Overview of high-dimensional time series regression methods.
problem Estimation and inference with high-dimensional time series data.
method Limit theory for high-dimensional dependent data, asymptotic theory for time series regression, statistical learning methods.
result Main limit theory results and asymptotic theory for high-dimensional time series regression.
Develops inequalities for high-dimensional linear processes with dependent innovations.
problem Estimating high-dimensional VAR(p) systems and HAC covariance estimation.
method Concentration inequalities for l∞ norm of vector linear processes with sub-Weibull, mixingale innovations. result Obtained concentration bounds for the maximum entrywise norm of lag-h autocovariance matrices. Paper generalizes Gaussian universality and CGMT to dependent data, impacting data augmentation in high-dimensional logistic regression.
problem Limitation of Gaussian universality and CGMT in handling dependent data.
method Generalizes Gaussian universality and CGMT to dependent data (block dependence, m-dependence, mixing). Establishes a novel CGMT framework.
result Gaussian universality holds for high-dimensional logistic regression under various types of dependence.
A new model integrates LSTM and copulas for high-dimensional financial data.
problem Modeling high-dimensional dependencies across financial markets.
method Variational LSTM with regular vine copulas.
result Outperforms benchmarks in cross-market portfolio forecasting.
We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimension…
The success of modern Artificial Intelligence (AI) technologies depends critically on the ability to learn non-linear functional dependencies from large, high dimensional data sets. Despite recent high-profile successes, empirical evidence indicates that the high predictive performance is often paired with low robustne…
Novel framework controls FDR in high-dimensional, dependent data.
problem FDR control failure in high-dimensional, dependent data.
method Dependency-aware T-Rex selector integrating hierarchical graphical models and martingale theory.
result First to control FDR in high-dimensional, dependent data.
New method for cross-validation in high-dimensional data with dependent or heavy-tailed covariates.
problem Inconsistent cross-validation in high-dimensional settings with dependent or heavy-tailed covariates.
method ROTI-GCV framework for cross-validation under proportional asymptotics regime.
result Demonstrated accuracy of ROTI-GCV in synthetic and semi-synthetic settings.
Paper proves conditions for estimating precision matrices with Laplacian constraints.
problem Estimating high-dimensional precision matrices with Laplacian constraints.
method Minimizing Stein's loss with conditions on graph connectivity and Laplacian constraints.
result High-dimensional consistency achieved with Laplacian constraints, independent of graph structure.
New method optimizes portfolios with options, addressing asymmetry, dimensionality, and dependence.
problem Optimizing portfolios with options, especially when distributions are asymmetric, dimensions are high, and payoffs are dependent.
method Developed a new dependency matrix based on conditional probabilities of options' payoffs, computed using copula structures.
result Empirical evidence shows the approach is efficient, fast, and scalable to large portfolios of options.
The paper develops a method to model high-dimensional data with many variables and weak signals.
problem Modeling high-dimensional dependent data with many explanatory variables and low signal-to-noise ratio.
method Penalized regression for high-dimensional data, factor modeling of residuals, high-dimensional white noise testing, projected Principal Component Analysis.
result Established asymptotic properties of the proposed method for high-dimensional data.
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution …
Paper develops a new estimator for high-dimensional panel data with common shocks.
problem Cross-sectionally dependent errors driven by common shocks in high-dimensional panel data.
method Factor-augmented sparse-group LASSO estimator combining MIDAS aggregation with latent factors.
result The estimator outperforms standard LASSO for prediction and estimation in settings with cross-sectional dependence.
Deep neural nets approximate high-dimensional HJB equations efficiently.
problem Approximating solutions to high-dimensional HJB equations.
method Deep neural networks for approximating solutions.
result Deep neural networks can approximate solutions without the curse of dimensionality.
New method estimates high-dimensional GoM models efficiently.
problem Estimating GoM models for high-dimensional polytomous data.
method Flattening three-way quasi-tensor into a matrix, performing singular value decomposition.
result Established finite-sample error bounds for estimated parameters.
