New method estimates covariance in deep heteroscedastic regression without labels.
problem Estimating covariance in deep heteroscedastic models is challenging due to sample-dependent covariance and lack of ground truth.
method Proposes a self-supervised approach using KL Divergence and 2-Wasserstein distance for covariance estimation and a neighborhood-based heuristic for pseudo labels.
result Demonstrates effective pseudo labels and a computationally cheaper yet accurate deep heteroscedastic regression.
The role of uncertainty quantification (UQ) in deep learning has become crucial with growing use of predictive models in high-risk applications. Though a large class of methods exists for measuring deep uncertainties, in practice, the resulting estimates are found to be poorly calibrated, thus making it challenging to …
Improves deep learning performance on noisy datasets using inverse-variance weighting.
problem Heteroscedastic regression with varying noise levels.
method Batch Inverse-Variance (BIV) loss function for neural networks.
result Significantly improves network performance on noisy datasets compared to other methods.
Bayesian neural network models improve uncertainty quantification in multivariate regression.
problem Uncertainty quantification in multivariate regression models with heteroscedastic noise.
method Proposes Bayesian Last Layer neural network models and EM algorithms for parameter learning.
result Capable of disentangling aleatoric and epistemic uncertainty.
Improved heteroscedastic regression using neural networks with provably accurate mean estimates and calibrated variance.
problem Optimizing neural network parameters for heteroscedastic regression leads to suboptimal mean and variance estimates.
method Two simple modifications to optimization to retain accuracy of mean-only models and offer best-in-class variance calibration.
result Mean estimates from the proposed method are provably as accurate as those from a homoscedastic model.
Bayesian model captures mean and variance of response variables.
problem Complex, predictor-dependent relationships and heteroscedastic patterns in data.
method Sum-of-tessellations for mean, product-of-tessellations for variance.
result Model captures nuanced variance structures and provides reliable predictive uncertainty.
Proposes HDBEN for heteroscedastic regression with improved sparsity and variance modeling.
problem Violation of constant error variance in high-dimensional regression.
method HDBEN framework using hierarchical Bayesian priors with ℓ1 and ℓ2 penalties. result Achieves posterior concentration, variable selection consistency, and asymptotic normality.
Improved conformalized quantile regression for adaptive prediction intervals.
problem Lack of adaptiveness in the conformal step of conformalized quantile regression.
method Cluster explanatory variables by permutation importance and apply k conformal steps.
result Improved prediction intervals are more adaptive to heteroscedasticity.
CLAPS improves conformal regression by adaptively scaling interval widths based on last-layer Laplace uncertainty.
problem Lack of adaptive interval width scaling in conformal regression for heterogeneous inputs.
method CLAPS uses heteroscedastic last-layer Laplace uncertainty to adaptively scale interval widths, combining aleatoric and epistemic uncertainties.
result CLAPS provides competitive interval efficiency with nominal-level coverage, reducing to aleatoric scaling as epistemic uncertainty decreases.
Regression trees are becoming increasingly popular as omnibus predicting tools and as the basis of numerous modern statistical learning ensembles. Part of their popularity is their ability to create a regression prediction without ever specifying a structure for the mean model. However, the method implicitly assumes ho…
New method predicts aphasia severity with narrower uncertainty intervals.
problem Predicting aphasia severity in stroke patients using neuroimages.
method Sparse heteroscedastic Bayesian high-dimensional regression with H-PROBE algorithm.
result H-PROBE provides narrower prediction intervals for aphasia severity.
Enhances Gaussian process models for handling variable error variances and multiple responses.
problem Limited ability of Gaussian process models to capture abrupt changes and heteroscedastic errors.
method Introduces a novel heteroscedastic Gaussian process (HeGP) framework coupled with variational inference and EM algorithm.
result Effective modeling of multivariate responses with varying error variances.
Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates the latent function and the noise function together in a unified non-parametric B…
A simple method treats heteroscedastic variance variatively, improving model calibration and sample quality.
problem Brittle optimization impacts model likelihoods for mean and variance estimation.
method Proposes a variational approach to heteroscedastic variance, improving predictive mean and variance calibration.
result The proposed method significantly improves parameter calibration and sample quality for regression and VAEs.
To restore the historical sea surface temperatures (SSTs) better, it is important to construct a good calibration model for the associated proxies. In this paper, we introduce a new model for alkenone (U37K′) based on the heteroscedastic Gaussian process (GP) regression method. Our nonparametric app…
In this work we propose a heteroscedastic generalization to RVM, a fast Bayesian framework for regression, based on some recent similar works. We use variational approximation and expectation propagation to tackle the problem. The work is still under progress and we are examining the results and comparing with the prev…
VHVM models financial time series with varying volatility.
problem Modeling heteroscedastic behavior in multivariate financial time series.
method Variational autoencoder and recurrent neural network for capturing relationships and temporal dynamics.
result VHVM outperforms GARCH and SV models on FX datasets.
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a Gaussian distribution. …
Paper supports robust estimation in regression with heavy-tailed errors.
problem Support estimation in high-dimensional heteroscedastic mean regression.
method Use of Huber loss function and adaptive LASSO penalty for robust estimation.
result Sign-consistency and optimal rates of convergence in ℓ∞ norm. Study on online regression with noise, achieving near-optimal regret bounds.
problem Online generalized linear regression with stochastic noise.
method Sharp analysis of FTRL algorithm for stochastic label noise.
result Achieved near-optimal regret bounds for O(σ2dlogT)+o(logT). 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.
We improve optimization for data with varying variance.
problem Optimizing data with varying variance.
method Generalized learning and optimization frameworks for data-driven optimization.
result Asymptotic and finite sample guarantees for stochastic programs.
Improved heteroscedastic regression with machine learning techniques.
problem Estimating weights in heteroscedastic linear regression with varying noise.
method Alternating minimization with weighted least squares and pseudogradient descent.
result Achieved a tighter error bound for estimating weights.
LCMQR improves prediction intervals by adapting to local heteroscedasticity.
problem Efficient and adaptive prediction intervals for local heteroscedasticity.
method LCMQR combines multi-quantile information with kernel-based localization.
result LCMQR constructs tighter intervals than prior methods, especially in heterogeneous environments.
New method combines HQR and WACI for better time series prediction intervals.
problem Challenges in creating reliable prediction intervals for time series forecasting.
method Combining Heteroscedastic Quantile Regression (HQR) with Width-Adaptive Conformal Inference (WACI).
result Combined approach meets or surpasses typical benchmarks for validity and efficiency.
This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over input dependent noise variance (heteroscedasticity) and input dependent signal varia…
A simple approach to obtaining uncertainty-aware neural networks for regression is to do Bayesian linear regression (BLR) on the representation from the last hidden layer. Recent work [Riquelme et al., 2018, Azizzadenesheli et al., 2018] indicates that the method is promising, though it has been limited to homoscedasti…
Scheduling surgeries is a challenging task due to the fundamental uncertainty of the clinical environment, as well as the risks and costs associated with under- and over-booking. We investigate neural regression algorithms to estimate the parameters of surgery case durations, focusing on the issue of heteroscedasticity…
Unified predictive uncertainty disentangled using deep split ensembles.
problem Understanding and quantifying uncertainty in NNs for real-world applications.
method Deep split ensemble approach using multivariate Gaussian mixture model.
result Inherently well-calibrated models with high flexibility to group features.
We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required on the model, except the existence of a suitable function that controls the local suprema of the empirical process. So far, only the case of…
Simple method improves deep classifier accuracy under noisy labels.
problem Training deep classifiers with noisy labels.
method Probabilistic approach using temperature parameterized softmax.
result Improves accuracy, log-likelihood and calibration on noisy datasets.
