Recent research has used margin theory to analyze the generalization performance for deep neural networks (DNNs). The existed results are almost based on the spectrally-normalized minimum margin. However, optimizing the minimum margin ignores a mass of information about the entire margin distribution, which is crucial …
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48 results for “Marginalization”
The paper defines marginal tubes and proves their null nature.
problem Understanding the geometry of spacelike surfaces in spacetimes.
method Introducing marginal tubes and studying spacelike surfaces with double null coordinates.
result If every spacelike section of a marginal tube is a marginal surface, then the marginal tube is null.
Margin system for margin loans using cash and stock as collateral is considered in this paper, which is the line of defence for brokers against risk associated with margin trading. The conditional probability of negative return is used as risk measure, and a recursive algorithm is proposed to realize this measure under…
An active margin system for margin loans is proposed for Chinese margin lending market, which uses cash and randomly selected stock as collateral. The conditional probability of negative return(CPNR) after a forced sale of securities from under-margined account in a falling market is used to measure the risk faced by t…
In order to protect brokers from customer defaults in a volatile market, an active margin system is proposed for the transactions of margin lending in China. The probability of negative return under the condition that collaterals are liquidated in a falling market is used to measure the risk associated with margin loan…
Random projections have been applied in many machine learning algorithms. However, whether margin is preserved after random projection is non-trivial and not well studied. In this paper we analyse margin distortion after random projection, and give the conditions of margin preservation for binary classification problem…
Paper introduces negative margin loss for better few-shot classification accuracy.
problem Improving few-shot classification accuracy with metric learning.
method Introduces negative margin loss and analyzes its impact on feature discriminability.
result Negative margin loss outperforms regular softmax loss on few-shot classification benchmarks.
Margin enlargement over training data has been an important strategy since perceptrons in machine learning for the purpose of boosting the robustness of classifiers toward a good generalization ability. Yet Breiman (1999) showed a dilemma that a uniform improvement on margin distribution does NOT necessarily reduces ge…
On the Insufficiency of the Large Margins Theory in Explaining the Performance of Ensemble Methodsstat.ML
Boosting and other ensemble methods combine a large number of weak classifiers through weighted voting to produce stronger predictive models. To explain the successful performance of boosting algorithms, Schapire et al. (1998) showed that AdaBoost is especially effective at increasing the margins of the training data. …
Proposes a new distance metric for multi-marginal optimal transport.
problem Computational scalability in multi-marginal optimal transport.
method Random one-dimensional projections to construct sliced multi-marginal Wasserstein distance.
result Sliced multi-marginal Wasserstein distance is a metric with dimension-free sample complexity.
The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem in many models, such as those with hidden variables or uncertain parameters. Unfo…
We investigate the geometric properties of marginally trapped surfaces (surfaces which have null mean curvature vector) in the spaces of oriented geodesics of Euclidean 3-space and hyperbolic 3-space, endowed with their canonical neutral Kaehler structures. We prove that every rank one surface in these four manifolds i…
We study adversarial robustness of neural networks from a margin maximization perspective, where margins are defined as the distances from inputs to a classifier's decision boundary. Our study shows that maximizing margins can be achieved by minimizing the adversarial loss on the decision boundary at the "shortest succ…
The paper improves SVM margin-based generalization bounds.
problem Improving generalization bounds for SVMs.
method Revisiting and improving classic generalization bounds in terms of margins, complementing with a nearly matching lower bound.
result Almost settles the generalization performance of SVMs in terms of margins.
Near-Exponential Convergence Rates for kNN Classification
problem Convergence rates for kNN classification
method Introducing Boltzmann margin
result First near-exponential convergence rates for kNN classification
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.
Improved Sample Complexities for Deep Networks and Robust Classification via an All-Layer Margincs.LG
For linear classifiers, the relationship between (normalized) output margin and generalization is captured in a clear and simple bound -- a large output margin implies good generalization. Unfortunately, for deep models, this relationship is less clear: existing analyses of the output margin give complicated bounds whi…
We introduce a useful tool for analyzing boosting algorithms called the ``smooth margin function,'' a differentiable approximation of the usual margin for boosting algorithms. We present two boosting algorithms based on this smooth margin, ``coordinate ascent boosting'' and ``approximate coordinate ascent boosting,'' w…
New DP algorithms with margin guarantees for various hypothesis sets.
problem Differential privacy in machine learning with margin guarantees.
method Developed pure and efficient DP learning algorithms for linear, kernel-based, and neural network hypotheses.
result Margin guarantees are independent of input dimension and hypothesis type.
Unified binary and multiclass margin-based classification methods.
problem No consensus on multiclass loss functions analogous to binary margin loss.
method Showed multiclass loss functions can be expressed in relative margin form.
result Extended classification-calibration result to multiclass.
We provide a new local class-purity theorem for Lipschitz continuous DNN classifiers. In addition, we discuss how to achieve classification margin for training samples. Finally, we describe how to compute margin p-values for test samples.
New method for interpreting non-linear models using forward marginal effects.
problem Interpreting non-linear models' feature effects is challenging.
method Introducing forward marginal effects and partitioning feature space for better interpretation.
result Improved interpretation of non-linear prediction functions.
