Study improves curvature estimate for stable marginally outer trapped hypersurfaces with a free boundary.
problem Curvature estimate for stable marginally outer trapped hypersurfaces with a free boundary.
method Iteration argument based on uniform area bound.
result Improved curvature estimate for stable marginally outer trapped hypersurfaces.
New algorithm refutes AdaBoostV's optimal margin conjecture.
problem Optimizing minimal margins with few base hypotheses.
method Iterative combination of base hypotheses, proving lower bound.
result New algorithm is optimal, refutes AdaBoostV's conjecture.
An explicit solution found for maximizing/minimizing agreement in a 2x2 table.
problem Maximizing or minimizing agreement between clusterings with given marginals.
method Formal framework for several agreement measures, explicit solution for 2x2 table.
result An explicit solution for the 2x2 case.
We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; minimizing the KL dive…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this paper, the inference process is first defined to be the minimization of a convex f…
We study an area minimization problem for spacelike zero mean curvature surfaces in four dimensional Lorentz-Minkowski space. The areas of these surfaces are compared of with the areas of certain marginally trapped surfaces having the same boundary values.
A new method accelerates deep neural network training using minimal margin score.
problem Training deep neural networks is computationally expensive.
method Introduces minimal margin score (MMS) for selecting samples.
result Significant acceleration in training deep neural networks.
This paper proposes MMD-SVR to improve SVR's margin distribution for better generalization.
problem Improving SVR's generalization performance by maximizing the margin distribution of the whole dataset.
method Introducing MMD-SVR with coupled constraints to convert a non-convex optimization problem into a convex one.
result MMD-SVR significantly improves prediction accuracy and generalization compared to classic SVR.
Data augmentation improves model robustness by enforcing a margin.
problem Understanding how data augmentation provably improves model robustness.
method Analyzed linear and nonlinear models, quantifying the margin introduced by data augmentation.
result Commonly used data augmentation techniques may only introduce significant margin after adding exponentially many points.
A new method for unsupervised domain adaptation using Gaussian processes.
problem Reducing target domain error by aligning input and output distributions.
method Max-margin Gaussian process approach to achieve hypothesis consistency.
result Our method effectively minimizes maximum discrepancy and maximizes margins.
New integrable systems for marginally trapped surfaces in 4D Lorentz-Minkowski space.
problem Constructing new representations for marginally trapped surfaces in L4. method Developed new Weierstrass-type representations to solve a linear PDE.
result Explicit examples of marginally trapped surfaces with non-vanishing mean curvature.
SUMO provides unbiased log marginal likelihood estimation for latent variable models.
problem Biased estimates of log marginal likelihood in latent variable models.
method Randomized truncation of infinite series for unbiased estimation.
result Models trained with SUMO give better test-set likelihoods than standard methods.
This study analyzes adversarial training on linearly separable data and finds that gradient updates can achieve large margins in polynomial iterations.
problem Ensuring robustness in machine learning models trained on linearly separable data.
method Analysis of adversarial training with gradient updates on linearly separable data.
result Gradient updates in adversarial training can achieve large margins in polynomial iterations, whereas non-smooth methods require exponentially many iterations.
Paper analyzes GMM for separable data with various parameter structures.
problem Classifying separable data with logistic models and their generalizations.
method Introduces and analyzes Generalized Margin Maximizer (GMM) for logistic models with specific parameter structures.
result GMM outperforms max-margin classifiers in various parameter settings and structures.
New margin-based regularization and selective sampling improve deep neural network performance.
problem Improving deep neural network performance on various classification tasks.
method Multi-margin regularization (MMR) and minimal margin score (MMS) for selective sampling.
result Improved results on multiple classification tasks across domains.
CMRM improves robustness in noisy label settings without requiring privileged knowledge.
problem Learning with noisy labels without privileged knowledge.
method Conformal Margin Risk Minimization (CMRM) framework.
result CMRM consistently improves accuracy and reduces mislabeling under various noise conditions.
Paper improves DP-ERM for binary linear classification with large-margin subsets.
problem Differentially private binary linear classification with large-margin subsets.
method Efficient (ε,δ)-DP algorithm with empirical zero-one risk bound. result Improved empirical zero-one risk bound for binary linear classification.
