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. …
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48 results for “Gaussian residuals”
GaussDetect-LiNGAM eliminates Gaussianity tests for causal discovery.
problem Causal direction identification without Gaussianity assumptions.
method Leverages the equivalence between noise Gaussianity and residual independence in reverse regression.
result Gaussianity tests replaced with robust kernel-based independence tests.
Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the fact that many repeated evaluations of the forward model are often required. In…
Residual Component Analysis: Generalising PCA for more flexible inference in linear-Gaussian modelscs.LG
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situation where the data v…
We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the effects have the same distribution, we show that the distribution of the residuals of …
Fast calculation of Gaussian Process multiple-fold cross-validation residuals and their covariancesstat.ME
We speed up Gaussian process cross-validation calculations and improve model diagnostics.
problem Efficiently calculating cross-validation residuals and their covariances in Gaussian processes.
method Generalized fast Gaussian process leave-one-out formulae to multiple-fold cross-validation, highlighting covariance structures.
result Correcting for residual covariances in cross-validation improves back to Maximum Likelihood Estimation.
Deep Gaussian processes on manifolds improve performance on complex data.
problem Complex data on manifolds that shallow models struggle with.
method Residual deep Gaussian processes on Riemannian manifolds.
result Significant improvement in prediction quality and uncertainty calibration.
Two methods improve Gaussian process predictive distributions' calibration.
problem Improving the reliability of Gaussian process predictive intervals.
method Introduces two methods: cps-gp and bcr-gp, both adapting conformal predictive systems to GP interpolation.
result Both methods provide finite-sample marginal calibration and smooth predictive distributions.
We add size factor to CAPM and normalize residuals by Volatility Index.
problem Capturing the size effect in CAPM and making residuals Gaussian.
method Insert size effect, normalize residuals by Volatility Index, and fit model to real-world data.
result The new model shows long-term stability and connects to Stochastic Portfolio Theory.
Proposes a new regression method using -norms for non-Gaussian noise.
problem Non-Gaussian noise in residuals affects the performance of local least squares regression.
method Introduces local polynomial -norm regression, replacing weighted least squares with weighted -norm estimation.
result Demonstrates superior performance over local least squares in one-dimensional data and higher dimensions.
Improves out-of-distribution detection in neural networks.
problem Detecting out-of-distribution examples in neural networks.
method Normalizing flows and residual flow architecture for expressive density modeling.
result Significantly improved true negative rate (77.5%) compared to state-of-the-art (56.7%).
We propose a novel exponentially-modified Gaussian (EMG) mixture residual model. The EMG mixture is well suited to model residuals that are contaminated by a distribution with positive support. This is in contrast to commonly used robust residual models, like the Huber loss or , which assume a symmetric contami…
Generalised Boosted Forestsstat.ME
The paper improves random forest models for non-Gaussian responses.
problem Improving random forest models for non-Gaussian responses.
method Extends boosting random forests to model exponential family responses using residuals and weights.
result Generalized boosted forests reduce bias and provide conservative confidence intervals.
Residual Component Analysisstat.ML
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situa…
New GP kernel handles mixed-categorical data, improving model accuracy.
problem Improving Gaussian process models for mixed-categorical data.
method Extends continuous exponential kernels to handle mixed-categorical variables.
result The proposed GP model gives higher likelihood and smaller residual error.
TRA detects causal direction from bivariate data using geometric shapes.
problem Inferring causal direction from observational data is challenging and unreliable.
method TRA compares rank-based copula-standardized residual clouds to detect causal direction.
result TRA is robust and superior in detecting causal direction across various scenarios.
The VIX is used to model corporate bond volatility and returns.
problem Modeling volatility and returns for corporate bonds using observable data.
method Applied stochastic volatility models using the VIX index to corporate bond rates and spreads.
result Residuals of corporate bond returns divided by VIX are closer to Gaussian white noise.
Theoretical limits of deep residual networks show consistent covariance structures.
problem Understanding the limits of deep residual networks.
method Analyzing the behavior of deep residual networks with skip connections as width and depth approach infinity.
result Theoretical analysis confirms that the covariance structure remains consistent regardless of the order of width and depth.