Paper improves ISDA margin calculation using LSMC.
problem Efficiently calculating initial margin for financial contracts.
method Extends Least Squares Monte-Carlo (LSMC) technique.
result Improved efficiency in estimating margin sensitivities.
New findings show margins are not sufficient for explaining gradient boosting performance.
problem The inadequacy of margin explanations in explaining the performance of gradient boosting.
method Demonstrated and proved a stronger margin-based generalization bound for boosted classifiers.
result Proved a stronger margin-based generalization bound that explains the performance of modern gradient boosters.
Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically either uses MCMC schemes which target the joint posterior of the parameters and some…
In critical decision-making scenarios, optimizing accuracy can lead to a biased classifier, hence past work recommends enforcing group-based fairness metrics in addition to maximizing accuracy. However, doing so exposes the classifier to another kind of bias called infra-marginality. This refers to individual-level bia…
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and sufficient comparisons induce the success of classical approaches. However, colle…
Paper reinterprets marginal productivity theory using vectorial products, challenging traditional ethical interpretations.
problem Challenges traditional ethical interpretations of marginal productivity theory.
method Formulates marginal productivity theory using vectorial marginal products, contrasting with traditional scalar approach.
result Vectorial marginal products conflict with traditional distributive shares picture of property.
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.
MACQ method explains deep learning models by analyzing feature contributions across prediction levels.
problem Explaining deep learning model predictions.
method Global gradient-based, model-agnostic approach focusing on marginal attribution.
result MACQ separates feature contributions from interaction effects and visualizes 3-way relationships.
Bayesian evidence helps compare models but can overfit.
problem Comparing hypotheses consistent with observations.
method Marginal likelihood, Occam's razor, PAC-Bayes bounds.
result Marginal likelihood can negatively correlate with generalization.
A mesh-free method solves continuum-marginal optimal transport problems.
problem Recovering minimum-energy velocity fields from time-continuous probability marginals.
method Embeds weak continuity equation in a reproducing kernel Hilbert space, optimizing with mini-batch stochastic methods.
result Accurately recovers drift and maintains marginal consistency in synthetic experiments.
Study of marginally trapped surfaces in a perturbed Schwarzschild spacetime.
problem Understanding marginally trapped surfaces in perturbed Schwarzschild spacetime.
method Developed a method to study spacelike surfaces in a double null coordinate system.
result For every incoming null hypersurface nearly spherically symmetric, there exists a unique embedded marginally trapped surface.
The paper introduces canonical parameters for marginally trapped surfaces in Minkowski space.
problem Determining marginally trapped surfaces in Minkowski space.
method Introducing canonical parameters and proving existence and uniqueness theorems.
result Every marginally trapped surface is determined by three smooth functions.
Study examines liquidation, leverage, and optimal margin requirements in Bitcoin futures markets.
problem Understanding and optimizing margin requirements in Bitcoin futures markets.
method Empirical analysis using generalized extreme value theory and BitMEX data.
result Margin requirements need to be significantly higher to reduce daily margin calls.
New margin-based learning guarantees improve generalization bounds.
problem Improving generalization bounds for machine learning models.
method Relative deviation margin bounds using empirical margin loss and Rademacher complexity.
result Distribution-dependent generalization bounds for unbounded loss functions.
Paper corrects Max-Margin loss for multi-label tasks.
problem Max-Margin loss inconsistency in multi-label classification.
method Introduced Restricted-Max-Margin loss.
result Consistent loss for multi-label tasks under milder conditions.
The paper proposes effective margin regularization to improve adversarial robustness in deep neural networks.
problem Adversarial vulnerability of deep neural networks (DNNs).
method Regularization of effective weight norm during training to maximize effective margins.
result Effective margin regularization (EMR) boosts adversarial robustness in both standard and adversarial training.
Study generalization of voting classifiers using margin-based bounds.
problem Understanding the generalization of ensemble classifiers like voting.
method Proved margin-based generalization bounds using PAC-Bayes theory and Dirichlet posteriors.
result Provided state-of-the-art guarantees on classification tasks.
In this paper, we reformulate the forest representation learning approach as an additive model which boosts the augmented feature instead of the prediction. We substantially improve the upper bound of generalization gap from to , while - the margin r…
Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of boosting algorithms was initiated by Schapire, Freund, Bartlett and Lee (1998) an…
Max-min margin Markov networks improve consistency in structured prediction.
problem Statistical inconsistency in max-margin methods for structured prediction.
method Defining a max-min margin formulation to overcome statistical inconsistency.
result Proves consistency and provides an explicit algorithm with finite sample generalization bounds.
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.
We present a new active sampling method we call min-margin which trains multiple learners on bootstrap samples and then chooses the examples to label based on the candidates' minimum margin amongst the bootstrapped models. This extends standard margin sampling in a way that increases its diversity in a supervised manne…
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…
New margin bound improves generalization for voting classifiers.
problem Improving generalization bounds for voting classifiers.
method Established a new margin-based generalization bound.
result Derives an optimal weak-to-strong learner with matching theoretical lower bound.
Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent researchers reveal that maximizing the margin distribution of whole training dataset ra…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased" choice corresponds to the distribution of maximum entropy. The calculation of t…