We analyze bias-variance of margin losses.
problem Understanding model overfitting/underfitting.
method Bias-variance decomposition for strictly convex margin losses.
result Expected risk decomposes into central model risk and data variation.
Recurring international financial crises have adverse socioeconomic effects and demand novel regulatory instruments or strategies for risk management and market stabilization. However, the complex web of market interactions often impedes rational decisions that would absolutely minimize the risk. Here we show that, for…
A new method for optimal transport using neural ODEs that preserves marginal constraints.
problem Optimal transport between two continuous distributions with specific cost functions.
method Iterative construction of neural ODEs to minimize transport cost while preserving marginal constraints.
result Monotonic interior approach that decreases transport cost efficiently.
We present a max-margin nonparametric latent feature model, which unites the ideas of max-margin learning and Bayesian nonparametrics to discover discriminative latent features for link prediction and automatically infer the unknown latent social dimension. By minimizing a hinge-loss using the linear expectation operat…
MMA training maximizes margins for adversarial robustness.
problem Adversarial robustness of neural networks.
method Directly maximizes margins through adaptive adversarial training.
result MMA training improves adversarial robustness compared to fixed ε adversarial training.
Novel upper bound for unsupervised domain adaptation considers joint error.
problem Addressing the issue of mixing samples from different classes when matching marginal distributions.
method Proposes a general upper bound that penalizes undesirable joint error, uses constrained hypothesis space, and introduces cross margin discrepancy.
result Our proposal outperforms related approaches in image classification error rates on domain adaptation benchmarks.
Deep networks converge in direction, with implications for predictions and margins.
problem Understanding convergence and alignment in deep learning networks.
method Developed a theory of unbounded nonsmooth Kurdyka-Łojasiewicz inequalities for functions definable in an o-minimal structure.
result Network weights, predictions, training errors, and margin distribution converge in direction and align with gradient flow.
Study improves adversarial classification using distributionally robust models.
problem Improving robustness against adversarial attacks in classification models.
method Distributionally robust chance constraints with Wasserstein ambiguity, reformulated as a regularized ramp loss minimization problem.
result Standard descent methods can converge to the global minimizer for the distributionally robust adversarial classification model.
Study how regularization and optimization affect margin in deep models.
problem Understanding margin maximization in deep learning models.
method Analyze the limit of loss minimization with diverging norm constraints and margin paths.
result Discovers lexicographic max-margin solutions for homogeneous models and shows convergence under certain conditions.
Enhances ordinal embedding with less data by focusing on margin distribution.
problem Insufficient labeled data for ordinal embedding.
method Proposes Distributional Margin based Ordinal Embedding (DMOE) to improve generalization with less data.
result Demonstrates improved generalization performance with less labeled data.
Improves Gaussian process regression without bias.
problem Bias in Gaussian process regression estimates.
method Adaptive computation selection to minimize bias.
result Guaranteed small bias in log marginal likelihood estimates.
MWGAN tackles multi-marginal matching problem with Wasserstein GAN.
problem Learning mappings to match a source domain to multiple target domains with cross-domain correlations.
method Develops a novel Multi-marginal Wasserstein GAN (MWGAN) with inner- and inter-domain constraints to minimize Wasserstein distance.
result Theoretical and empirical evaluations show MWGAN's effectiveness on balanced and imbalanced translation tasks.
Proposes MFSWB for marginal fairness in SWB, improving efficiency and performance.
problem Achieving marginal fairness in SWB averaging.
method Defining MFSWB as a constrained SWB problem, proposing two surrogate problems and a new slicing distribution.
result Surrogate MFSWB problems effectively minimize distances to marginals and encourage marginal fairness.
This work analyzes the maximum-margin bias in quasi-homogeneous neural networks.
problem Analyzing the maximum-margin bias in quasi-homogeneous neural networks.
method Geometric analysis of gradient dynamics for quasi-homogeneous models.
result Gradient flow implicitly favors a subset of parameters, leading to asymmetric norm minimization.
New insights into deep learning: reducing training data significantly improves performance.
problem Understanding and improving generalization in deep learning models.
method Analyzing the distribution of classification margins and dynamically reducing the training set.
result The area under the curve of the margin distribution is a good measure of generalization.
