The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and -symmetric spaces. In parti…
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48 results for “shift invariance”
New shifting chain map enhances quandle invariants for links.
problem Enhancing quandle invariants for links and surfaces.
method Introducing a shifting chain map σ and its pull-back σ# to transform cocycles.
result Shifting chain map σ# transforms 2-cocycles to 3-cocycles, enhancing invariants.
We describe a pair of invariants for actions of finite groups on shifts of finite type, the left-reduced and right-reduced shifts. The left-reduced shift was first constructed by U. Fiebig, who showed that its zeta function is an invariant, and in fact equal to the zeta function of the quotient dynamical system. We als…
New framework learns sufficient invariant features robustly across distribution shifts.
problem Learning robust models under distribution shifts between training and test datasets.
method Sufficient Invariant Learning (SIL) framework and Adaptive Sharpness-aware Group Distributionally Robust Optimization (ASGDRO) algorithm.
result Empirical evaluations confirm ASGDRO's robustness against distribution shifts.
The paper addresses instability in CNNs' first layer by proving max pooling's shift invariance.
problem Instability in CNNs' first layer, leading to sensitivity to small input shifts.
method Establishing conditions for max pooling's shift invariance and deriving a measure of stability.
result Max pooling approximates a nearly shift-invariant complex modulus under certain conditions.
RIA method improves OoD generalization for covariate shift.
problem Improving out-of-distribution generalization under covariate shift.
method Adversarial label invariant graph data augmentations for OoD generalization.
result RIA method achieves high accuracy compared to OoD baselines.
Estimates model performance under distribution shift using domain-invariant predictors.
problem Poor performance of models on test distributions different from training distributions.
method Uses domain-invariant predictors as a proxy for unknown target labels.
result Shows that the complexity of latent representations influences target risk.
Causal invariant geographic network representations with feature and structural distribution shiftscs.LG
Proposes FSM-IRL to learn invariant network representations considering feature and structural shifts.
problem Spatial heterogeneity and temporal dynamics lead to OOD generalization issues in geographic networks.
method Introduces FSM-IRL model that accounts for feature and structural distribution shifts using causal attention and reweighting.
result Demonstrates strong learning capabilities on geographic and social network datasets in OOD scenarios.
The paper explores how to make machine learning models robust to domain shifts.
problem Machine learning models are unreliable in domains different from training.
method Introducing a broad formal notion of invariance and causal structures.
result The true underlying causal structure of the data plays a critical role in robustness.
Paper tackles distribution shifts in prediction models with unobserved confounding.
problem Distribution shifts in prediction models with unobserved confounding.
method Linear structural causal model, invariant covariate representations, data-driven representation learning method.
result Optimizes for a lower-dimensional linear subspace and a prediction model confined to that subspace, achieving nearly ideal gap between target and source risk.
We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals. In the first instance, we deal with the shift-invariant dictionary learning probl…
Proposes a new method to improve CNNs' shift invariance and accuracy.
problem Improving CNNs' shift invariance and prediction accuracy.
method Replaces RMax with CMod, a Gabor-like structure, to increase shift invariance and accuracy.
result Achieves superior accuracy on ImageNet and CIFAR-10 classification tasks.
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtu…
This paper develops methods for obtaining distribution-free prediction regions for invariant representations.
problem Distributional shifts in machine learning models.
method Invariant risk minimization and weighted conformity scores.
result Proves the effectiveness of adaptive conformal intervals for uncertainty estimation.
Framework detects shape shifts in functional profiles using Fréchet mean and shape invariant model.
problem Detecting shape shifts in functional profiles.
method Combining Fréchet mean and shape invariant model for interpretable parameterization of profile deviations.
result Potential shifts in shape deformation process distinguished by significant shifts in amplitude and/or phase.
New method learns models to adapt to domain shifts at test time.
problem Learning models robust to distribution shifts in practical applications.
method Adaptive Risk Minimization (ARM) framework.
result Performance gains of 1-4% on image classification problems.
Deep neural networks approximate functions in shift-invariant spaces with controlled error.
problem Approximating functions in shift-invariant spaces with neural networks.
method Using deep ReLU neural networks, estimating approximation error bounds based on network width and depth.
result Deep neural networks achieve optimal approximation rates for Sobolev spaces up to a logarithmic factor.