Proposes FarmHazard model for hazard regression with correlated covariates.
problem Model selection challenges in high-dimensional data with correlated covariates.
method Factor-Augmented Regularized Model for Hazard Regression (FarmHazard) that learns latent factors and idiosyncratic components.
result Proves model selection and estimation consistency under mild conditions.
New method learns dependencies in high-dimensional data without graph assumptions.
problem Learning dependencies in nonparametric and high-dimensional settings.
method Neighbourhood lattice decomposition for nonparametric CI learning.
result Compact, non-graphical representation of CI exists in any graphical model.
Policy gradient methods have enjoyed great success in deep reinforcement learning but suffer from high variance of gradient estimates. The high variance problem is particularly exasperated in problems with long horizons or high-dimensional action spaces. To mitigate this issue, we derive a bias-free action-dependent ba…
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal distributions and (conditional) bivariate copulas. Yet, this adaptability is accompanied b…
We investigate the problem of modeling symbolic sequences of polyphonic music in a completely general piano-roll representation. We introduce a probabilistic model based on distribution estimators conditioned on a recurrent neural network that is able to discover temporal dependencies in high-dimensional sequences. Our…
New robust method for high-dimensional data analysis in imaging studies.
problem Analyzing high-dimensional data with complex dependence and outliers.
method Robust high-dimensional regression with coefficient thresholding and Huber loss.
result Statistical consistency and computational convergence under high-dimensional settings.
New method infers graph from dependent matrix data.
problem Inferring graph from dependent matrix data.
method Sparse-group lasso-based frequency-domain formulation with ADMM approach.
result Local convergence of inverse PSD estimators to true value.
A new method uses deep learning to efficiently solve complex physics equations in high dimensions.
problem Efficiently solving high-dimensional time-dependent PDEs with dynamic solutions.
method Deep adaptive sampling framework for PINNs extended to spacetime domains using normalizing flows.
result The method effectively identifies and tracks high-residual regions in both space and time.
We proposed a new statistical dependency measure called Copula Dependency Coefficient(CDC) for two sets of variables based on copula. It is robust to outliers, easy to implement, powerful and appropriate to high-dimensional variables. These properties are important in many applications. Experimental results show that C…
PCCs combine PCA and copulas for high-dimensional tail dependence modeling.
problem Modeling tail dependence in high-dimensional data.
method Principal Component Copulas (PCCs) integrating PCA and copulas.
result PCCs provide excellent performance on systemic risk measures.
Cluster GARCH model improves multivariate GARCH for high-dimensional asset returns.
problem Modeling high-dimensional asset returns with flexible tail dependencies and cluster structures.
method Introduced a novel multivariate GARCH model with flexible convolution-t distributions, tractable likelihood and derivatives for dynamic correlation structure.
result Cluster GARCH model outperforms existing models in daily returns of 100 assets, both in-sample and out-of-sample.
High-dimensional time series prediction is needed in applications as diverse as demand forecasting and climatology. Often, such applications require methods that are both highly scalable, and deal with noisy data in terms of corruptions or missing values. Classical time series methods usually fall short of handling bot…
We consider constraint-based methods for causal structure learning, such as the PC-, FCI-, RFCI- and CCD- algorithms (Spirtes et al. (2000, 1993), Richardson (1996), Colombo et al. (2012), Claassen et al. (2013)). The first step of all these algorithms consists of the PC-algorithm. This algorithm is known to be order-d…
We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This problem arises in learning interconnections of networks of dynamical systems with …
This paper models how features influence event triggers in high-dimensional networks.
problem Estimating context-dependent networks in high-dimensional marked point processes.
method Leveraging compositional time series and regularization methods, the paper considers autoregressive multinomial and logistic-normal models for network estimation.
result The logistic-normal model leads to a convex negative log-likelihood objective and captures dependence across categories.
