Proposes a deep neural network approach for image response regression.
problem Associations between medical images and covariates.
method Spatially varying coefficient models with deep neural networks.
result Explicitly accounts for spatial smoothness and subject heterogeneity.
We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly corrupted manifold-valued responses, a bottleneck issue commonly encountered in pr…
SpINNEr uses matrix regression to analyze brain connectivity, improving accuracy over other methods.
problem Analyzing multi-dimensional data like brain imaging arrays using traditional scalar regression methods.
method SpINNEr applies matrix regression with nuclear norm and lasso norms to encourage low rank and sparse solutions.
result SpINNEr outperforms other methods in estimating brain connectivity, especially in well-connected regions.
An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to the assumptions of Euclidean geometry. Rather, they occupy non-linear spaces, a.…
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.
Differentially private geodesic regression for non-Euclidean data.
problem Protecting sensitive data on non-linear spaces like manifolds.
method K-Norm Gradient (KNG) mechanism for Riemannian manifolds.
result Theoretical bounds for sensitivity of geodesic regression parameters.
New method uses nuclear and ℓ1 penalties for matrix regression, improving brain disorder detection.
problem Modeling high-dimensional matrix predictors with binary responses.
method Convex optimization with ADMM for low-rank and sparse structures.
result Effective in identifying brain disorder-related connectivity patterns.
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.
New framework for regression trees with multivariate response and dynamic mean vectors.
problem Characterizing and implementing regression trees for multivariate responses.
method High dimensional model with dynamic mean vectors over multi-dimensional change axes.
result Optimal rate of convergence and asymptotic valid confidence intervals for change points.
CeCNN predicts SE and AL from UWF images, improving myopia screening.
problem Predicting axial length and spherical equivalence from UWF fundus images.
method Copula-enhanced Convolutional Neural Network (CeCNN) for multiresponse regression.
result CeCNN improves prediction of SE and AL compared to baseline CNNs.
PEER tackles multi-response regression with incomplete outcomes efficiently.
problem Challenges in estimating, predicting, and computing with large-scale multi-response regression and incomplete outcomes.
method PEER converts multi-response regression into parallel univariate-response regressions.
result PEER achieves consistency in estimation, prediction, and variable selection.
This paper reviews SDR methods for multivariate response regression.
problem Handling sufficient dimension reduction for multivariate response regression.
method Characterizes SDR estimators as inverse or forward regression methods.
result Pooled marginal, projective resampling, distance-based, ordinary least squares, partial least squares, and semiparametric SDR estimators are discussed.
Unified framework for image classification and regression using cGAN-generated samples.
problem Lack of unified KD methods for both classification and regression tasks.
method cGAN-KD framework based on cGANs.
result Unified framework for both classification and regression tasks, compatible with other KD methods.
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.
New method calibrates diffusion models for image regression tasks.
problem Ensuring reliability of diffusion models for critical applications.
method Risk-Controlling Prediction Sets (RCPS) with convex optimization.
result Calibrated entrywise intervals and risk control with minimal mean interval length.
Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for constructing sparse estimates of the multivariate regression coefficient matrix that accoun…
Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of dimensionality, the saturation discontinuity due to capillarity effects, and the time-depende…
Enhances tensor regression for interpretability and performance.
problem Interpreting and modeling multidimensional tensor data with structural heterogeneity.
method Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR) with hybrid regularization and nonnegativity constraints.
result NS-KTR outperforms conventional methods in synthetic and real hyperspectral datasets.
Cephalometric tracing method is usually used in orthodontic diagnosis and treatment planning. In this paper, we propose a deep learning based framework to automatically detect anatomical landmarks in cephalometric X-ray images. We train the deep encoder-decoder for landmark detection, and combine global landmark config…
Estimation of response functions is an important task in dynamic medical imaging. This task arises for example in dynamic renal scintigraphy, where impulse response or retention functions are estimated, or in functional magnetic resonance imaging where hemodynamic response functions are required. These functions can no…
The paper explores strong identifiability and parameter learning in regression models with heterogeneous responses.
problem Understanding heterogeneity in data populations through conditional distributions of a response variable.
method Investigation of strong identifiability, convergence rates, and posterior contraction behavior in finite mixture of regression models.
result Theoretical findings on conditions for strong identifiability and rates of convergence in regression mixture models.
Improves regression efficiency by separating material and immaterial parts of responses.
problem Improving estimation efficiency in nonlinear multivariate regressions.
method Kernel envelope (KENV) estimator for nonparametric response envelopes in reproducing kernel Hilbert space.
result KENV achieves lower in-sample prediction risk than kernel ridge regression in non-trivial immaterial components.
We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a…
BART is extended to handle various response variables.
problem Modeling nonlinear regression functions for diverse response types.
method Generalized Bayesian Additive Regression Trees (GBART) for exponential family distributions.
result The posterior concentrates at a minimax rate for certain response distributions.
