A method for identifying joint and individual subspaces from multi-view data.
problem Unclear conditions for reliably identifying joint and individual subspaces from noisy, high-dimensional measurements.
method Rigorously quantifies conditions based on signal rank, principal angles, and noise levels. Characterizes spectrum perturbations of product of projection matrices.
result Estimates joint and individual subspaces more accurately than existing approaches in simulations and real-world applications.
In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue reminiscent of the well-known Procrustes problem. A Bayesian approach is investigat…
This paper analyzes AJIVE for estimating shared subspace across multiple datasets, revealing its strengths and limitations.
problem Estimating shared subspace across multiple datasets with varying degrees of misalignment.
method Angle-based Joint and Individual Variation Explained (AJIVE) method, a two-stage spectral approach.
result AJIVE's performance in high signal-to-noise ratio (SNR) regimes and its non-diminishing error in low-SNR settings.
Proposes a new algorithm to estimate invariant subspaces across multilayer networks.
problem Estimating invariant subspaces across heterogeneous multiple networks.
method Bias-corrected joint spectral embedding algorithm that recursively calibrates diagonal bias and iteratively updates the subspace estimator.
result Established entrywise subspace perturbation bound and entrywise eigenvector central limit theorem for the algorithm.
Proposes HeteroJIVE for joint subspace estimation in multi-view data with statistical and structural heterogeneity.
problem Joint subspace estimation in multi-view data with varying statistical and structural heterogeneity.
method HeteroJIVE: A weighted two-stage spectral algorithm addressing statistical and structural heterogeneity.
result HeteroJIVE achieves the O(K−1/2) rate without iterative refinement, validating the oracle-optimal weighting scheme. Model improves covariance estimation from shared and distinct datasets.
problem Limited sample sizes and shared covariance structure across related datasets.
method Spiked covariance model with shared subspace, closed-form pooling weight, and asymptotic guarantees.
result Improves estimation of high-dimensional covariance matrices from related datasets.
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the jo…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span a low dimensional linear subspace in the space of symmetric matrices, our aim i…
Low-rank matrix regression refers to the instances of recovering a low-rank matrix based on specially designed measurements and the corresponding noisy outcomes. In the last decade, numerous statistical methodologies have been developed for efficiently recovering the unknown low-rank matrices. However, in some applicat…
Algorithm removes spurious concepts from neural network representations without harming task performance.
problem Spurious correlations hinder neural network out-of-distribution generalization.
method Iterative algorithm that identifies two orthogonal subspaces in neural network representation.
result Algorithm outperforms existing methods on computer vision and natural language processing benchmarks.
Proposes joint LCA for multiview data to identify shared and view-specific components.
problem Extracting shared components sequentially from multiview data.
method Formulates a matrix decomposition model with joint and individual structures, proposes a penalty term objective function, and employs a refitting procedure.
result Achieves simultaneous estimation and rank selection for cross covariance.
Method estimates multivariate counterfactual distributions efficiently and accurately.
problem Estimating multivariate counterfactual distributions in causal models with correlation structures.
method Proposes a method leveraging a one-dimensional subspace to capture correlation structures and efficiently estimate multivariate counterfactual distributions.
result Demonstrates superior performance over existing methods on synthetic and real-world data.
Discovering and clustering subspaces in high-dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. Earlier methods divided the problem into two separate stages of finding the similarity matrix and finding clusters. Simil…
Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization (out-of-samples), and cost-effectiveness (linearization). To this end, a novel linearized subsp…
RaSE screens variables via random subspaces, identifying joint effects.
problem Missing joint effects of predictors in ultra-high dimensional data.
method Random Subspace Ensemble (RaSE) framework combining subspace evaluation criteria.
result RaSE identifies signals with no marginal effect or high-order interactions.
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss…
Bayesian method for semi-structured models accounts for both types of uncertainty.
problem Lack of work on epistemic uncertainty in semi-structured regression models.
method Bayesian approximation with subspace inference for joint posterior sampling.
result Validated approach recovers structured effect posteriors and approaches full-space posterior.
In the last two decades, unsupervised latent variable models---blind source separation (BSS) especially---have enjoyed a strong reputation for the interpretable features they produce. Seldom do these models combine the rich diversity of information available in multiple datasets. Multidatasets, on the other hand, yield…
This work optimizes induced correlation in joint graph embeddings.
problem Optimizing correlation across embedded networks in joint graph embeddings.
method Developed corr2Omni algorithm to estimate optimal Omnibus weights.
result corr2Omni algorithm improves inference fidelity compared to classical Omnibus construction.
This paper solves matrix blind joint block diagonalization with noise.
problem Identifying the diagonalizer and block diagonal structure of matrices under noise.
method Bi-block diagonalization method.
result The method can identify the exact solution under certain conditions.
Ankle sprains and instability are major public health concerns. Up to 70% of individuals do not fully recover from a single ankle sprain and eventually develop chronic ankle instability (CAI). The diagnosis of CAI has been mainly based on self-report rather than objective biomechanical measures. The goal of this study …
Paper bounds subspace estimator error from noisy projections.
problem Estimating subspaces from noisy data.
method Derives perturbation bound on optimal subspace estimator.
result Fundamental result with implications in matrix completion and clustering.
Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace…
Bayesian methods reduce variance in subspace identification for small data sets.
problem High variance in traditional subspace identification methods for large models or small sample sizes.
method Investigation of Bayesian estimation solutions (regularized and shrinkage estimators) for subspace identification.
result Bayesian estimators reduce estimation risk by up to 40% compared to traditional methods.
