New method handles correlated responses and interaction effects in multi-response regression.
problem Handling correlated responses and interaction effects in multi-response regression.
method MADMMplasso, an ADMM-based approach for multi-response regression with overlapping groups and interaction effects.
result The proposed method outperforms in prediction and variable selection for correlated responses and interaction effects.
Bayesian neural networks improve cancer dynamics prediction.
problem Predicting cancer dynamics under treatment due to heterogeneity and sparse data.
method Hierarchical Bayesian model using baseline covariates and Bayesian neural networks for nonlinear interactions.
result Bayesian neural networks outperform linear models in predicting cancer dynamics with interactions.
Interactive privacy mechanisms improve spectral density estimation under local differential privacy.
problem Estimating spectral density of Gaussian time series with local differential privacy constraints.
method Two-stage process: Laplace mechanism followed by privatized sample analysis.
result Interactive mechanisms achieve faster rates for spectral density estimation.
Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications s…
A new method quickly identifies key variables and interactions.
problem Identifying key variables and interactions in high-dimensional data.
method Kernel trick for sparse orthogonal decomposition in O(# covariates) time.
result Outperforms existing methods for large, high-dimensional data sets.
The paper proposes a method to analyze categorical feature interactions in large datasets using graph covariance and LLMs.
problem Analyzing complex datasets with numerous categorical features and timestamps.
method Binarization of categorical features using one-hot encoding, computation of graph covariance, identifying significant feature pairs, and using LLMs to generate explanations.
result The method identifies meaningful feature pairs and potential data stories underlying categorical feature interactions.
BEGIN network models binary data without parametric assumptions.
problem Conditional independence in non-parametric families of binary data.
method BEGIN network models binary data using sparse linear representations and block factorizations.
result BEGIN network captures conditional independence for arbitrary binary and multinomial variables.
We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity surfaces. In analyzing this phenomenon, we prove the covariance of surface balances…
Paper sets fundamental limits for distributed covariance estimation with constrained communication.
problem Estimating high-dimensional covariance matrices in a feature-split setting with limited communication.
method Developed a Conditional Strong Data Processing Inequality (C-SDPI) to establish minimax lower bounds and an optimal estimation protocol.
result Achieved nearly optimal estimation protocol with sample and communication requirements matching lower bounds up to logarithmic factors.
Taking into account high-order interactions among covariates is valuable in many practical regression problems. This is, however, computationally challenging task because the number of high-order interaction features to be considered would be extremely large unless the number of covariates is sufficiently small. In thi…
New copula-based models for binary outcomes capture complex interactions.
problem Complex interaction effects in binary outcome models.
method Additive models with copula-based components, no discretization required.
result Better or comparable predictive performance compared to other methods.
Develops a method for estimating networks and covariate associations in compositional data.
problem Estimating network interactions and covariate associations for compositional data.
method Hierarchical Bayesian model with spike-and-slab priors for edge and covariate selection, variational EM for inference.
result The proposed method outperforms existing methods in network recovery accuracy.
Adaptive Bayesian model for covariate-dependent power spectra analysis.
problem Estimating complex relationships and interactions between covariates and power spectra.
method Bayesian sum of trees model with local power spectrum estimation and reversible-jump MCMC for tree modifications.
result The method can accurately recover both smooth and abrupt changes in power spectra across multiple covariates.
New non-separable covariance kernels for spatiotemporal data derived from harmonic oscillator physics.
problem Capturing complex spatiotemporal dependencies in Gaussian processes.
method Hybrid spectral method based on the harmonic oscillator, deriving explicit covariance kernels.
result Explicit non-separable covariance kernels with space-time interactions.
Transposable data represents interactions among two sets of entities, and are typically represented as a matrix containing the known interaction values. Additional side information may consist of feature vectors specific to entities corresponding to the rows and/or columns of such a matrix. Further information may also…
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
Proposes extensions to semi-parametric models using BART for shared covariates.
problem Avoiding poor coverage properties and reducing bias in linear predictor estimates.
method Modifies tree-generation moves in BART to handle shared covariates between linear and non-parametric components.
result Competitive performance in modelling complex interactions and predicting student achievements.
