Paper extends multivariate rank tests for robust subspace detection.
problem Testing distributional similarity in multivariate data.
method Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport.
result Trade-off between detection power and false alarm rate via projections.
We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks by the average value and generalise Spearman's ρto extreme ranks. Our main …
New method improves calibration in multi-output probabilistic models.
problem Challenges in achieving multivariate calibration in multi-output regression.
method General regularization framework to enforce multivariate calibration during training for arbitrary pre-rank functions.
result Significant improvement in calibration across all pre-rank functions without sacrificing predictive accuracy.
New GoF test improves change point detection in multivariate time series.
problem Detecting changes in multivariate time series data efficiently and robustly.
method Developed a novel multivariate rank-energy GoF test (sRE) for change point detection.
result sRE-based CPD outperforms existing methods in AUC and F1-score.
Identifies interpretable generative model for multivariate data.
problem Black-box architectures of deep generative models are often unidentified and difficult to interpret.
method Introduces Deep Discrete Encoder (DDE) Copula, a hierarchical binary latent variable model inside a copula framework.
result Establishes conditions for identification of DDE copula parameters and proves posterior consistency.
Proposes a method to identify subgroup structure and estimate covariate effects for multivariate response data.
problem Identifying subgroup structure and estimating covariate effects in multivariate response data.
method Joint heterogeneity and reduced-rank learning framework using rank-constrained pairwise fusion penalization.
result Established the asymptotic properties of the estimators and proposed a predictive information criterion for rank selection.
OTCP extends conformal prediction to multivariate data using optimal transport.
problem Uncertainty quantification in multivariate machine learning models.
method OTCP leverages optimal transport to rank multivariate conformity scores.
result Preserves distribution-free coverage guarantees in multidimensional settings.
A new model detects and localizes anomalies in multivariate time series data.
problem Anomaly diagnosis in multivariate time series data, especially localization.
method Attention Low-Rank Transformer (ALoRa-T) with low-rank regularization and Attention Low-Rank score.
result The proposed method significantly outperforms state-of-the-art methods in anomaly detection and localization.
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sp…
CRL framework groups features for multivariate learning with sparse and dense problems.
problem Sparse and dense problems in supervised multivariate learning.
method Clustered reduced-rank learning (CRL) with joint matrix regularizations.
result CRL framework is more interpretable and relaxes sparsity assumption.
Proposes a new method for multivariate functional regression.
problem Multivariate functional regression with complex relationships.
method Nested reduced-rank regularization (NRRR) approach.
result Consistent and effective in fitting multivariate functional regression models.
This work tackles multivariate CDFs and copulas using tensor factorization.
problem Learning multivariate distributions, especially for mixed random variables, is challenging.
method Introducing a low-rank model for efficient sampling, inference, and uncertainty quantification.
result The proposed model outperforms traditional methods in various applications.
TSRGA scales multivariate linear regression for feature-distributed data.
problem Multivariate linear regression for feature-distributed data with high dimensions and many computing nodes.
method Two-stage relaxed greedy algorithm (TSRGA) for multivariate linear regression.
result TSRGA is highly scalable and can yield low-rank coefficient estimates.
Improved GoF statistics using entropy-regularized optimal transport for multivariate rank.
problem Developing efficient multivariate rank statistics for statistical testing and generative modeling.
method Entropy-regularized optimal transport maps to address computational and sample complexity issues.
result Proposed soft rank energy and maximum mean discrepancy achieve fast convergence rates and are differentiable.
This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-partic…
Neural optimal transport improves multivariate conformal prediction.
problem Multivariate quantile regression challenges and existing methods ignore joint distribution geometry.
method Combines neural optimal transport with amortized optimization for efficient training and faster inference.
result Constructs tighter and more informative predictive regions for multivariate conformal prediction.
New algorithms select and rank features from MTS without feature extraction.
problem Feature extraction step for MTS classification.
method Directly computes similarity between time series and assesses cluster structure matching labels.
result Techniques match labels well without feature extraction.
Paper proposes LATC for multivariate time series prediction and missing data imputation.
problem Large-scale, incomplete, and corrupted multivariate time series data.
method Transforms multivariate time series into a tensor structure, models global and local trends, and uses autoregressive norm.
result Integration of global and local trends improves missing data imputation and rolling prediction.
Paper studies quantized LRMR with random dithering for correlated tasks.
problem Estimating coefficient matrix in quantized multivariate regression.
method Uniform quantization with random dithering, constrained and regularized Lasso estimators.
result Achieves minimax optimal rate with dithering, slightly worsens quantization effect.
Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning methods for Anomaly Detection/ranking. This paper proposes a new algorithm based o…
A method for rank verification in multivariate Gaussian data, improving on existing approaches.
problem Determining the top K means in multivariate Gaussian data with any covariance structure. method Selective inference tools to generalize the two-sided difference-of-means test for any K and covariance structure. result The method provides a generalization for rank verification in multivariate Gaussian data with any covariance structure.
Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for scoring rules for multivariate distributions, which encompasses the existing quadra…
Proposes a method for ranking items across multiple aspects based on user feedback.
problem No principled solution exists for generating multiple item rankings over different aspects.
method Developed a directional multi-aspect ranking criterion using probabilistic multivariate tensor factorization.
result Demonstrated effectiveness of the proposed method through comprehensive experiments on real datasets.
Paper uses optimal transport-based statistics for change point detection.
problem Change point detection in multivariate data.
method Soft rank energy and entropically regularized optimal transport.
result Soft rank energy performs better in real datasets with strong continuity and convergence properties.
