The spectral -support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral -support norm, whose additional para…
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48 results for “normative modeling”
HBR improves normative modeling of neuroimaging data across multiple sites.
problem Dealing with nuisance variation in neuroimaging data across different sites.
method Hierarchical Bayesian regression (HBR) for multi-site normative modeling.
result HBR provides more accurate normative ranges compared to existing methods.
Study improves image classifier robustness to random p-norm corruptions.
problem Improving robustness of image classifiers to real-world imperceptible corruptions.
method Training and testing with random p-norm corruptions, evaluating robustness against different p-norms.
result Training with a combination of p-norm corruptions significantly improves robustness.
SAM improves generalization in overparameterized models, but its behavior in tensorized models is less understood.
problem Understanding the implicit regularization of SAM in tensorized models.
method Scale-invariance analysis and gradient flow analysis to derive Norm Deviation as a measure of core norm imbalance, and propose Deviation-Aware Scaling (DAS).
result DAS achieves competitive or improved performance over SAM, while offering reduced computational overhead.
The study analyzes robustness of estimators in linear models with adversarial errors.
problem Analyzing robustness of estimators in linear models with adversarial errors.
method Develops a general theory for minimum norm interpolating estimators and RERM in linear models without conditions on errors.
result Quantitative bound for the prediction error relating it to Rademacher complexity, norm of minimum norm interpolator of errors, and subdifferential size.
Optimal scaling found to depend on operator norm across large models and datasets.
problem Lack of unifying principle for optimal hyperparameter scaling across models and datasets.
method Discovered that optimal scaling is conditioned on the operator norm of the output layer.
result The optimal learning rate/batch size pair consistently has the same operator norm value.
Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a range of applications and the standard trace-norm relaxation can behave very poorly …
We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, w…
Using the -norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, ca…
We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), whi…
The paper explores why a specific type of predictor works well in noisy data.
problem Understanding why a specific type of predictor (minimum-norm interpolator) works well in noisy data.
method The paper uses uniform convergence and zero-error predictors in a norm ball to explain the success of the minimum-norm interpolator.
result The minimum-norm interpolator is consistent, and this can be explained by uniform convergence of zero-error predictors in a norm ball.
A new metric predicts model performance on unseen data.
problem Predicting performance on out-of-distribution data without labels.
method Uses model predictions to pseudo-label data, trains a new model, and measures difference from in-distribution models.
result Empirically outperforms existing methods on image and text classification tasks.
The Generalization Error of the Minimum-norm Solutions for Over-parameterized Neural Networksstat.ML
We study the generalization properties of minimum-norm solutions for three over-parametrized machine learning models including the random feature model, the two-layer neural network model and the residual network model. We proved that for all three models, the generalization error for the minimum-norm solution is compa…
In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product). Induced by the t-product, we first rigorously deduce the tensor sp…
Efficiently regularizes deep learning models using Jacobian nuclear norm.
problem Regularizing deep learning models to prevent overfitting and improve generalization.
method Proposes a denoising-style approximation to penalize the Jacobian nuclear norm without computing the Jacobian matrix.
result Demonstrates that penalizing the average squared Frobenius norm of and is equivalent to penalizing the Jacobian nuclear norm for function compositions.
The trace norm is widely used in multi-task learning as it can discover low-rank structures among tasks in terms of model parameters. Nowadays, with the emerging of big datasets and the popularity of deep learning techniques, tensor trace norms have been used for deep multi-task models. However, existing tensor trace n…
This paper presents a normalization mechanism called Instance-Level Meta Normalization (ILM~Norm) to address a learning-to-normalize problem. ILM~Norm learns to predict the normalization parameters via both the feature feed-forward and the gradient back-propagation paths. ILM~Norm provides a meta normalization mechanis…
This thesis presents the Conditional Value-at-Risk concept and combines an analysis that covers its application as a risk measure and as a vector norm. For both areas of application the theory is revised in detail and examples are given to show how to apply the concept in practice. In the first part, CVaR as a risk mea…
New method approximates complex kernel norms with random features, making learning tractable.
problem Complexity of learning with kernel methods in high dimensions.
method Random features approximations to norms, focusing on .
result For , the number of random features required is polynomial in the sample size, making learning tractable.
FedNNNN improves FL by adjusting model update vector norms.
problem Slow convergence and low prediction accuracy in FL.
method Norm-Normalized Neural Network Aggregation (FedNNNN) with momentum control.
result Up to 5.4% accuracy improvement on multiple datasets.
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to recover…
Abstract compares two norms in holomorphic quadratic differentials.
problem Comparing two norms in holomorphic quadratic differentials.
method Comparison between Avila-Gouëzel-Yoccoz norm and Teichmüller norm.
result Comparison of two norms in holomorphic quadratic differentials.
Localized sum-of-norms clustering separates balls in data.
problem Clustering arbitrarily close data points in multivariate data.
method Localized sum-of-norms optimization for clustering.
result Proves a bound on clustering error in stochastic ball model.
