Defines Wodzicki residue using groupoids and fibered distributions.
problem Defining and understanding the Wodzicki residue in noncommutative geometry.
method Using groupoid language and filtered manifolds, defining the residue and showing its properties.
result The groupoidal residue is a trace on pseudodifferential operators and matches the usual residue in certain cases.
Simplifies residual flows to make flow-based modeling more practical.
problem Extremely high computational cost of residual flows limits their applicability.
method Introduces Quasi-Autoregressive (QuAR) approach to residual flows.
result Significantly reduces compute time and memory requirements for flow-based modeling.
Extends residue theory to flags of holomorphic distributions.
problem Calculating the residue class of flags of holomorphic distributions.
method Developed an effective method to calculate the class in certain cases.
result Established a relation between degrees, tangency order, Euler characteristic, and curve degree.
We show a residues formula for maps generically transversal to regular holomorphic distributions.
Multi-output is essential in machine learning that it might suffer from nonconforming residual distributions, i.e., the multi-output residual distributions are not conforming to the expected distribution. In this paper, we propose "Wrapped Loss Function" to wrap the original loss function to alleviate the problem. This…
Extends Hawkes process for flexible residual modeling in point processes.
problem Modeling high-frequency financial data with complex residual distributions.
method Introduces self and mutually exciting point process with discretely Markovian dynamics.
result Flexible residual distributions improve intensity modeling and high-frequency data estimation.
Robust forecast framework reduces distribution error by 63%.
problem Accurate distribution forecast for planning decisions.
method Backtest-based bootstrap and adaptive residual selection.
result Reduces Absolute Coverage Error by more than 63%.
We revisit residual algorithms in both model-free and model-based reinforcement learning settings. We propose the bidirectional target network technique to stabilize residual algorithms, yielding a residual version of DDPG that significantly outperforms vanilla DDPG in the DeepMind Control Suite benchmark. Moreover, we…
A new algorithm improves stochastic linear bandit performance using residual bootstrap.
problem Improving performance in stochastic linear bandit problems.
method Residual bootstrap exploration to estimate mean reward and pull the arm with the highest estimate.
result Proposed algorithm exttt{LinReBoot} achieves high-probability sub-linear regret under mild conditions.
New method for distributional off-policy evaluation using Bellman residual minimization.
problem Learning return distribution from offline data generated by a different policy.
method Energy Bellman Residual Minimizer (EBRM) method.
result Established finite-sample error bound for EBRM estimator.
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.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
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%).
Computer vision model automates residual plot assessment for diagnosing model assumptions.
problem Automating residual plot assessment for model diagnostics.
method Trains a computer vision model to predict disparity between residual distributions and reference distributions using Kullback-Leibler divergence.
result Computer vision model is less sensitive to non-linearity but more sensitive than human judgment and conventional tests.
Extends VAEs to handle complex Bayesian network structures.
problem Handling complex dependency structures in Bayesian networks.
method Extends VAEs with graphical residual flows to model arbitrary dependency structures.
result Demonstrates improved performance on synthetic datasets.
This research improves asset life prediction by integrating deep learning with mixture distributions.
problem Predicting residual useful life for assets with multiple failure modes.
method Integrates mixture (log)-location-scale distribution with deep learning.
result Proposed models outperform existing methods in predicting residual useful life.
Two methods are proposed to filter correlations in DCC-GARCH residuals for foreign exchange rates.
problem Filtering correlations in DCC-GARCH residuals for accurate foreign exchange rate prediction.
method Two approaches: estimating correlation matrix as a parameter and using eigenvalue decomposition.
result The DCC-GARCH residual can be almost independent using these methods.
A beta function for double layers is defined and analyzed.
problem Defining and analyzing a beta function for double layers.
method Holomorphic function definition and analytic continuation.
result Residues of the beta function are integrals of invariants.
In this paper we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving-average (SARMA) models under the assumption that the errors are uncorrelated but not necessarily independent.We relax the standard independence assumption on the error term in order to extend the range …
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.
Motivated by the application of real-time pricing in e-commerce platforms, we consider the problem of revenue-maximization in a setting where the seller can leverage contextual information describing the customer's history and the product's type to predict her valuation of the product. However, her true valuation is un…
Graph neural networks suffer from oversmoothing, but adding residual connections helps.
problem Oversmoothing in deep graph neural networks where features become indistinguishable.
method Analyzed asymptotic oversmoothing rates with and without residual connections using the multiplicative ergodic theorem.
result Adding residual connections effectively mitigates or prevents oversmoothing.