We study density estimation for classes of shift-invariant distributions over . A multidimensional distribution is "shift-invariant" if, roughly speaking, it is close in total variation distance to a small shift of it in any direction. Shift-invariance relaxes smoothness assumptions commonly used in non-p…
This research focuses on invariant probabilistic predictions, showing they are not robust under distribution shifts.
problem The challenge of creating robust probabilistic predictions that remain consistent under distribution shifts.
method A causality-inspired framework to investigate invariance and robustness of probabilistic predictions with respect to proper scoring rules.
result Arbitrary distribution shifts do not admit invariant and robust probabilistic predictions, unlike point predictions.
MADOD meta-learns invariant features for OOD detection across unseen domains.
problem Simultaneous covariate and semantic shifts in real-world machine learning applications.
method Meta-learning and G-invariance to learn robust, domain-invariant features.
result Superior performance in semantic OOD detection across unseen domains.
Boosted Control Functions improve prediction under distributional shifts.
problem Prediction under distributional shifts in the presence of hidden confounding.
method Boosted Control Function (BCF) and ControlTwicing algorithm.
result BCF allows for distribution generalization and invariance under nonlinear, non-identifiable structural functions.
The paper tackles policy learning in dynamic environments using causal methods.
problem Existing reinforcement learning algorithms assume static mechanisms, but real-world systems often have changing mechanisms.
method The paper introduces multi-environment contextual bandits and policy invariance to handle environmental shifts.
result An optimal invariant policy is guaranteed to generalize across environments under suitable assumptions.
Discrepancy between training and testing domains is a fundamental problem in the generalization of machine learning techniques. Recently, several approaches have been proposed to learn domain invariant feature representations through adversarial deep learning. However, label shift, where the percentage of data in each …
MIP framework improves urban flow prediction by adapting to distribution shifts.
problem Distribution shifts in urban flow data make prediction models unreliable.
method Memory-enhanced Invariant Prompt learning with learnable memory bank.
result MIP ensures robust predictions by focusing on invariant features.
We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of operator-theoretic methods we derive a criterion for finiteness of the uniton number whic…
New approach combines invariance and information bottleneck for OOD generalization.
problem OOD generalization failures in classification tasks.
method Revisit linear regression tasks, prove information bottleneck constraint necessary, propose combined approach.
result Combined invariance and information bottleneck approach improves OOD generalization.
FNNs detect EEG signals without position dependence.
problem Detecting EEG signals without position dependence.
method Shift invariant functional neural networks (FNNs) using FDA methods.
result FNNs outperform FDA benchmarks in EEG classification.
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset shifts and can be used for prediction in new, unseen environments. However, the…
Given a TQFT in dimension d+1, and an infinite cyclic covering of a closed (d+1)-dimensional manifold M, we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated in R. Williams' work in symbolic dynamics. The Turaev-Viro module associated to…
A method to remove mean-shift noise from PCA using knockoffs.
problem High sensitivity of PCA to mean-shift contamination in high-dimensional data.
method Introducing knockoff mean-shift perturbation to separate and remove mean-shift components from PCA.
result The mean-shift spikes are spectrally separable from stable eigenvalues, allowing for robust PCA.
New regularizer improves neural network robustness and generalization.
problem Ineffective weight decay for networks with homogeneous activation functions.
method Proposes an invariant regularizer to penalize intrinsic weight norms.
result Improves generalization and adversarial robustness on various datasets.
We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a time-invariant filter. It was shown by Juditsky and Nemirovski (2009) that when the $\ell_2…
This work analyzes IRM and ERM from sample complexity perspective, revealing different behaviors under various distribution shifts.
problem Choosing between IRM and ERM for OOD generalization.
method Sample complexity analysis comparing IRM and ERM under different data generation mechanisms.
result IRM is preferred over ERM for certain distribution shifts, leading to better OOD generalization.
The paper proposes a method to create domain-invariant representations using Wasserstein distance.
problem Domain shifts in training data affect machine learning model performance across different domains.
method The method combines classification/regression losses with a GAN-type discriminator to minimize the Wasserstein distance between domains.
result The approach produces the highest minimum classification accuracy and most invariant representation across domains.