Multivariate binary data is becoming abundant in current biological research. Logistic principal component analysis (PCA) is one of the commonly used tools to explore the relationships inside a multivariate binary data set by exploiting the underlying low rank structure. We re-expressed the logistic PCA model based on …
A graph neural network improves multivariate post-processing of ensemble forecasts.
problem Systematic biases in ensemble forecasts and loss of dependencies across forecast dimensions.
method A composite-Loss Graph Neural Network (dualGNN) trained with a composite loss function combining ES and VS.
result The dualGNN outperforms traditional methods in multivariate verification metrics and captures spatial relationships.
Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.
problem Inadmissibility of the corrected Akaike information criterion for estimating Kullback-Leibler discrepancy.
method Loss estimation framework to demonstrate inadmissibility and provide improved estimators.
result Improved estimators of Kullback-Leibler discrepancy are provided and perform well in reduced-rank situations.
In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems both in the number of events in the observed history n and the number of event types d (i.e. dimensions). The proposed Low-Rank Hawkes Process (LRHP) framework introduces a low-rank approximation of the kernel m…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor selection and rank reduction are the most popular strategies for obtaining lower-d…
The paper proposes a novel tensor-based method for non-parametric density estimation.
problem Effective non-parametric density estimation in high-dimensional multivariate data.
method Tensor factorization and low-rank model of characteristic tensor for improved density estimation.
result The method significantly improves density estimation especially for high-dimensional data and/or sample-starved regimes.
We consider the problem of modeling multivariate time series with parsimonious dynamical models which can be represented as sparse dynamic Bayesian networks with few latent nodes. This structure translates into a sparse plus low rank model. In this paper, we propose a Gaussian regression approach to identify such a mod…
Proposes MVG-CRPS for robust multivariate forecasting.
problem Outliers in multivariate forecasting lead to significant errors.
method Integrates CRPS for MVG distributions, optimizing with MVG-CRPS.
result Improves robustness, accuracy, and uncertainty quantification.
Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature …
The paper monitors artificial neural networks using embeddings and multivariate control charts.
problem Ensuring the stability of artificial neural networks during deployment.
method Monitoring the latent feature representation (embedding) of ANN outputs using multivariate control charts based on data depth and ranks.
result The proposed method effectively detects nonstationary data streams in ANN outputs.
New method extends conformal prediction to multivariate settings using optimal transport.
problem Limited applicability of conformal prediction to multivariate real-valued scores.
method Use optimal transport to define vector-ranks and multivariate quantile regions for finite-sample coverage.
result Constructs the first multivariate conformal predictive distributions with finite-sample calibration.
Regularizes ML algorithms for robust multivariate analysis against distribution shifts.
problem Ensuring robustness of multivariate analysis algorithms against distribution shifts.
method Integrates a causal regularisation term into the loss function of multivariate analysis algorithms.
result Demonstrates improved out-of-distribution generalisation with reduced-rank regression and partial least squares.
Learning how to rank multivariate unlabeled observations depending on their degree of abnormality/novelty is a crucial problem in a wide range of applications. In practice, it generally consists in building a real valued "scoring" function on the feature space so as to quantify to which extent observations should be co…
The paper analyzes the generalizability of linear autoencoders and multivariate linear regression.
problem Limited theoretical understanding of linear autoencoders' performance.
method Proposes a PAC-Bayes bound for multivariate linear regression and shows LAEs as constrained models.
result The proposed PAC-Bayes bound is tight and correlates with practical metrics.
Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, an…
A new kernel-based nonconformity score improves multivariate prediction regions.
problem Tackling the challenge of compressing multivariate residual vectors into scalars while preserving geometric structure.
method Introducing a Multivariate Kernel Score (MKS) that decomposes into an anisotropic MMD, providing finite-sample coverage guarantees and convergence rates.
result The MKS produces prediction regions that explicitly adapt to geometric structure, reducing volume compared to ellipsoidal baselines.
Multi-SpaCE generates valid counterfactual explanations for multivariate time series data.
problem Lack of transparency in deep learning models for multivariate time series data.
method Multi-objective counterfactual explanation method using NSGA-II for multivariate time series data.
result Ensures perfect validity and superior performance compared to existing methods.
We establish a foundation for multivariate counterfactual identification using dynamic optimal transport.
problem Addressing the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data.
method Establish a foundation for multivariate counterfactual identification using continuous-time flows, including non-Markovian settings, with tools from dynamic optimal transport.
result Characterise the conditions under which flow matching yields a unique, monotone, and rank-preserving counterfactual transport map, ensuring consistent inference.
It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is random…
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
problem Challenges in fitting regression models with multivariate responses and covariates.
method Low-rank tensor formats on regression coefficients and tensor-variate normal distribution for errors.
result Maximum likelihood estimators for tensor-on-tensor regression via block-relaxation algorithms.
In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses which is invariant to the functional form of the transformation function. We prove t…
We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a q-dimensional response, with a shared p-dimensional predictor variable. To control the complexity of the model, we employ a functional fo…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across groups, and a sparse linear combination of the dictionary elements is estimated…
Optimal transport improves multivariate prediction uncertainty quantification.
problem Uncertainty quantification in multivariate learning tasks, especially in regression and classification.
method Introducing a novel Conformal Prediction procedure using optimal transport to handle multivariate score functions and construct flexible prediction regions.
result Ensures finite-sample, distribution-free coverage guarantees for multivariate prediction sets.