Proposes GPLFR for predicting high-dimensional outputs with few data.
problem Predicting high-dimensional outputs from limited data.
method GPLFR combines Gaussian process and linear-Gaussian decoding for high-dimensional prediction.
result GPLFR outperforms existing methods in predicting high-dimensional outputs.
Proposes SHORE model for efficient MOR with sparsity and scalability.
problem Challenges of interpretability and scalability in MOR with high-dimensional outputs.
method Incorporates sparsity requirements and a two-stage optimization framework for efficient compression.
result Theoretical and empirical validation of the proposed framework's efficiency and accuracy.
This study compares multivariate vs univariate machine learning for multi-output regression.
problem When to use multivariate ensemble techniques over separate univariate models.
method Comparative analysis of different multivariate approaches for multi-output regression.
result Multivariate ensemble techniques outperform separate univariate models in simulations.
The paper presents a novel approach to multi-output regression using probabilistic circuits.
problem Capturing correlations between multiple output dimensions in large-scale regression problems.
method Employing a mixture of single-output Gaussian process experts encoded via a probabilistic circuit.
result The method can capture correlations between output dimensions and often outperforms other approaches.
Reduced-rank method improves least-squares regression under output regularity.
problem Least-squares regression with infinite dimensional outputs.
method Reduced-rank method for solving least-squares problems with output regularity assumptions.
result Learning bounds and improved statistical performance compared to full-rank method.
Proposes a deep ordinal regression framework using optimal transport loss and unimodal output probabilities.
problem Lack of unimodal output probabilities in recent ordinal regression models.
method Introduces a deep learning framework based on optimal transport loss and unimodal output distribution, inspired by the Proportional Odds model.
result Demonstrates improved performance and unimodal output probabilities on real-world datasets compared to existing methods.
A new method quantizes output space for multi-target regression.
problem Predicting multiple continuous targets using shared predictors.
method MRQ method that quantizes output space to model dependencies and scale.
result MRQ achieves high scalability and competitive accuracy.
A new conformal prediction framework for graph-valued outputs using Z-Gromov-Wasserstein distances.
problem Lack of principled uncertainty quantification for graph-valued supervised prediction.
method Proposes a conformal prediction framework using Z-Gromov-Wasserstein distances for graph-valued outputs.
result Provides distribution-free coverage guarantees for graph-valued outputs.
Bayesian kernel regression improves functional output prediction.
problem Functional output regression in supervised learning.
method Kernel methods, leveraging covariance structure within function values.
result Enhanced prediction accuracy and handling of high-dimensional nonlinearity.
RVFL NNs perform well without direct links and output bias for regression.
problem Effect of direct links and output bias on RVFL performance.
method Classical and two new methods for generating hidden nodes' parameters tested.
result Direct links and output bias do not significantly improve RVFL accuracy for typical nonlinear regression problems.
Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have limited representational power. We present the Gaussian Process Autoregressive Regr…
In many applications of supervised learning, multiple classification or regression outputs have to be predicted jointly. We consider several extensions of gradient boosting to address such problems. We first propose a straightforward adaptation of gradient boosting exploiting multiple output regression trees as base le…
Solves regression problems with CP by converting to classification.
problem Challenges in CP for heteroscedastic, multimodal, or skewed regression outputs.
method Converts regression to classification, uses CP for classification to obtain CP sets for regression.
result Simple approach yields good results on practical problems.
Safe active learning for multi-output Gaussian processes reduces data acquisition costs and ensures safety.
problem Expensive data acquisition and safety concerns in multi-output regression problems.
method Proposes a safe active learning approach considering data informativeness and safety constraints.
result Improved convergence compared to competitors on simulated and real-world datasets.
Study confirms learning rates for vector-valued spectral algorithms, proving consistency.
problem Theoretical confirmation of learning rates for vector-valued spectral algorithms.
method Rigorous analysis of learning rates for various vector-valued spectral algorithms, including kernel ridge regression and gradient descent.
result Upper and lower bounds on learning rates for vector-valued spectral algorithms, proving minimax optimality in various scenarios.
New method learns output embeddings for structured prediction.
problem Structured prediction with output embeddings.
method Jointly learns output embedding and regression function.
result Structured predictor is a consistent estimator with smaller complexity.
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
Enhances robustness of MOGP regression for multiple correlated outputs.
problem Model misspecification and outliers in MOGP regression.
method Extends RCGP framework to multi-output setting.
result Provable robust MOGP with joint correlation capture.
A scalable method for efficient inference in Gaussian process regression networks.
problem Intractable inference in Gaussian process regression networks (GPRN).
method Tensorization of output space, tensor/matrix-normal variational posteriors, joint optimization, and exploiting Kronecker product structure.
result Captures posterior dependencies and improves inference quality for large number of outputs.
The report analyzes infinite-dimensional output space regression.
problem Learning theory in vector-valued RKHS regression.
method Integral operator technique with spectral theory for non-compact operators.
result Results with minimal assumptions using Chebyshev's inequality.
Active learning method reduces labeling cost for regression models with aggregated data.
problem Reducing labeling cost for training regression models with aggregated data.
method Sequentially selects sets to be labeled using mutual information quantifying model parameter uncertainty.
result Achieves better predictive performance with fewer labeled sets.