Efficient exploration remains a major challenge for reinforcement learning. One reason is that the variability of the returns often depends on the current state and action, and is therefore heteroscedastic. Classical exploration strategies such as upper confidence bound algorithms and Thompson sampling fail to appropri…
Proposes a new robust expectile regression method for high-dimensional data.
problem Heterogeneity in high-dimensional data with heteroscedastic variance or inhomogeneous covariate effects.
method Iteratively reweighted ℓ1-penalization for robust expectile regression (retire).
result Oracle convergence rate after log(log d) iterations in high-dimensional settings.
Reweighting improves risk bounds in certain data regions.
problem Improving risk bounds in classification and heteroscedastic regression.
method Weighted empirical risk minimization with a data-dependent weight function.
result A weighted ERM estimator can achieve superior performance in specific sub-regions.
Estimates variance function using aggregation methods in regression models.
problem Estimating variance function in regression models.
method Two-step procedure involving model selection or convex aggregation, using two independent samples.
result Consistency of the proposed method in L2 error for MS and C aggregations.
Spatio-temporal problems are ubiquitous and of vital importance in many research fields. Despite the potential already demonstrated by deep learning methods in modeling spatio-temporal data, typical approaches tend to focus solely on conditional expectations of the output variables being modeled. In this paper, we prop…
A new method improves quantile regression for high-dimensional data.
problem Handling heteroscedastic, multimodal, or skewed data in quantile regression.
method Dynamic prototypes-based probability density estimation with conformalized high-density quantile regression.
result Enhanced prediction regions with valid coverage guarantees and scalability to higher dimensions.
Develops conformalized prediction intervals for bounded continuous outcomes.
problem Predicting continuous outcomes within bounded ranges, especially when models are misspecified.
method Conformal prediction intervals based on transformation regression models, accounting for heteroscedasticity and asymmetry.
result Valid finite-sample coverage confirmed in simulations and real data applications.
Proposes a method to improve classification robustness against label noise.
problem Improving classification robustness against label noise.
method Extends a simple regression approach to classification, modeling labels as samples from a logistic-normal distribution.
result The method improves robustness against label noise in classification.
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the errors have uniformly …
GGMPs improve non-Gaussian conditional density estimation.
problem Multimodality, heteroscedasticity, and strong non-Gaussianity in conditional density estimation.
method GGMP combines local Gaussian mixture fitting, cross-input component alignment, and per-component heteroscedastic GP training.
result GGMPs improve distributional approximation on synthetic and real-world datasets.
The paper proposes a method for predicting equity premium using penalized quantile regression.
problem Heteroscedasticity and heavy-tails in equity premium prediction.
method Penalized quantile regression with consistent variable selection across multiple quantiles.
result The proposed method outperforms benchmark methods and reveals interesting predictor relationships.
Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not explicitly measure the uncertainties. This is conceptually similar to heteroscedastic ne…
New method for probabilistic prediction sets with conditional validity.
problem Marginal coverage guarantee of existing methods.
method Combines conformal methods with approximate conditional validity.
result Consistently outperforms existing approaches in conditional coverage.
Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point estimate of the target. In addition, the model does not take into account the u…
Proposes a new method for robust uncertainty quantification in regression tasks.
problem Robust uncertainty estimation for deep neural networks in regression tasks.
method Generalized Auxiliary Uncertainty Estimator (AuxUE) scheme, considering both aleatoric and epistemic uncertainties.
result DIDO method provides robust uncertainty estimates in noisy inputs, scalable to image-level and pixel-wise tasks.
We propose a novel method for automatic pain intensity estimation from facial images based on the framework of kernel Conditional Ordinal Random Fields (KCORF). We extend this framework to account for heteroscedasticity on the output labels(i.e., pain intensity scores) and introduce a novel dynamic features, dynamic ra…
In the stochastic bandit problem, the goal is to maximize an unknown function via a sequence of noisy evaluations. Typically, the observation noise is assumed to be independent of the evaluation point and to satisfy a tail bound uniformly on the domain; a restrictive assumption for many applications. In this work, we c…