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
Classifies connected components of meromorphic differentials with residue conditions.
problem Understanding the structure of meromorphic differentials with residue constraints.
method Analyzes the multi-scale compactification and residue conditions.
result Classified connected components of generalized strata of meromorphic differentials.
DIET tests conditional independence using marginal dependence measures of residual information.
problem Computational intractability of conditional randomization tests (CRTs).
method DIET avoids fitting large models by leveraging marginal independence statistics of information residuals.
result DIET achieves higher power than other tractable CRTs on synthetic and real benchmarks.
Study on endomorphism and automorphism groups of specific quandles.
problem Characterizing endomorphism and automorphism groups of residually finite and profinite quandles.
method Proved properties of endomorphism monoids and automorphism groups for residually finite and profinite quandles.
result Endomorphism and automorphism groups of residually finite quandles are residually finite.
A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.
problem Ill-conditioning in Dirac-Frenkel residual minimization leads to non-unique parameter dynamics.
method Introduces a history variable (momentum) to select better-conditioned parameter velocities, preserving residual minimization while promoting smooth parameter evolutions.
result The approach leads to increased robustness in singular and near-singular PDE solution regimes.
RSIC identifies multiple ranks of interest in NMF by analyzing residual sensitivity.
problem Determining the optimal rank in NMF.
method RSIC analyzes sensitivity of relative residuals to different initializations.
result RSIC identifies meaningful ranks consistent with data structure.
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…
Deep residual networks implicitly converge to neural ODEs.
problem Link between discrete and continuous deep learning models.
method Establishing implicit regularization for residual networks towards neural ODEs.
result Deep residual networks initialized as discretizations of neural ODEs converge to such ODEs during training.
We count meromorphic differentials with fixed residues and poles of fixed orders.
problem Counting meromorphic differentials with fixed residues and poles of fixed orders.
method Intersection theory on compactified moduli spaces of differentials.
result Complete solution to the problem with interesting combinatorial properties.
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.
Deviance-style normalization for sparse, jointly overdispersed count matrices
problem Jointly overdispersed count matrices
method Dirichlet-multinomial deviance residualization
result Preserves exact sparsity, evaluates in constant time, recovers multinomial residual
This paper classifies components of meromorphic differential strata.
problem Understanding the boundary of multi-scale compactification of meromorphic differentials.
method Classifying connected components of residueless meromorphic differentials.
result Classification of connected components of strata of residueless meromorphic differentials.
The paper proves Gorenstein contractions for multiscale differentials on nodal curves.
problem Proving Gorenstein contractions for multiscale differentials on nodal curves.
method Addressing the conjecture by Ranganathan and Wise, showing contractions level by level.
result Multiscale differentials can be contracted to Gorenstein singularities, level by level, from the top down.
Establishes functoriality of Baum-Bott residues under specific conditions.
problem Functoriality of Baum-Bott residues under certain conditions.
method Establishes functoriality of Baum-Bott residues under specific conditions.
result The singular set of a foliation has dimension at least \( k-1 \).
Improved multivariate conformal prediction by standardizing residuals.
problem Weak conditional coverage in heteroskedastic multivariate settings.
method Natural extension of univariate normalization to multivariate setting, whitening residuals and standardizing local variance.
result Standardized residuals yield asymptotic conditional coverage under certain distributions.
Framework calculates positional influence in causal residual Transformers.
problem Understanding positional influence in causal residual Transformers.
method Adjoint-sensitivity framework for positional influence in causal residual Transformers.
result Exact evolution of adjoint-energy influence density and decomposition into residual transmission, nonlocal Volterra, and local channels.
Proposes a neural network method to correct residual distortions in coordinate transformations.
problem Nonlinear and spatially dependent distortions in coordinate transformation models.
method Residual-based neural network approach focusing on systematic distortions.
result The method improves accuracy and stability in challenging conditions.
This paper studies deep learning methodologies for portfolio optimization in the US equities market. We present a novel residual switching network that can automatically sense changes in market regimes and switch between momentum and reversal predictors accordingly. The residual switching network architecture combines …
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.
A new method for pricing European options in changing market conditions.
problem Lack of closed-form solutions for pricing European options in regime-switching models.
method Physics-informed residual learning (PIRL) for efficient option pricing.
result PIRL eliminates the need for retraining and offers near-instantaneous pricing.
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.
PRISMA uses PDE residuals for fast, robust, and accurate inference.
problem Slow gradient-based optimization and instability in PDE residual-based methods.
method Integrates PDE residuals directly into the model's architecture via attention mechanisms in the spectral domain.
result Competitive accuracy with significantly lower inference costs and faster speeds.