KAPLAN-HR models survival data without manual interactions, outperforming existing methods.
problem Survival analysis challenges with complex covariates and time-varying effects.
method Kolmogorov-Arnold Networks (KAN) for nonparametric hazard estimation.
result KAPLAN-HR matches or exceeds existing methods in clinical survival data.
Covariance is shown as a commutator in random variable calculus.
problem Expressing covariance as a commutator of operators.
method Demonstrated through commutator identities involving expectations and products of functions.
result Revealed the underlying Lie algebraic structure in efficient influence curve calculus.
Understanding how features interact with each other is of paramount importance in many scientific discoveries and contemporary applications. Yet interaction identification becomes challenging even for a moderate number of covariates. In this paper, we suggest an efficient and flexible procedure, called the interaction …
Detection of interactions between treatment effects and patient descriptors in clinical trials is critical for optimizing the drug development process. The increasing volume of data accumulated in clinical trials provides a unique opportunity to discover new biomarkers and further the goal of personalized medicine, but…
Efficient inference for multimodal Gaussian mixture models of interacting dynamical systems.
problem Efficient inference for multimodal distributions in stochastic dynamical systems.
method Graph neural networks with moment matching for sample-free inference and structured covariance approximations.
result Sample-free inference with improved efficiency and stability compared to Monte Carlo alternatives.
While sample sizes in randomized clinical trials are large enough to estimate the average treatment effect well, they are often insufficient for estimation of treatment-covariate interactions critical to studying data-driven precision medicine. Observational data from real world practice may play an important role in a…
In this paper, we introduce a new directed graphical model from Gaussian data: the Gaussian graphical interaction model (GGIM). The development of this model comes from considering stationary Gaussian processes on graphs, and leveraging the equations between the resulting steady-state covariance matrix and the Laplacia…
Federated Granger causality learns reliable interactions without sharing data.
problem Uncertainty in federated Granger causality estimates.
method Closed-form covariance recursions and spectral-radius-based convergence conditions.
result Uncertainty depends only on client data statistics and is independent of model parameters.
Feature interactions can contribute to a large proportion of variation in many prediction models. In the era of big data, the coexistence of high dimensionality in both responses and covariates poses unprecedented challenges in identifying important interactions. In this paper, we suggest a two-stage interaction identi…
Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter in the usual jet bundle formulation. Actually a natural Lagrangian can be writt…
iLOCO measures feature interactions without assumptions, providing statistical inference.
problem Lack of methods to statistically infer feature interactions.
method iLOCO metric and LOCO inference for distribution-free, efficient computation.
result First inferential approach to detecting feature interactions.
New algorithms for batch decision-making with high-dimensional user data.
problem Maximizing treatment efficacy in groups of users.
method Teamwork LASSO Bandit algorithm, switching between teamwork and selfish stages.
result Upper bound on expected cumulative regret for the proposed algorithm.
AniDS improves molecular force field modeling by learning anisotropic noise.
problem Molecular force field modeling suffers from oversimplified assumptions about atomic motions.
method AniDS introduces anisotropic noise generation for better modeling of directional and structural variability.
result AniDS outperforms existing methods on benchmarks, achieving significant improvements in force prediction accuracy.
Deep neural networks tackle high-dimensional nonparametric interaction models.
problem Estimating structured regression functions in high-dimensional data.
method Analyze kth order nonparametric interaction models in growing and high dimensions, introducing debiasing techniques. result Debiased deep neural networks achieve optimal rates of convergence in both growing and high dimensions.
Proposes a deep neural network for predicting survival times with cure fractions.
problem Predicting survival times with cure fractions in medical studies.
method Flexible survival models integrated into a deep neural network framework.
result Better predictive performance and realistic covariate effects.
