Develops efficient inference for noise heterogeneity in machine learning models.
problem Downstream procedures based on residuals can be biased in additive noise models.
method Semiparametrically efficient inference using a novel Hilbert-valued one-step estimator.
result Constructs tests and confidence intervals for residual independence and goodness of fit.
Tests if market noise is explained by limit order book variables.
problem Determining if market microstructure noise is fully explained by specific limit order book variables.
method Compares two quasi-maximum likelihood estimators of volatility, one including residual noise and one not, in a nonparametric framework.
result Examines central limit theory of quasi-maximum likelihood estimation in the presence of residual noise.
Residual networks improve noise stability, leading to better performance.
problem Degradation problem in training Residual Neural Networks.
method Introduced simplified versions of ResNets and PlnNets, showing equivalence in expressive power.
result Residual networks have better noise stability, leading to improved generalization.
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.
GRRT recovers sparse signals without prior sparsity or noise variance knowledge.
problem Recovering sparse signals without prior sparsity or noise variance knowledge.
method Generalized residual ratio thresholding (GRRT) for SOMP and BOMP.
result Finite sample and finite SNR guarantees for exact support recovery.
Alternative to likelihood-based LSNM model selection, residual independence testing is more robust to noise misspecification.
problem Cause-effect inference in location-scale noise models with misspecified noise distributions.
method Residual independence testing as an alternative to likelihood-based model selection.
result Residual independence testing is more robust to noise misspecification.
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
problem Constructing reliable confidence regions for linear regression models with non-symmetric noise.
method Residual-Permuted Sums (RPS) method, which permutes residuals instead of perturbing their signs.
result RPS provides exact finite sample coverage probabilities and is uniformly strongly consistent.
The paper extends SARMA models by relaxing independence assumptions on error terms.
problem Testing adequacy of SARMA models with non-independent errors.
method Study of asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations under weak noise assumptions.
result Established asymptotic behavior of portmanteau tests for SARMA models.
New technique RRT improves OMP performance without knowing sparsity or noise.
problem Recovering sparse high-dimensional vectors without knowing sparsity or noise statistics.
method Residual ratio thresholding (RRT) to operate OMP without a priori knowledge.
result RRT achieves comparable performance to OMP with known statistics.
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.
Noise statistics oblivious algorithm improves robust regression with sparse outliers.
problem Robust regression with sparse outliers in the presence of Gaussian noise.
method Developed a noise statistics oblivious algorithm called RRT-GARD by modifying GARD.
result RRT-GARD performs nearly as well as GARD with known noise statistics.
Proposes a new regression method using Lp-norms for non-Gaussian noise.
problem Non-Gaussian noise in residuals affects the performance of local least squares regression.
method Introduces local polynomial Lp-norm regression, replacing weighted least squares with weighted Lp-norm estimation. result Demonstrates superior performance over local least squares in one-dimensional data and higher dimensions.
A deep learning model improves seismic noise reduction.
problem Seismic noise attenuation in pre-stack data processing.
method N2N-Seismic model based on residual neural networks.
result The model significantly outperforms conventional approaches in noise reduction metrics.
Deep heteroskedastic models overfit, showing a phase transition with regularization strength.
problem Overfitting in deep heteroskedastic regression models.
method Theoretical framework based on statistical field theory, empirical verification, and hyperparameter simplification.
result A phase transition in model behavior with varying regularization strength.
Unified ODE model explains residual and non-residual networks.
problem Unclear relationship between residual and non-residual networks.
method Introducing a damping term in an ODE model to interpolate between ResNet and CNN architectures.
result Unified framework for understanding residual and non-residual networks.
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.
Jointly reduces echo, reverberation, and noise using neural networks.
problem Simultaneous reduction of acoustic echo, reverberation, and noise.
method Multichannel Gaussian modeling and neural network for joint optimization of filters.
result Outperforms individual and joint non-spectral models.
New techniques for compressive sensing without noise or signal statistics.
problem Support recovery in underdetermined linear regression models without prior noise and signal statistics.
method Proposes RRM and RRTA to operate OMP algorithm without noise variance or signal sparsity knowledge.
result Establishes high SNR consistency for OMP without prior noise and signal statistics.
Paper proves noise-tolerant SSC using greedy methods under coherence conditions.
problem Proving noise-tolerant SSC using greedy methods under coherence conditions.
method Derives coherence-based sufficient conditions for correct neighbor identification using MP/OMP in the presence of bounded noise.
result MP/OMP succeed in identifying correct neighbors under certain noise levels, leading to higher clustering accuracy.
SRFRN accelerates image super-resolution using shallow residual units.
problem High computational complexity and time in deep learning image super-resolution.
method SRFRN uses a bicubic interpolated low-resolution image and residual representative units (RFR) for faster and more efficient high-resolution image reconstruction.
result SRFRN achieves superior performance and faster execution time compared to existing methods.
Regularization helps resolve ambiguity in mean-variance models, improving predictive uncertainty quantification.
problem Signal-to-noise ambiguity in overparameterized mean-variance models.
method Statistical field theory framework to explain phase transition.
result Regularization reduces variability and improves predictive uncertainty quantification.
