New framework shows ERM is optimal for both interpolation and extrapolation in domain generalization.
problem Formalizing and solving the challenges of domain generalization.
method Reformulated domain generalization as an online game between a risk-minimizing player and an adversary.
result ERM is minimax-optimal for both interpolation and extrapolation in domain generalization.
Hybrid framework merges data and domain knowledge for better spatial interpolation.
problem Spatial interpolation overlooks domain knowledge and limits to spatial coordinates.
method Integrates data-driven features with rule-assisted spatial dependency function mapping.
result Superior performance in two application scenarios, capturing localized features.
Method generates intermediate domains to align source and target domains.
problem Challenges of domain adaptation with significant domain divergence.
method Progressive domain augmentation via domain interpolation and multiple subspace alignment.
result Achieves state-of-the-art performance on multiple domain adaptation tasks.
Piecewise polynomial interpolation-based gradient descent reduces oracle complexity for smooth loss functions.
problem Optimizing empirical risk minimization loss functions
method Piecewise polynomial interpolation-based gradient descent
result Oracle complexity is reduced for smooth loss functions
Prediction and interpolation for long-range video data involves the complex task of modeling motion trajectories for each visible object, occlusions and dis-occlusions, as well as appearance changes due to viewpoint and lighting. Optical flow based techniques generalize but are suitable only for short temporal ranges. …
Generative model learns shape drift for quantifying domain uncertainty in hemodynamics.
problem Quantifying domain uncertainty in medical image segmentation for biomarker estimation.
method Conditional stochastic interpolant framework based on LDDMM registration.
result Generative model can create random perturbations of shapes for biomarker estimation.
CNNs predict spatial fields from sparse data.
problem Predicting complete spatial fields from limited observations.
method Convolutional Neural Networks (CNNs) trained on a single partially observed field.
result CNNs can flexibly capture local spatial patterns without explicit covariance modeling.
This paper is about interpolating minimal surfaces between two real analytic curves, a and b, each of which are simple real analytic curves, using the Björling-Schwarz formula in the domain where it is valid, changing the normal distributions on inital curves. We insert curves l1,...lL at specific locations and cla…
Study geometric structures in transfer learning to avoid negative transfer.
problem Understanding information-theoretic limits of transfer learning without exploiting domain geometry.
method Integrates geometric structure into linear regression models, using Gram matrices of source and target domains.
result Proposes an interpolation estimator that matches minimax lower bound and outperforms existing methods.
The annihilating filter-based low-rank Hankel matrix approach (ALOHA) is one of the state-of-the-art compressed sensing approaches that directly interpolates the missing k-space data using low-rank Hankel matrix completion. The success of ALOHA is due to the concise signal representation in the k-space domain thanks to…
A new model for imputing missing values in time series data across domains.
problem Imputing missing values in time series data across domains with domain shifts and high missing rates.
method A diffusion-based imputation model that integrates shared spectral components and domain-specific temporal structures, with cross-domain consistency alignment.
result Our model effectively handles missing values and domain shifts, outperforming existing methods.
A common approach for defining a reward function for Multi-objective Reinforcement Learning (MORL) problems is the weighted sum of the multiple objectives. The weights are then treated as design parameters dependent on the expertise (and preference) of the person performing the learning, with the typical result that a …
Paper calculates eigenvalue decay rates for neural network kernels on general domains.
problem Determining eigenvalue decay rates for neural network kernels on arbitrary domains.
method Proved dynamics of wide neural networks approximates NTK on general domains, used minimax optimality and interpolation spaces.
result Provided strategy to calculate eigenvalue decay rates for neural network kernels.
This work combines recurrent models with diffusion for probabilistic time series forecasting.
problem Scalability and capturing high-dimensional distributions and cross-feature dependencies in time series forecasting.
method Combines recurrent neural networks' efficiency with diffusion models' probabilistic modeling, using stochastic interpolants and conditional generation.
result Offers scalable probabilistic time series forecasting methods.
A new projection method for convex optimization reduces computation costs.
problem Efficiently projecting points into convex sets for deep learning.
method Interpolation-based projection for cheaper computation.
result The proposed method converges for linear and convex constraints.
Paper introduces a method to explain deep learning models and identify good generalization.
problem Limited interpretability of neural networks hinders progress and real-world applications.
method Polytope interpolation method for local explainability and generalization assessment.
result Developed a method to identify deep learning models with good generalization properties.