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.
CEFOL uses deep learning for dynamic programming with recursive utility.
problem Challenges in solving dynamic programming problems with recursive utility.
method Introduces a separate neural network for certainty equivalent, uses first-order optimality conditions to learn value and policy functions.
result CEFOL achieves high accuracy in learning value and policy functions, matching VFI benchmarks.
In this paper, for an even dimensional compact manifold with boundary which has the non-product metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a 4-dimensional manifold, we compute this conformal invariant pair under some conditions and point out the way of computat…
New knot groups found to be bi-orderable using pretzel knots.
problem Understanding bi-orderability of knot groups.
method Applied Mayland's technique to pretzel knots to show their commutator subgroups are residually-torsion-free nilpotent.
result Found new examples of bi-orderable knot groups for non-fibered or alternating knots.
This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the time of parameter estimation. The paper provides explicit formulas for those err…
Study tests how U.S. equity prices align with global asset frequencies using financial variables.
problem Testing whether U.S. equity prices align with global asset frequencies using financial variables.
method Examines SPX and RUT gaps, uses OIS-based funding, volatility, trading-friction, financial-condition variables, and residual information.
result Gains in fit survive broad-dollar neutralization, alternative blocks, PCA, residualization, and nested horizon selection, supporting reduced-form P-Q alignment.
In recent years, the RFRS condition has been used to analyze virtual fibering in 3-manifold topology. Agol's work shows that any 3-manifold with zero Euler characteristic satisfying the RFRS condition on its fundamental group virtually fibers over the circle. In this note we will show that a finitely generated nilpoten…
Improved nonparametric regression with debiasing for root-n consistency.
problem Challenges in achieving root-n consistency and normal distribution for nonparametric estimators.
method Debiasing technique by adding a correction term to nonparametric estimators.
result Achieves root-n consistency and asymptotic normality.
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.
Deep residual networks can approximate any continuous function using control theory.
problem Universal approximation capabilities of deep residual neural networks.
method Relating residual networks to control systems and using Lie algebraic techniques.
result Deep residual networks with adequately deep layers can approximate any continuous function on a compact set.
We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy o…
Study Transformer layers under cross-entropy training using mean field control.
problem Understanding the behavior of Transformer layers in cross-entropy training.
method Continuous-depth mean field control analysis, treating depth as time and layer parameters as controls.
result Derivation of a Pontryagin condition for the limiting population problem, involving the softmax residual.
Method for conditional sampling with pre-trained normalizing flows.
problem Conditional sampling for incomplete observations.
method Variational Schur conditional sampling with normalizing flows.
result Successfully applied to invertible residual networks for inference and classification.
New method learns PDE solutions from low-fidelity data.
problem Challenges in learning PDE surrogates with scarce data.
method Flow matching in infinite-dimensional space with conditional neural operators.
result Accurately learns PDE solutions across different resolutions and fidelities.
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…
RR-GNN improves GNN prediction intervals by accounting for graph heteroscedasticity and structural biases.
problem Uncertainty quantification in GNNs for high-stakes domains.
method Graph-Structured Mondrian CP, Residual-Adaptive Nonconformity Scores, Cross-Training Protocol.
result Improved efficiency and no loss of coverage compared to CP baselines.
Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow…
i-DenseNets improve parameter efficiency and performance in density estimation.
problem Improving parameter efficiency and performance in density estimation models.
method Invertible Dense Networks (i-DenseNets) with learnable weighted concatenation and Concatenated LipSwish activation function.
result i-DenseNets outperform Residual Flows and other flow-based models in bits per dimension.
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.
Aleatoric uncertainty is an intrinsic property of ill-posed inverse and imaging problems. Its quantification is vital for assessing the reliability of relevant point estimates. In this paper, we propose an efficient framework for quantifying aleatoric uncertainty for deep residual learning and showcase its significant …
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.
Study the intersection of positive closed currents using tangent currents and King's residue formula.
problem Investigate the intersection of positive closed currents in complex manifolds.
method Employ tangent currents and King's residue formula to establish a natural condition for intersection.
result Derive an integral representation of the intersection of positive closed currents.
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
We prove that the "generic condition" used in singularity theorems of general relativity is generic in the space of Lorentzian metrics on a given manifold, in the sense that it is satisfied for all metrics in a residual set in the Whitney Ck-topology, for k depending on the dimension of the manifold.
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.
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 L-hidden-layer linear ResNets. result GD and SGD can converge to global minimum for deep linear ResNets with specific transformations.