Study improves ERM for heavy-tailed data with dependent inputs.
problem Empirical Risk Minimization with dependent and heavy-tailed data.
method Extending risk bounds for ERM with heavy-tailed, dependent data.
result Established risk bounds for ERM with dependent and heavy-tailed data.
Novel algorithm SAODE improves high-dimensional stream classification in seasonal data.
problem Handling seasonal concept drift in high-dimensional stream classification.
method SAODE classifier that includes time as a super parent to handle seasonal drift.
result SAODE consistently outperforms other methods in stream and concept drift classification.
There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive model…
New copula models learn to forget dependencies, improving data representation.
problem Restrictive assumptions and poor scaling in existing copula models.
method Diffusion and flow-based copulas that progressively forget dependencies.
result Provable valid copulas at all times, superior performance in complex dependencies.
New methods integrate nonlinear, sparse, and multi-view aspects for high-dimensional data analysis.
problem Integrating nonlinear dependence, sparsity, and multi-view data in high-dimensional datasets.
method Proposes HSIC-SGCCA, SA-KGCCA, and TS-KGCCA methods for multi-view high-dimensional data analysis.
result HSIC-SGCCA outperforms competing methods in multi-view variable selection.
The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection based on linear dependency between input features and output values. In this pa…
High-dimensional VAEs inevitably collapse to prior, requiring large datasets for good performance.
problem Posterior collapse in VAEs leads to poor representation learning quality.
method Analyzed a minimal VAE in a high-dimensional limit, evaluating conditions for posterior collapse with respect to beta and dataset size.
result VAEs face 'inevitable posterior collapse' beyond a certain beta threshold, regardless of dataset size.
Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The number of parameters in the covariance matrix grows as the square of the number …
This paper deals with multivariate regression chain graphs (MVR CGs), which were introduced by Cox and Wermuth [3,4] to represent linear causal models with correlated errors. We consider the PC-like algorithm for structure learning of MVR CGs, which is a constraint-based method proposed by Sonntag and Peña in [18]. We …
BSTabDiff: Block-Subunit Diffusion Priors for HDLSS Tabular Data Generation
problem High-dimensional tabular data generation in HDLSS
method Block-subunit generative framework
result More realistic and stable synthetic data
Deep learning models complex multivariate extremes using geometric shapes.
problem Modeling complex extremal dependencies in high-dimensional data.
method Geometric representation and deep learning for flexible semi-parametric models.
result First approach to modeling limit sets using deep learning for high-dimensional data.
HD-BWDM improves clustering validation in high-dimensional data.
problem Determining the right number of clusters in high-dimensional data.
method HD-BWDM integrates random projection, PCA, trimmed clustering, and medoid-based distances.
result HD-BWDM remains stable and interpretable under high-dimensional projections and contamination.
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at an ever-growing scale, statistical machine learning faces some new cha…
Kernel Three-Pass Regression Filter improves forecasting efficiency for nonlinear dependencies.
problem Forecasting with high-dimensional predictors and latent factors.
method Developed a new estimator, Kernel Three-Pass Regression Filter (K3PRF), to address nonlinear dependencies.
result Empirically shows significant improvement in long-term forecasting performance.
We propose an algorithm for clustering high dimensional data. If P features for N objects are represented in an N×P matrix X, where N≪P, the method is based on exploiting the cluster-dependent structure of the N×N matrix XXT. Computational burden thus depends primarily on N, …
Skeleton clustering detects clusters in high-dimensional data without needing prototypes.
problem Detecting clusters in high-dimensional data with irregular shapes.
method Skeleton clustering combines prototype methods, density-based clustering, and hierarchical clustering using surrogate density measures.
result Skeleton clustering reliably detects clusters in multivariate and high-dimensional data.
The paper develops methods to create reliable prediction sets for complex mixture models in high-dimensional data.
problem Building accurate prediction sets for high-dimensional mixture models with feature-dependent weights.
method The authors introduce a debiasing procedure and a novel interval combination strategy to construct valid prediction sets.
result The proposed method provides reliable coverage guarantees for prediction sets in high-dimensional mixture models.