The paper improves stability estimates for soap bubble theorem in curved domains.
problem Stability estimates for the Soap Bubble Theorem in curved domains.
method Leveraging Gagliardo-Nirenberg-type interpolation inequalities.
result Optimal stability estimates for Lr deviations of mean curvature from being constant. Finite element method approximates scalar curvature in arbitrary dimensions.
problem Approximating scalar curvature using finite elements in arbitrary dimensions.
method Piecewise polynomial interpolants of a smooth Riemannian metric on a triangulated polyhedral domain.
result Finite element interpolants converge to scalar curvature with rate O(hr+1) in H−2(Ω) norm. Estimates spectral gap for Brownian motion on sticky-reflecting domains.
problem Estimating spectral gap for Brownian motion on sticky-reflecting domains.
method Interpolation method and novel applications of Reilly formula.
result Lower bounds for spectral gap derived for general domains.
FFRK automatically extracts features for spatial interpolation without external variables.
problem Spatial interpolation challenges, especially nonstationarity and lack of explanatory variables.
method Feature-Free Regression Kriging (FFRK) method that extracts geospatial features.
result FFRK outperforms classical methods in predicting heavy metal concentrations.
New method generates equilibrium glass configurations efficiently.
problem Sampling equilibrium configurations of amorphous materials is slow and difficult.
method Riemannian stochastic interpolation framework combining Riemannian stochastic interpolant and equivariant flow matching.
result Enforcing geometric and symmetry constraints significantly improves generative performance.
Diffusion models improve creativity by smoothing the score function, leading to interpolated data.
problem Improving creativity in diffusion models.
method Analyzing the effect of score smoothing on diffusion model dynamics.
result Score smoothing causes diffusion models to generate data that interpolate the training set.
C-Mixup improves generalization in regression tasks by adjusting label similarity.
problem Improving generalization in regression tasks with limited data.
method C-Mixup adjusts the probability of mixing examples based on label similarity.
result C-Mixup achieves better generalization and robustness compared to vanilla mixup.
The paper analyzes the generalization error of min-norm interpolators in transfer learning with limited test samples.
problem Characterizing the generalization error of min-norm interpolators in transfer learning with limited test samples.
method Characterizes the bias and variance of pooled min-ℓ2-norm interpolation under covariate shift and model shift. result Shows that adding data can hurt when SNR is low and is beneficial at higher SNR levels under certain conditions.
The paper defines flexible domains for minimal surfaces in Euclidean spaces and explores their properties.
problem Understanding the flexibility of domains in Euclidean spaces for minimal surfaces.
method Investigates the concept of flexibility in terms of minimal surfaces contained in domains.
result Defines flexible domains and shows how they can be approximated by minimal immersions.
Mixup improves model performance by interpolating random training examples.
problem Overfitting in machine learning models.
method Mixup is a regularization procedure that linearly interpolates random pairs of training examples.
result Mixup works well from a statistical learning theory perspective.
Efficiently prices American options with multiple assets using sparse grids.
problem Pricing American options with multiple underlying assets efficiently.
method Dynamic programming formulation followed by sparse grid interpolation.
result Sparse grids reduce the number of interpolation points and maintain function smoothness.
A new method generates meta-tasks using generative models for unsupervised learning.
problem Creating synthetic meta-tasks for unsupervised learning.
method Generative models with latent space interpolation for sampling.
result The method outperforms or is competitive with baselines on few-shot classification tasks.
New method estimates velocity fields for minimizing f-divergences without overfitting.
problem Minimizing statistical discrepancies between target and particle distributions.
method Directly estimate velocity fields using interpolation techniques, proving consistency under mild conditions.
result Consistent estimators of velocity fields improve accuracy in applications like domain adaptation and missing data imputation.
GNNs outperform NNs in interpolating bandlimited functions on Euclidean cubes.
problem Interpolating bandlimited functions on Euclidean cubes using GNNs vs. NNs.
method Investigates optimal GNN configurations and weights for function interpolation.
result GNNs require fewer weights and samples to interpolate bandlimited functions compared to NNs.
Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain adaptation. We propose AlignFlow, a generative modeling framework that models each dom…
Synthesizes robust estimators for domain adaptation.
problem Improving prediction accuracy in target domain with limited data.
method Synthesizes a family of robust least squares estimators using convex optimization.
result Robust strategies can outperform non-robust interpolations.