New insights into optimization and generalization for linear models.
problem Understanding the implicit regularization of optimization methods for linear models.
method Investigating the norms minimized by interpolating solutions and using projections to move between solutions.
result Proving that for over-parameterized linear classification, projections onto the data-span enable the use of under-parameterized techniques.
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods where feature selection is effected via mixed-norms. Several mixed-norm based spar…
Deep neural networks with adversarial training achieve sup-norm convergence for nonparametric regression.
problem Achieving sup-norm convergence for deep neural network estimators in nonparametric regression.
method Developed an adversarial training scheme to address the sup-norm convergence issue.
result Deep neural network estimators achieve optimal sup-norm convergence with the proposed adversarial training.
The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they can be well modeled by a hyper-Laplacian. However, the use of such distributions g…
We introduce a new family of matrix norms, the "local max" norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the literature as regularizers for matrix reconstruction problems. We show that this…
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproduci…
We introduce twisted Alexander norms of a compact connected orientable 3-manifold with first Betti number bigger than one generalizing norms of McMullen and Turaev. We show that twisted Alexander norms give lower bounds on the Thurston norm of a 3-manifold. Using these we completely determine the Thurston norm of many …
Paper tackles low-rank matrix recovery with column -norm regularization.
problem Low-rank matrix recovery problems with column sparsity constraints.
method Developed alternating majorization-minimization (AMM) methods with extrapolation and hybrid AMM.
result Global convergence analysis and superior performance in matrix completion problems.
We study a regularizer which is defined as a parameterized infimum of quadratics, and which we call the box-norm. We show that the k-support norm, a regularizer proposed by [Argyriou et al, 2012] for sparse vector prediction problems, belongs to this family, and the box-norm can be generated as a perturbation of the fo…
Unified normative modeling for neuroimaging phenotypes using denoising diffusion models.
problem Discarding multivariate dependence in neuroimaging pipelines.
method Denoising diffusion probabilistic models (DDPMs) with FiLM and SAINT backbones.
result Unified multivariate normative modeling with better calibration and dependence preservation.
In this paper, we propose -norm regularized models to seek near-optimal sparse portfolios. These sparse solutions reduce the complexity of portfolio implementation and management. Theoretical results are established to guarantee the sparsity of the second-order KKT points of the -norm regularized models…
We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as spe…
The paper studies the minimum ℓ₁-norm interpolator's risk behavior in over-parameterized settings.
problem Understanding the risk behavior of minimum ℓ₁-norm interpolators in high-dimensional settings.
method Exact characterization of the risk behavior through a system of two non-linear equations.
result Observation of a multi-descent phenomenon in the generalization risk of the minimum ℓ₁-norm interpolator.
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…
New L0 norm added to TDA for market analysis.
problem Improving TDA tools for market prediction.
method Defined and applied L0 norm in TDA for four markets.
result Enhanced TDA tools for market analysis.
The -support norm is a regularizer which has been successfully applied to sparse vector prediction problems. We show that it belongs to a general class of norms which can be formulated as a parameterized infimum over quadratics. We further extend the -support norm to matrices, and we observe that it is a special …
A new framework uses matrix flows to unify frequentist and Bayesian approaches for sparse GGMs.
problem Challenges in studying conditional independence among many variables with few observations.
method General framework for variational inference with matrix-variate Normalizing Flow in Gaussian Graphical Models.
result Unified benefits of frequentist and Bayesian frameworks for sparse GGMs.
We establish a natural and geometric 1-1 correspondence between projective toric varieties of dimension and horofunction compactifications of with respect to rational polyhedral norms. For this purpose, we explain a topological model of toric varieties. Consequently, toric varieties in algebraic geom…
CNN layers with large norms are still robust to adversarial attacks.
problem Understanding the relationship between layer norms and adversarial robustness in CNNs.
method Theoretical analysis of and norms, norm decay method, adversarial training frameworks.
result Adversarially robust CNNs can have comparable or larger layer norms than non-adversarially robust ones.
We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is introduced and studied. The rate of convergence for the estimate is obtained. Information…
Near-Interpolators: Rapid Norm Growth and the Trade-Off between Interpolation and Generalizationstat.ML
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.
Study on minimal hypersurfaces in a special normed space.
problem Characterizing minimal hypersurfaces in a specific normed space.
method Investigate translation and separable minimal hypersurfaces.
result New insights into the properties of minimal hypersurfaces.
New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.
problem Generalization bounds with strict assumptions like uniformly bounded loss.
method Relax uniform bounds assumptions to on-average bounded loss and gradient norm.
result Proposes a new generalization bound with a surrogate of model complexity.
This work improves trace norm regularization for multi-task learning with limited data.
problem Learning from few samples across multiple tasks.
method Trace norm regularization for a linear shared representation model.
result First estimation error bound for trace norm regularized estimator with scarce data.
The paper defines minimal norm tensors for curvature and divergence tensors, explaining Weyl and Cotten tensors.
problem Understanding curvature tensors and their minimal norm.
method Analyzing minimal norm tensors for third and fourth covariant tensors, including Riemannian curvature and divergence.
result Weyl tensor and Cotten tensor are identified as minimal norm tensors of Riemannian curvature and divergence tensors, respectively.