Interpretable text-response modelling for structured outcomes
problem Predicting structured responses alongside textual data
method Joint non-negative matrix factorisation and binomial regression
result Recovering stable response-relevant textual signals
We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
New algorithms for regression with adversarial responses on various metric spaces.
problem Regression with adversarial responses under non-i.i.d. sequences.
method Proves universal consistency for a wide range of non-stationary processes.
result Achieves universal consistency for a broader class of sequences than stationary processes.
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are independent is, however, too strong. In many applications, these responses are collec…
Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-ra…
Extends RRR to capture nonlinear interactions in multi-response regression.
problem Complex relationships in real-world data cannot be adequately modeled by linear interactions.
method Introduces Higher Order Reduced Rank Regression (HORRR) using tensor representations and Tucker decomposition.
result HORRR can capture nonlinear interactions in multi-response regression.
We improve kernel ridge regression for skewed responses using oversampling and adaptive partitioning.
problem Kernel ridge regression struggles with skewed response variables, leading to poor estimates.
method Combines adaptive partitioning with oversampling to address skewed responses in kernel ridge regression.
result The proposed method yields estimates with smaller risk compared to classical methods under mild conditions.
The paper provides risk bounds for learning many response functions using linear regression.
problem Learning many response functions from a single dataset.
method Ordinary least squares regression in a high-dimensional feature space.
result Convergence guarantees on worst-case excess prediction risk for infinite response functions with finite VC dimension.
A novel capsule network model improves surrogate modeling and uncertainty quantification from sparse data.
problem Surrogate modeling and uncertainty quantification of systems from sparse data.
method Adapted Capsule Network (CapsNet) architecture into image-to-image regression encoder-decoder network.
result The proposed approach accurately, efficiently, and robustly predicts responses for arbitrary diffusion fields.
Proposes methods to correct bias and missing data in regression models.
problem Nonignorable selection bias and missing response in regression models.
method Imputation-based and importance weighted regression methods, including repeated regression and doubly robust combination.
result Repeated regression can effectively correct bias and outperforms weighted regression in extrapolation.
This paper explores the impact of metric choice on Fréchet regression.
problem Choosing the right metric for Fréchet regression in complex data.
method Review and extensive numerical studies of existing dimension reduction methods.
result Different metrics significantly affect the estimation of central and central mean space.
Study robust linear regression without distributional assumptions for heavy-tailed responses.
problem Linear regression with heavy-tailed responses and no distributional assumptions.
method Combining truncated least squares, median-of-means, and aggregation theory to construct a non-linear estimator.
result Achieves excess risk of order d/n with optimal sub-exponential tail. 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…
A new model for complex cells accounts for insensitivity to image shifts.
problem Complex cells' response to image shifts.
method Linear combination of Gaussian derivatives at a single position.
result Maximum response insensitive to small shifts of the image.
Develops a regression model for partially observed dynamic tensor data.
problem Characterizing the relationship between dynamic tensor data and external covariates when data is only partially observed.
method Introduces low-rank, sparsity, and fusion structures on the regression coefficient tensor, and uses a loss function projected over observed entries. Developed an efficient non-convex alternating updating algorithm.
result Derived finite-sample error bounds for the estimator.
Slow feature analysis (SFA) is an unsupervised learning algorithm that extracts slowly varying features from a time series. Graph-based SFA (GSFA) is a supervised extension that can solve regression problems if followed by a post-processing regression algorithm. A training graph specifies arbitrary connections between …
We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is non differentiable when pairs of columns in the optimization variable are equal. This encourages pairwise equality of these columns in the estimator…
We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from responses in the same cluster, and an L1 penalty for simultaneous variable selection an…
In this paper, some patterns of the Neuron Response of deep Convolutional Neural Networks were observed.
In this paper, we propose a non-parametric conditional factor regression (NCFR)model for domains with high-dimensional input and response. NCFR enhances linear regression in two ways: a) introducing low-dimensional latent factors leading to dimensionality reduction and b) integrating an Indian Buffet Process as a prior…
We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes representing the human brain's structure or function, and obtained using neuroimaging techniques. RFDM, which is an extension of decision forests, requires…
Proposes MELODIC family for simultaneous binary logistic regression.
problem Simultaneous analysis of multiple binary response variables.
method Defines models in a reduced Euclidean space using a distance rule.
result Improves predictive accuracy through model interdependence.
Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. It can handle both a non-symmetric and a symmetric tensor respo…
New method for multivariate distribution regression using NPT metric.
problem Regression with multivariate distributional responses and Euclidean predictors.
method Fréchet regression with nonparanormal transport (NPT) metric.
result Efficient estimation and granular interpretation of predictor effects.