A new method boosts exploration in bandit algorithms, reducing regret.
problem Improving exploration in bandit algorithms with bounded or unbounded rewards.
method Residual Bootstrap Exploration (ReBoot) method that injects data-driven randomness.
result Proves logarithmic regret in Gaussian multi-armed bandits with appropriate variance inflation.
Variational auto-encoders (VAEs) are a popular and powerful deep generative model. Previous works on VAEs have assumed a factorized likelihood model, whereby the output uncertainty of each pixel is assumed to be independent. This approximation is clearly limited as demonstrated by observing a residual image from a VAE …
DRMMs enable flexible conditional sampling for interactive machine learning.
problem Limited flexibility in conditional sampling for deep generative models.
method Proposes Deep Residual Mixture Models (DRMMs) that allow flexible conditional sampling.
result DRMMs enable sampling with arbitrary combinations of conditioning variables and priors.
Develops a new multivariate regression model for complex outcomes.
problem Flexible, heterogeneous, and residual-dependent multivariate regression problems.
method MultiVCBART framework with Graphical Horseshoe priors.
result Empirically outperforms existing models on sparse, high-dimensional datasets.
Develops EFT for ResNets, revealing limitations of kernel-only approach.
problem Limitations of kernel-only approach in deep neural networks.
method Collective kernel EFT for pre-activation ResNets based on -only closure hierarchy.
result Numerical findings show equation residual accumulates to an error.
Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in general, not directly observable and it is poorly constrained to calculate. Further, it…
Proposes a robust method for high-dimensional linear models.
problem Inference in high-dimensional settings with heavy-tailed errors and clustered data.
method Residual randomization procedure for Lasso-based inference.
result Outperforms state-of-the-art methods in challenging settings.
Graph neural networks often assume vertex labels are independent, but we show this is rarely true and propose a method to improve predictions.
problem Graph neural networks often assume vertex labels are conditionally independent given their neighborhood features, which is rarely true.
method We model the joint distribution of residuals on vertices with a parameterized multivariate Gaussian and estimate parameters by maximizing the marginal likelihood of the observed labels.
result Our method achieves substantially higher accuracy than competing baselines and can be interpreted as the strength of correlation among connected vertices.
Study infinite-depth limits of neural networks with fixed width.
problem Understanding the behavior of neural networks as depth increases with fixed width.
method Analyzing finite-width residual networks with random Gaussian weights, focusing on the infinite-depth limit.
result The pre-activations converge to a zero-drift diffusion process, differing from the infinite-width limit.
The paper proposes a neural network architecture inspired by Langevin Monte Carlo for sampling from target distributions.
problem Sampling from complex target distributions efficiently.
method A neural network architecture inspired by Langevin Monte Carlo is proposed to map samples from a simple reference distribution to samples from the target.
result The proposed neural network architecture achieves approximation rates in the Wasserstein-2 distance for smooth, log-concave target distributions.
On the Estimation Performance of Generalized Power Method for Heteroscedastic Probabilistic PCAmath.OC
Paper proposes GPM for heteroscedastic PCA estimation.
problem Estimating ground truth from heterogeneous data.
method Generalized power method (GPM) for HQPOC.
result GPM achieves geometrically decreasing distances to ground truth.
REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysisphysics.comp-ph
REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis
problem Multidisciplinary design analysis of coupled engineering systems requires solving equilibrium states where all disciplinary coupling variables are consistent.
method Residual manifold surrogate modeling framework for coupled systems.
result REMAL learns a surrogate model of the joint residual manifold via multitask Gaussian process models.
New method diagnoses criticality in deep neural networks, improving performance.
problem Improving theoretical understanding and practical initialization of deep neural networks.
method Introducing partial Jacobians and deriving recurrence relations for their norms to analyze criticality.
result Proper stacking of LayerNorm and residual connections leads to a critical architecture for any initialization.
A robust Gaussian process model using Huber likelihood for outlier resistance.
problem Outliers in observational data sets affect Gaussian process regression's robustness.
method Proposes a Gaussian process model with Huber likelihood and weights based on projection statistics.
result Demonstrates improved statistical efficiency and robustness to outliers.