Beyond Invariance: Test-Time Label-Shift Adaptation for Distributions with "Spurious" Correlationsstat.ML
TTLSA adapts models to label shifts across domains with nuisance factors.
problem Adapting models to changes in label distributions with nuisance factors.
method TTLSA uses EM on unlabeled samples to adapt a trained model to new label distributions.
result TTLSA improves model performance over invariance methods and baseline methods.
New approach improves domain adaptation with label shift assumptions.
problem Improving domain adaptation when label distributions differ between source and target domains.
method Proposes generalized label shift () and modifies three DA algorithms (JAN, DANN, CDAN) to handle label distribution mismatches.
result Modified DA algorithms outperform base versions, especially with large label distribution mismatches.
Homomorphisms on quandle cohomology groups that raise the dimensions by one are studied in relation to the cocycle state-sum invariants of knots and knotted surfaces. Skein relations are also studied.
Prominent Roles of Conditionally Invariant Components in Domain Adaptation: Theory and Algorithmsstat.ML
New algorithm uses conditionally invariant components to improve domain adaptation performance.
problem Improving domain adaptation performance when source and target data distributions differ.
method Conditionally invariant components (CICs) and importance-weighted conditional invariant penalty (IW-CIP) algorithm.
result New algorithm provides target risk guarantees and addresses label-flipping features.
Estimating signals with linear recurrence relations under Gaussian noise is nearly as hard as sparse signals.
problem Estimating discrete-time signals with unknown linear recurrence relations in Gaussian noise.
method Analyzing shift-invariant subspaces and their Fourier coefficients as reproducing filters.
result The statistical complexity is nearly the same as for -sparse signals, and the estimator is tractable.
The paper analyzes covariate shift in nonparametric regression with Markovian data.
problem Covariate shift in regression problems with Markovian data.
method Extension of nonparametric convergence rates to Markovian dependence structures, using Hölder smoothness assumptions and similarity measures.
result Precise convergence rates for Nadaraya-Watson kernel estimators under specific Markovian conditions.
New method prevents classifiers from relying on spurious correlations.
problem Group invariant learning fails to prevent classifiers from depending on spurious correlations.
method Statistical independence tests to construct groups and reweight samples by group label proportion.
result New method significantly outperforms existing group invariant learning methods in generalizing to spurious correlation shifts.
New insights into SGD and generalization via shift-curvature and bias-curvature mechanisms.
problem Understanding the role of curvature in generalization and how SGD affects it.
method Derivation of new SGD steady-state distribution and analysis of shift-curvature and bias-curvature mechanisms.
result Shift-curvature is a significant factor in test performance, especially for small SGD noise.
Transfer learning aims to improve learning in target domain by borrowing knowledge from a related but different source domain. To reduce the distribution shift between source and target domains, recent methods have focused on exploring invariant representations that have similar distributions across domains. However, w…
Unsupervised Domain Adaptation aims to learn a model on a source domain with labeled data in order to perform well on unlabeled data of a target domain. Current approaches focus on learning \textit{Domain Invariant Representations}. It relies on the assumption that such representations are well-suited for learning the …
GALA framework learns invariant graph representations via environment augmentation with minimal assumptions.
problem Learning invariant graph representations from different environments without additional assumptions.
method Developed GALA framework with minimal assumptions of variation sufficiency and consistency. Uses an assistant model to differentiate graph environment changes.
result Extracting maximally invariant subgraphs to proxy predictions identifies underlying invariant subgraphs for successful out-of-distribution generalization.
Twisted Alexander invariants have been defined for any knot and linear representation of its group. The invariants are generalized for any periodic representation of the commutator subgroup of the knot group. Properties of the new twisted invariants are given. Under suitable hypotheses, reciprocality and bounds on the …
New estimator handles covariate shift with closed-form solution and super-efficiency.
problem Handling covariate shift in missing data and causal inference problems.
method Minimum Wasserstein distance estimation framework.
result Closed-form expression and super-efficiency relative to semiparametric efficient estimator.
In this paper, by modifying the argument shift method,we prove Liouville integrability of geodesic flows of normal metrics (invariant Einstein metrics) on the Ledger-Obata -symmetric spaces $K^n/\diag(K)$, where is a semisimple (respectively, simple) compact Lie group.