This paper aims to decrease the time complexity of multi-output relevance vector regression from O(VM^3) to O(V^3+M^3), where V is the number of output dimensions, M is the number of basis functions, and V<M. The experimental results demonstrate that the proposed method is more competitive than the existing method, wit…
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.
The paper develops exact and approximate conformal inference methods for multi-output regression.
problem Uncertainty quantification in multi-output regression predictions.
method Exact derivations and approximations of conformal inference p-values for linear multi-output predictors, and efficient methods for nonlinear predictors.
result Efficient methods for approximating conformal prediction regions for multi-output predictors, both linear and nonlinear.
This paper introduces hyperspherical prototype networks, which unify classification and regression with prototypes on hyperspherical output spaces. For classification, a common approach is to define prototypes as the mean output vector over training examples per class. Here, we propose to use hyperspheres as output spa…
This work simplifies Gaussian process regression for multiple outputs.
problem Exponential computational complexity in Gaussian process regression.
method Approximating the covariance kernel using eigenvalues and functions.
result Significant reduction in training and regression complexity.
We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in \cite{fan08sis}, is an efficient and highly scalable way to remove many irrelevant variab…
We propose two nonlinear regression methods, named Adversarial Orthogonal Regression (AdOR) for additive noise models and Adversarial Orthogonal Structural Equation Model (AdOSE) for the general case of structural equation models. Both methods try to make the residual of regression independent from regressors while put…
Unified study of nine multi-output conformal methods with generalized scores.
problem Challenges in extending conformal prediction to multi-output problems.
method Nine conformal methods with generalized multi-output conformity scores.
result Generalized scores ensure asymptotic conditional coverage and exact finite-sample marginal coverage.
We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of distribution calibration, and demonstrate its advantages over the existing defin…
Deep single-index Fréchet regression for metric space-valued outputs
problem Predicting outputs in non-Euclidean spaces
method DeSI (Deep Single-Index Fréchet Regression)
result Interpretable index direction for inputs
Multi-output regression seeks to borrow strength and leverage commonalities across different but related outputs in order to enhance learning and prediction accuracy. A fundamental assumption is that the output/group membership labels for all observations are known. This assumption is often violated in real application…
Proposes a deep tree-ensemble model for multi-output prediction.
problem Lack of efficient solutions for multi-output prediction.
method Integrates tree-embeddings into deep tree-ensembles for structured output prediction.
result Superior performance in multi-label classification and multi-target regression tasks.
In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating the conditional median. To address the challenge that both the input and output c…
We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like multi-task learning and structured out- put prediction. We show that multi-task ke…
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…
Introduces a new model for mapping matrices to matrices, subsuming linear regression.
problem Learning matrix-to-matrix mappings from data.
method Partial trace regression model, leveraging quantum information theory.
result Relevance demonstrated in matrix-to-matrix regression and positive semidefinite matrix completion.
We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables,…
The paper introduces a new FOR framework using Huber and ε-insensitive losses.
problem Handling outliers and sparsity in functional output regression.
method Proposes a flexible FOR framework with infimal convolution losses and computable algorithms.
result Demonstrates efficiency and effectiveness on synthetic and real-world data.
Paper introduces conformal prediction for reliable uncertainty quantification in landmark localization.
problem Systematic underestimation of total predictive uncertainty in landmark localization.
method Conformal prediction framework for multi-output regression, generating flexible prediction regions.
result Methods outperform existing approaches in validity and efficiency across 2D and 3D datasets.
DRE combines DNN with random feature regression for efficient neural network design.
problem Designing and training deep neural networks (DNN) efficiently and effectively.
method DRE architecture with two-layer neural networks, randomly drawn input and output weights trained with linear ridge regression.
result DRE outperforms state-of-the-art DNN in many data sets with lower computational cost.
A method for constructing tight prediction intervals for multiple numerical outputs.
problem Constructing tight prediction intervals for multiple related numerical outputs.
method A novel coordinate-wise standardization procedure that makes residuals comparable across output dimensions, estimating suitable scaling parameters using calibration data.
result The method produces tighter prediction intervals than existing baselines while maintaining valid simultaneous coverage.
In this paper, we propose hybrid building/floor classification and floor-level two-dimensional location coordinates regression using a single-input and multi-output (SIMO) deep neural network (DNN) for large-scale indoor localization based on Wi-Fi fingerprinting. The proposed scheme exploits the different nature of th…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify its statistics, using the minimum number of function evaluations. This problem …
The paper introduces a method for learning nonparametric Volterra kernels using Gaussian processes.
problem Learning nonparametric nonlinear operators from data.
method NVKM model using Volterra series and Gaussian processes for unobserved and observed input functions.
result The NVKM model can perform both single and multiple output regression and system identification.
Parallel gradient boosting speeds up multi-output regression.
problem Efficiently predicting entire conditional distributions.
method Modification of gradient boosting to use a common descent direction.
result Significantly faster and comparable performance to state-of-the-art boosting libraries.
Industrial process control systems try to keep an output variable within a given tolerance around a target value. PID control systems have been widely used in industry to control input variables in order to reach this goal. However, this kind of Transfer Function based approach cannot be extended to complex processes w…
This paper introduces a multi-output Gaussian process for censored data.
problem Modeling bias in censored data using correlations between multiple outputs.
method Heteroscedastic multi-output Gaussian process with input-dependent noise and variational inference.
result The model better estimates the true process under complex censoring dynamics.