New risk bound derived for multi-category margin classifiers.
problem Guaranteed risk dependency on categories, sample size, and margin parameter.
method Derived a new risk bound using Rademacher complexity and chaining method.
result Improved dependency on categories over state of the art.
Gradient descent converges to max-margin solution for hinge loss.
problem Applying gradient descent to the hinge loss for linear classifiers.
method Homotopic gradient descent applied to the hinge loss.
result Explicit convergence rates to max-margin solution for separable data.
GD at EoS edge minimizes logistic loss without monotonic convergence.
problem Understanding GD's implicit bias at the edge of stability.
method Theoretical analysis of logistic regression with constant stepsize GD.
result GD with any constant stepsize minimizes logistic loss over long time scales.
A new SVM classifier using L0/1 soft-margin loss for improved performance.
problem Improving SVM performance in binary classification tasks.
method Introducing L0/1 soft-margin loss and using the alternating direction method of multipliers. result The new L0/1-SVM model generates better performance with shorter computational time and fewer support vectors. New probabilistic complexity measures for linear and kernel methods.
problem Limitations of linear and kernel methods in machine learning.
method Introducing approximate notions of dimensional and margin complexity.
result Approximate complexity measures are both sufficient and necessary for learning.
The article introduces gamma-Psi-dimensions for margin multi-category classifiers.
problem Margin multi-category classifiers' generalization performance under minimal learnability hypotheses.
method Derives gamma-Psi-dimensions, handles capacity measures, and establishes upper bounds on metric entropies and Rademacher complexity.
result Gamma-Psi-dimensions improve over fat-shattering dimension and offer a promising alternative for multi-class to binary transitions.
Paper explores connections between loss functions and consistency in binary classification and regression.
problem Consistency in binary classification and regression applications.
method Characterization of conformable loss functions and derivation of a new Huber-type loss function.
result Margin-based loss functions are equivalent to loss functions of squared standardized logistic regression residuals.
Improved robustness of machine learning models with controlled Lipschitz constants.
problem Vulnerability of state-of-the-art models to adversarial attacks.
method Proposes a CLL loss that calibrates the margin and Lipschitz constant penalties, improving robustness certificates.
result Consistently outperforms other losses on CIFAR-10, CIFAR-100, and Tiny-ImageNet datasets.
New algorithms minimize PAC-Bayesian C-Bound for majority voting, leading to scalable and accurate predictors.
problem Improving majority vote classifiers using PAC-Bayesian bounds.
method Directly optimizing PAC-Bayesian guarantees on the C-Bound with gradient descent.
result Self-bounding majority vote learning algorithms with scalable and accurate predictors.
Max-margin learning is a powerful approach to building classifiers and structured output predictors. Recent work on max-margin supervised topic models has successfully integrated it with Bayesian topic models to discover discriminative latent semantic structures and make accurate predictions for unseen testing data. Ho…
We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest an exponential weighting aggregation scheme. We use this aggregation procedure to construct classifiers which adapt automatically to margin and complexity. Two main examples are worked out in which adaptivity is a…
We derive the Space-Time Positive Mass theorem in arbitrary dimensions, without topological constraints. The main new tools are skin structures and surgeries on minimal and marginally outer trapped hypersurfaces.
Study stability and rigidity of axisymmetric marginally outer trapped surfaces.
problem Stability and rigidity of axisymmetric marginally outer trapped surfaces.
method Refined results from initial data sets with Killing vector fields, using new foliation lemma.
result Conditions for the stability of axisymmetric MOTS and new foliation lemma.
Improved exploration in RL with latent state marginalization.
problem Complexity of deep probabilistic models limits their practical use in reinforcement learning.
method Adopting latent variable policies within the MaxEnt framework, with low-cost marginalization of latent states.
result Effective marginalization leads to better exploration and more robust training.
Advances robustness of metric learning by adversarial margin in input space.
problem Improving robustness of metric learning algorithms.
method Imposing adversarial margin in input space, minimizing perturbation loss.
result Enlarged adversarial margin improves generalization and robustness.
Small deformations of marginally (outer) trapped surfaces are considered by using their stability operator. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere to prove several interesting results. The concept of 'core' of a black hole is introduced: it is a minimal …