Budney recently constructed an operad that encodes splicing of knots. He further showed that the space of (long) knots is generated over this operad by the space of torus knots and hyperbolic knots, thus generalizing the satellite decomposition of knots from isotopy classes to the level of the space of knots. Infection…
In this paper, we propose a novel method for projecting data from multiple modalities to a new subspace optimized for one-class classification. The proposed method iteratively transforms the data from the original feature space of each modality to a new common feature space along with finding a joint compact descriptio…
GPS model predicts subspace-valued functions efficiently.
problem Accurate and efficient prediction of subspace-valued functions.
method Gaussian Process Subspace regression (GPS) model, using multivariate Gaussian distributions on Euclidean space.
result GPS provides accurate, smooth predictions with uncertainty quantification.
New method fuses audio and magnetic data to identify underlying subspaces.
problem Identifying complex trends in multi-modality data.
method Robust Group Subspace Recovery (RoGSuRe) algorithm based on group sparsity and bi-sparsity pursuit.
result Competitive performance in clustering and classification of multi-modal data.
This paper considers the problem of robust subspace recovery: given a set of N points in RD, if many lie in a d-dimensional subspace, then can we recover the underlying subspace? We show that Tyler's M-estimator can be used to recover the underlying subspace, if the percentage of the inliers is larger t…
Theoretical guarantees for STE, a robust subspace recovery method.
problem Recovering a low-dimensional subspace from corrupted data.
method Subspace-constrained Tyler's estimator (STE) with initialization conditions.
result STE can effectively recover the subspace under certain conditions.
A new framework for PPLS combines noise estimation, optimization, and calibration.
problem Probabilistic PLS models need interpretable latent factors and calibrated uncertainty.
method End-to-end pipeline combining noise estimation, constrained optimization, and prediction calibration.
result Achieves near-nominal coverage and native calibrated uncertainty across benchmarks.
Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As this model is often unknown for many classes of the signals, we need to select su…
Proposes methods to identify and estimate counterfactual distributions with confounding.
problem Estimating counterfactual distributions in the presence of confounding.
method Nonparametric identification and semiparametric estimation using conditional copulas and machine learning.
result Valid inference for individual-level effects and nonparametric identifiability of latent confounding subspace.
New method estimates active subspaces for jump-discontinuous functions.
problem Estimating active subspaces for discontinuous functions like ABMs.
method Extending active subspaces to discontinuous functions, using Gaussian process.
result Identifies important parameters in ABM simulations of refugee movement.
Proposes a method to predict responses from covariates over time.
problem Predicting responses from covariates with changing conditional distributions over time.
method Invariant Subspace Decomposition (ISD) framework that splits the conditional distribution into time-invariant and time-dependent components.
result The decomposition can be used for zero-shot and time-adaptation prediction tasks.
We study sparse principal components analysis in high dimensions, where p (the number of variables) can be much larger than n (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We introduce two complementary not…
Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general structured principal subspace estimation problem which includes as special cases no…
Study optimizes shared singular subspace estimation from noisy matrices.
problem Estimating shared singular subspaces across multiple noisy matrices.
method Low-rank matrix denoising framework with Stack-SVD and novel estimators.
result Stack-SVD achieves minimax rate-optimality for identical shared subspaces, and novel estimators for partial sharing.
We introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We examine the case of the undercomplete BSSD (uBSSD). Applying temporal concatenation we reduce this problem to ISA. The associated `high …
Paper proves IRLS converges to subspace from any start, with practical benefits.
problem Robust subspace estimation in machine learning.
method Iteratively Reweighted Least Squares (IRLS) with dynamic smoothing regularization.
result IRLS converges linearly to the underlying subspace from any initialization under deterministic conditions.
SIG model identifies invariant variables for MSDA with fewer domain constraints.
problem Challenges in enforcing minimal changes across domains for MSDA.
method Subspace identification theory and variational inference.
result SIG model outperforms existing techniques on various benchmark datasets.
We present the Bayesian Case Model (BCM), a general framework for Bayesian case-based reasoning (CBR) and prototype classification and clustering. BCM brings the intuitive power of CBR to a Bayesian generative framework. The BCM learns prototypes, the "quintessential" observations that best represent clusters in a data…
We study the problem of robust subspace recovery (RSR) in the presence of adversarial outliers. That is, we seek a subspace that contains a large portion of a dataset when some fraction of the data points are arbitrarily corrupted. We first examine a theoretical estimator that is intractable to calculate and use it to …
We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To capture such complex structures, a double core tensor (DCOT) factorization mode…
ALPCAHUS clusters data from multiple subspaces with varying noise.
problem Heteroscedastic data with varying noise levels.
method Develops a heteroscedastic PCA method for subspace clustering.
result Improves subspace clustering by accounting for sample-wise noise variances.
In this paper, we exhibit the tradeoffs between the (training) sample, computation and storage complexity for the problem of supervised classification using signal subspace estimation. Our main tool is the use of tensor subspaces, i.e. subspaces with a Kronecker structure, for embedding the data into lower dimensions. …
Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of a s-Hölder function f in RD which varies along a central subspace of dimension d while d≪D. A direct approximation of f in RD with an ε acc…
Estimates joint causal effects using single-variable interventions on nonlinear models.
problem Estimating joint causal effects from single-variable interventions.
method Identifiability result and practical estimator for decomposing causal effects.
result Joint effects can be inferred without joint interventional data for nonlinear additive models.