New generalization concept considers distribution of errors, not just average error.
problem Classical generalization fails to capture distributional differences in classifier outputs.
method Formal conjectures about distributional generalization based on model architecture, training procedure, and data distribution.
result Distributional generalization can be expected in specific conditions, as evidenced by empirical results.
New method generates clean data from corrupted observations.
problem Generating clean data from corrupted observations.
method Iterative update of a transport map using black-box corruption channel access.
result Converges to a self-consistent transport map that effectively inverts the corruption channel.
Domain Translation is the problem of finding a meaningful correspondence between two domains. Since in a majority of settings paired supervision is not available, much work focuses on Unsupervised Domain Translation (UDT) where data samples from each domain are unpaired. Following the seminal work of CycleGAN for UDT, …
We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising…
The paper tackles MSDA by learning dictionary atoms in Wasserstein space.
problem Mitigating data distribution shifts across multiple source domains to target domain.
method Dictionary learning and optimal transport in Wasserstein space; DaDiL algorithm for learning.
result Improved classification performance by 3.15%, 2.29%, and 7.71% in benchmarks.
This paper shows how forward rate interpolations are equivalent to discount factor interpolations in yield curve construction.
problem The challenge of choosing between different interpolation methods for yield curve construction.
method Demonstrates the equivalence between forward rate interpolations and discount factor interpolations.
result Some popular interpolation methods on forward rates are equivalent to classical interpolation methods on discount factors.
Study compares Fourier estimators to mitigate asynchrony effects in finance.
problem Impact of asynchrony on instantaneous financial estimates.
method Comparison of Malliavin-Mancino and Cuchiero-Teichmann estimators.
result Malliavin-Mancino estimator produces more stable estimates under asynchrony.
Adaptive transfer learning model for varying mechanisms across domains.
problem Improving inference in a target domain by leveraging related source domains with varying mechanisms.
method Semi-parametric domain-varying coefficient model (DVCM) for structured transfer learning.
result Minimax rate-optimal adaptive transfer learning estimator with provable negative transfer safeguards.
The paper proves a positive mass theorem for non-compact static domains in hyperbolic space.
problem Proving a positive mass theorem for non-compact static domains in hyperbolic space.
method Formulating and proving a positive mass theorem under natural dominant energy conditions, using elliptic boundary conditions on spinors.
result Retrieve a sharper version of a recent result by Souam about the rigidity of non-compact static domains.
New G2-holonomy manifolds from 5d N=1 theories domain walls.
problem Geometrizing domain walls in 5d N=1 theories.
method Constructing 7-manifolds by fibering a Calabi-Yau over a real line.
result 7-manifolds with G2-holonomy from domain walls in 5d theories. Neural networks trained with PGD achieve sharp regression rates in interpolation spaces.
problem Nonparametric regression using over-parameterized neural networks in interpolation spaces.
method Over-parameterized two-layer neural networks trained with Preconditioned Gradient Descent (PGD) and early stopping.
result Achieves a sharp regression rate of \(\cO(n^{-\frac{2αs'}{2αs'+1}})\) in interpolation spaces \(\bth{\cH_K}^{s'}\).
New FX option interpolations impact implied volatilities.
problem Different interpolations of FX option quotes lead to varying implied volatilities.
method Analysis of various exact interpolations of broker quotes.
result Different interpolations result in different implied volatilities.
Kernel interpolation is inconsistent for norms with smoothness above a constant.
problem Inconsistency of kernel interpolation in reproducing kernel Hilbert spaces.
method Lower bounds for generalization error in Sobolev norms.
result Kernel interpolation is always inconsistent for norms with smoothness above a constant.
Bayesian interpolants explain neural network inferences concisely.
problem Understanding neural network inferences.
method Adapting Craig interpolants for neural networks.
result Produces precise, understandable explanations.
Domain randomization (DR) is a successful technique for learning robust policies for robot systems, when the dynamics of the target robot system are unknown. The success of policies trained with domain randomization however, is highly dependent on the correct selection of the randomization distribution. The majority of…
Near-interpolating models grow norms quickly, affecting generalization.
problem Understanding the trade-off between interpolation and generalization in near-interpolating models.
method Random matrix theory and eigendecay analysis of data covariance matrix.
result Near-interpolating models exhibit rapid norm growth and worse generalization trade-offs.