Paper studies M-estimators with derivatives and residual distribution for robust adaptive tuning.
problem Tackles robustness and adaptive tuning of M-estimators with heavy-tailed noise.
method Provides formulae for derivatives, characterizes residual distribution, proposes adaptive criterion.
result Characterizes distribution of residuals and proposes adaptive criterion as out-of-sample error proxy.
Statistical Robust Chinese Remainder Theorem for Multiple Numbers: Wrapped Gaussian Mixture Modelstat.ML
Generalized Chinese Remainder Theorem (CRT) has been shown to be a powerful approach to solve the ambiguity resolution problem. However, with its close relationship to number theory, study in this area is mainly from a coding theory perspective under deterministic conditions. Nevertheless, it can be proved that even wi…
DeRegiME forecasts with regime structure, improving probabilistic predictions across various time series.
problem Probabilistic forecasting discards residual uncertainty, and distribution shifts are hard to capture.
method DeRegiME uses a sparse variational Gaussian process with a nonstationary regime-mixing kernel to separate latent uncertainty regimes.
result DeRegiME improves NLPD by 20.3% on average across benchmarks, with gains on CRPS and MSE.
The paper investigates non-linear and heavy-tailed predictability in transition-energy financial markets.
problem Incomplete representation of dependence structure in Gaussian-linear forecasting frameworks.
method Develops a hybrid forecasting framework combining Student-t Vector Autoregressions with nonlinear recurrent residual learning architectures.
result The proposed framework consistently improves predictive accuracy relative to conventional models, especially during macro-financial stress.
Deep linear ResNets converge globally with certain transformations.
problem Global convergence of training deep linear ResNets.
method Gradient descent and stochastic gradient descent for training -hidden-layer linear ResNets.
result GD and SGD can converge to global minimum for deep linear ResNets with specific transformations.
CCVFM uses coreset to improve generative models by refining residual flows.
problem Generating multimodal distributions from scratch is challenging.
method Augments hierarchical rectified flow with a data-informed source distribution using a coreset.
result CCVFM achieves competitive few-step generation without a learned noise-to-data map.
Study uses Wasserstein distance to identify causal orders and unmix sources.
problem Identifying causal relationships and separating sources in non-Gaussian data.
method Wasserstein distance for non-Gaussianity, linear ICA, causal inference.
result Exact identification of ICA unmixing matrix and causal orders.
CN-SBM clusters cancer samples and regions based on copy number variants.
problem Clonal evolution in cancer monitored by noisy copy number variants.
method Probabilistic framework using bipartite categorical block model.
result Improved model fit and clinically relevant subtypes identified.
We consider the problem of simultaneous reduction of acoustic echo, reverberation and noise. In real scenarios, these distortion sources may occur simultaneously and reducing them implies combining the corresponding distortion-specific filters. As these filters interact with each other, they must be jointly optimized. …
Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.
problem Existence of non-residually finite hyperbolic groups
method Direct implication
result Existence of non-residually finite rigid hyperbolic groups
Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these resul…
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core and Alexander quandles) is established. Further, residual…
Least-Squares Independence Regression for Non-Linear Causal Inference under Non-Gaussian Noisestat.ML
The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model…
Every non-trivial knot group is fully residually perfect.
problem Understanding the residual properties of knot groups.
method Analyzing the residual properties of knot groups using group theory.
result Every non-trivial knot group is fully residually perfect.
Improving Linear System Solvers for Hyperparameter Optimisation in Iterative Gaussian Processescs.LG
The paper speeds up hyperparameter optimisation in Gaussian processes.
problem Scaling hyperparameter optimisation to large datasets.
method Improvements to linear system solvers (pathwise gradient, warm starting, early stopping).
result Speed-ups of up to 72x and residual norm decreases of up to 7x.
Protein contacts contain important information for protein structure and functional study, but contact prediction from sequence remains very challenging. Both evolutionary coupling (EC) analysis and supervised machine learning methods are developed to predict contacts, making use of different types of information, resp…