The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data …
BDSG generates samples on distribution boundaries, improving anomaly detection.
problem Difficulty in capturing multimodal supports and approximating distribution tails.
method Invertible Residual Network (IResNet) and Residual Flow (ResFlow) for density estimation; compound loss function for boundary samples.
result Competitive performance on synthetic and multimodal data compared to existing methods.
MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.
problem Understanding the coarse-graining procedure in MLP residual networks
method Analyzing a pure MLP residual stack on synthetic Markov chain sequences
result MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution
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. …
The paper introduces a diagnostic method to detect grokking transitions in models before test accuracy improves.
problem Detecting the transition from training to generalization in machine learning models.
method Summarize task-dependent observables as empirical distributions, map them to Wasserstein/quantile coordinates, and analyze using Hankel dynamic mode decomposition.
result The diagnostic method achieves AUROC \(\approx\) 0.93 for grokking-vs-non-grokking discrimination at the run level.
Study proposes a new method for deep portfolio optimization using residual factors.
problem Non-stationary financial market makes traditional machine learning methods ineffective.
method Predict distribution of residual factors using a novel neural network architecture with financial inductive biases.
result Demonstrated improved performance on U.S. and Japanese stock market data.
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 ℓ1, which assume a symmetric contami…
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforci…
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.
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.
Residual Prior Diffusion integrates coarse latent priors with diffusion models for better generative tasks.
problem Diffusion models struggle with representing both large-scale and fine-scale details in data distributions.
method Two-stage framework: first a coarse prior model captures large-scale structure, then a diffusion model represents the residual.
result RPD accurately captures fine-scale details while preserving large-scale structure, outperforming standard diffusion models.
Causality-aware methods outperform linear residualization in confounding adjustment for anticausal prediction.
problem Adjusting for confounding in anticausal prediction tasks.
method Causality-aware counterfactual confounding adjustment.
result Causality-aware methods asymptotically outperform linear residualization in predictive performance.
A new ensemble learning method called Residual Likelihood Forests improves performance and reduces model size.
problem Improving machine learning classification performance with compact models.
method Sequential optimization of conditional likelihoods in a boosting-like framework, combining multiplicatively.
result Significant performance improvements and reduced model size compared to other ensemble methods.
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 …
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.
DAS-PINNs uses deep learning to solve complex PDEs more accurately.
problem Solving high-dimensional PDEs with high accuracy.
method Deep neural networks and generative models for adaptive sampling.
result DAS-PINNs significantly improves solution accuracy for low regularity and high-dimensional problems.
We study conformal Spin-subgeometry of submanifolds in a semi-Riemannian Spin-manifold, focusing on conformal Spin-manifolds (M,[h]) and their Poincaré-Einstein metrics (X,g+). Our approach is based on the spectral theory of Dirac operator in the ambient Spin-manifold, and associated spinor valued meromorp…
Fast nonparametric conditional independence testing via two-stage regression
problem Fast nonparametric conditional independence testing
method BLITZ (Broad-to-Local Independence Testing via residualiZation)
result Better null calibration than fast kernel, random-feature, and regression-based competitors
The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.
problem Analyzing worst-case distortion risk metrics and weighted entropy with limited information.
method General distributions, partial information (mean and variance), various entropies and risk measures.
result Provides worst-case results for distortion risk metrics and weighted entropy.
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.
New method improves predictive systems with better theoretical guarantees.
problem Constructing predictive systems with out-of-sample calibration guarantees.
method Residual Distribution Predictive Systems (RDPs) that nest conformal predictive systems and offer flexibility.
result Empirically, RDPs perform competitively with conformal predictive systems and can be implemented with various regression methods.
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.
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.
Paper proposes a deep hedging method for Bermudan swaptions to manage residual profit and loss.
problem Real-world market conditions differ from ideal assumptions in traditional hedging methods, leading to residual profit and loss.
method Deep hedging framework applied to Bermudan swaptions, allowing flexible risk measures and hedge strategies.
result Effective residual profit and loss management demonstrated through numerical analysis.
We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the input images. We work with ResNet-56 and ResNet-110 trained on the CIFAR-10 dat…
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.