate are shown to hold under the previous conditions. Simulation experiments are used to verify the theoretical results and to study the impact of block length on the separation.

math.ST↗

arXiv2022

Order Determination for Tensor-valued Observations Using Data Augmentation

Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated procedure for the optimal selection of the reduced dimensionality. Our approach combines a recently proposed data augmentation procedure with the higher-order singular value decomposition (HOSVD) in a tensorially natural way. We give theoretical guidelines on how to choose the tuning parameters and further inspect their influence in a simulation study. As our primary result, we show that the procedure consistently estimates the true latent dimensions under a noisy tensor model, both at the population and sample levels. Additionally, we propose a bootstrap-based alternative to the augmentation estimator. Simulations are used to demonstrate the estimation accuracy of the two methods under various settings.

stat.ME↗

arXiv2022

Sliced Inverse Regression in Metric Spaces

In this article, we propose a general nonlinear sufficient dimension reduction (SDR) framework when both the predictor and response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces whose kernels are fully determined by the distance functions of the metric spaces, then leverage the inherent structures of these spaces to define a nonlinear SDR framework. We adapt the classical sliced inverse regression of \citet{Li:1991} within this framework for the metric space data. We build the estimator based on the corresponding linear operators, and show it recovers the regression information unbiasedly. We derive the estimator at both the operator level and under a coordinate system, and also establish its convergence rate. We illustrate the proposed method with both synthetic and real datasets exhibiting non-Euclidean geometry.

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