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…
Efficiently refits black box predictions with wild refitting method.
problem Computing high-probability upper bounds on prediction errors.
method Three-step procedure: residuals, symmetrization, and solving a modified prediction problem.
result Wild refitting provides an upper bound on prediction error with high probability.
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. …
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.
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to estimate high-dimensional factor models, using the empirical spectral density of …
New method views residual networks as stochastic differential equations.
problem Improving generalization of neural networks.
method Applying modified equations to show residual networks as weak approximations of stochastic differential equations.
result Stochastic training of residual networks can be understood through the lens of optimal control of backward Kolmogorov's equations.
New diagnostic method detects misspecified models in inverse PDE problems.
problem Misleading residual-norm diagnostics in inverse PDE problems.
method Structure-sensitive sequential diagnostic using e-processes.
result Rejects fitted models that produce biased predictions.
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.
Novel LSTM network predicts pulsar timing residuals with few-shot data.
problem Predicting pulsar timing residuals with limited data.
method Long Short-Term Memory (LSTM) network optimized with model-agnostic meta-learning and particle swarm optimization.
result Robust generalization and accurate predictions across high-frequency test domains with minimal data.
Enhances speech from reverberated and noisy signals using Wide Residual Networks.
problem Improving intelligibility of speech from reverberated and noisy signals.
method Wide Residual Network architecture with residual connections for processing contextually correlated representations.
result Enhanced speech from the proposed method succeeded for both enhancement and speech recognition tasks.
The distribution of Chern-Simons invariants on 3-manifolds resembles quadratic residues.
problem Distribution of Chern-Simons invariants on 3-manifolds.
method Analyzing the values of the Chern-Simons function on conjugacy classes of representations.
result Chern-Simons invariants tend to become equidistributed on the circle with white noise fluctuations.
A simple strategy prevents negative transfer in transfer learning.
problem Negative transfer in transfer learning where source representations harm target performance.
method Residual feature integration with a trainable target-side encoder.
result The method provably prevents negative transfer with theoretical guarantees.
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…
New method improves matrix completion accuracy, especially in noisy data.
problem Noisy matrix completion in recommendation systems and signal processing.
method Residual Spectral Matching criterion and pseudo-gradient algorithms.
result Improved numerical performance in noisy data environments.
Two new methods improve causal inference without noise assumptions.
problem Improving causal inference without distributional assumptions.
method Adversarial Orthogonal Regression (AdOR) and AdOSE methods.
result Effective in synthetic and real-world experiments.
LANCA uses ANM to learn latent causal factors without supervision.
problem Learning latent causal factors without supervision.
method LANCA employs a deterministic Wasserstein Auto-Encoder coupled with a differentiable ANM Layer.
result LANCA outperforms baselines on physics and photorealistic environments.
FactorGCL uses hypergraph learning to predict stock returns by mining hidden factors.
problem Mining effective factors in data-driven models is challenging due to low signal-to-noise ratio in market data.
method FactorGCL employs a hypergraph structure and temporal residual contrastive learning to extract hidden factors.
result FactorGCL outperforms existing methods and mines effective hidden factors for predicting stock returns.
Spatial Adapter adds structured spatial representation to frozen predictors.
problem Efficiently adding spatial structure to pre-trained models.
method Structured spatial decomposition and closed-form covariance for residual fields.
result Adapter improves spatial prediction and uncertainty quantification.
We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and moreover indicates that the noise band is composed of multiple subbands that do not fully mix. Our findings allow us …
New approach quantifies overfitting in high-dimensional regression.
problem Quantifying and avoiding overfitting in large neural networks.
method Information bottleneck theory to minimize residual information while maximizing relevant bits.
result Characterized the relative information efficiency of randomized regression compared to optimal algorithms.
The study improves stock market valuation using volatility and earnings data.
problem Improving stock market valuation metrics.
method Time series model for asset returns, multivariate kernel density estimation, linear regression.
result The valuation measure is an improvement over Shiller's P/E ratio.
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.
RECLAIM discovers causal graphs in cyclic, noisy systems.
problem Discovering causal relationships in cyclic, noisy systems.
method RECLAIM uses EM with residual normalizing flows to handle cycles and noise.
result RECLAIM effectively discovers causal graphs in both synthetic and real-world datasets.
Develops goodness-of-fit tests for noisy submanifold samples.
problem Testing non-linear models on noisy submanifold samples.
method Non-linear least-square problem solution and χ2 distribution application. result Residual follows χ2 distribution with parameters related to model order and dimension. Improved real-time UAV terrain following with RVM-RLS filter.
problem Accurate real-time waypoints estimation under measurement noise in nonlinear, time-varying systems.
method Residual Variance Matching Recursive Least Squares (RVM-RLS) filter guided by RVME criterion.
result Improved waypoints estimation accuracy by approximately 88% compared to benchmarks.
We present a theoretically grounded approach to train deep neural networks, including recurrent networks, subject to class-dependent label noise. We propose two procedures for loss correction that are agnostic to both application domain and network architecture. They simply amount to at most a matrix inversion and mult…
Image denoising techniques are essential to reducing noise levels and enhancing diagnosis reliability in low-dose computed tomography (CT). Machine learning based denoising methods have shown great potential in removing the complex and spatial-variant noises in CT images. However, some residue artifacts would appear in…