Researchers develop a new SMC sampler for Wishart processes to improve dynamic covariance inference.
problem Challenging inference of dynamic covariance in various scientific fields.
method Introduce Sequential Monte Carlo (SMC) sampler for the Wishart process.
result SMC sampling provides more robust estimates and out-of-sample predictions of dynamic covariance.
Proposes I-prior extension for additive interaction models.
problem Challenges in estimating and selecting models with interactions.
method Extends I-prior methodology to multiple covariates, introducing a parsimonious model specification.
result Improves estimation and model selection for additive interaction models.
VEC-SBM detects communities using side information like texts and images.
problem Community detection in social networks with side information.
method Proposes a novel algorithm based on iterative refinement techniques.
result Optimally recovers latent communities with side information.
Graph neural networks help assess how global changes affect plant-pollinator networks.
problem Interpreting GNN results to understand how global changes impact plant-pollinator networks.
method Simulation study and application on Spipoll dataset to assess effects of global changes on pollination networks.
result GNNs can detect interactive effects between covariates and plant genera on pollination network connectivity.
Bayesian model learns multiscale interactions in complex systems.
problem Understanding dynamic interplay between processes at different time scales.
method Bayesian learning framework with Particle Gibbs with Ancestor Sampling (PGAS) algorithm.
result Demonstrated the effectiveness of the proposed approach through simulations.
Medical practitioners use survival models to explore and understand the relationships between patients' covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or pri…
Study examines how imputation accuracy affects prediction accuracy in regression problems with missing covariates.
problem Missing covariates in regression or classification problems.
method Simulation and empirical analysis using UCI datasets and statistical inference.
result Imputation accuracy impacts prediction accuracy, especially with Machine Learning methods.
Longitudinal study designs are indispensable for studying disease progression. Inferring covariate effects from longitudinal data, however, requires interpretable methods that can model complicated covariance structures and detect nonlinear effects of both categorical and continuous covariates, as well as their interac…
TraCeR uses transformers to analyze survival data with longitudinal covariates.
problem Handling longitudinal covariates and assessing model calibration in survival analysis.
method Transformer-based survival analysis framework with factorized self-attention architecture.
result TraCeR achieves significant performance improvements over state-of-the-art methods.
We find a closed-form determinant for a specific sparse covariance matrix model.
problem Finding the determinant of a specific class of sparse positive definite matrices.
method Using Fourier transform of local factors, Normal Factor Graph Duality Theorem, and Matrix Determinant Lemma.
result We derive a closed-form expression for the determinant.
Study high-dimensional covariance matrix estimators for complex portfolios, improving financial metrics.
problem Estimating covariance matrices in high-dimensional portfolios with nested and one-factor structures.
method Combining random matrix theory, free probability, deterministic equivalents, and two-step covariance estimators.
result Two-step estimators improve financial metrics in complex and one-factor covariance models.
STVNN models spatiotemporal data using covariance matrices.
problem Challenges in modeling spatiotemporal interactions in multivariate time series.
method Introduces SpatioTemporal coVariance Neural Network (STVNN) that operates on sample covariance matrix and uses joint spatiotemporal convolutions.
result STVNN is stable to online estimation uncertainties and outperforms temporal PCA.
In healthcare applications, temporal variables that encode movement, health status and longitudinal patient evolution are often accompanied by rich structured information such as demographics, diagnostics and medical exam data. However, current methods do not jointly optimize over structured covariates and time series …
PliableBVS extends Bayesian lasso for modeling interactions with modifying variables.
problem Modeling interactions between large and small sets of variables, especially in omics studies.
method Bayesian variable selection with spike-and-slab priors and hierarchical structure.
result PliableBVS outperforms pliable lasso in identifying active main and interaction effects.
Improves MARS for nonparametric multivariate regression with dimension reduction.
problem High number of basis functions in MARS for high-order interactions.
method Linear combinations of covariates for dimension reduction, facilitating gradient calculation and eigen-analysis for estimation.
result Asymptotic theory and numerical studies show improved performance over MARS.
We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) problem using operator-valued kernels. We show that some of the existing formulations of this problem are special cases of our framework. We then propose a c…