Max-margin deep generative models improve predictive performance in supervised and semi-supervised learning.
problem Insufficient discriminative ability of deep generative models in making accurate predictions.
method Introduce max-margin principle to improve discriminative learning while retaining generative capability.
result Significant improvement in prediction performance with max-margin learning.
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.
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…
Gradient descent and SGD can converge to max-margin directions in ReLU models.
problem Understanding the implicit bias of gradient methods in ReLU models.
method Characterization of loss function landscape, analysis of GD and SGD convergence, exploration of multi-neuron network learning.
result Gradient descent and SGD can converge to max-margin directions in ReLU models.
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…
Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attemp…
This work explains early-stage alignment of logistic regression parameters with max-margin direction.
problem Early-stage alignment of logistic regression parameters with max-margin direction.
method Analyzes gradient descent dynamics and uses dataset geometry to track radial and tangential flows.
result Parameter vector weakly aligns with max-margin direction within O(exp(exp(-δ))) iterations, demonstrating faster weak alignment.
Adam's bias shifts from full-batch to max-margin of different norms for separable data.
problem Understanding Adam's implicit bias in the incremental batch setting.
method Analyzing incremental Adam on linearly separable data, constructing datasets, and using a proxy algorithm.
result Incremental Adam can converge to different max-margin classifiers depending on the dataset and batching scheme.
Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian modeling and predictive strengths of max-margin learning. However, Monte Carlo sampli…
In this paper we propose an approach to preference elicitation that is suitable to large configuration spaces beyond the reach of existing state-of-the-art approaches. Our setwise max-margin method can be viewed as a generalization of max-margin learning to sets, and can produce a set of "diverse" items that can be use…
New findings on the max margin problem in neural networks.
problem Understanding the max margin problem in neural networks.
method Analyzing gradient flow and max margin problem in linear and ReLU networks.
result The KKT point is not always an optimum of the max margin problem.
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.
Adaptive kernel model for multi-view learning reduces overfitting and scales with data.
problem Overfitting and high computational cost in multi-view learning.
method Bayesian framework, Dirichlet process Gaussian mixtures, random Fourier features, max-margin constraints, MCMC sampler.
result Adaptive learning of shift-invariant kernels from data.
We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A discriminative factor model is then developed, integrating the max-margin rank-lik…
Supervised topic models utilize document's side information for discovering predictive low dimensional representations of documents. Existing models apply the likelihood-based estimation. In this paper, we present a general framework of max-margin supervised topic models for both continuous and categorical response var…
New word distributions capture multiple meanings and outperform existing methods.
problem Capturing semantic information for words with multiple meanings.
method Gaussian mixtures with an energy-based max-margin objective.
result Multimodal word distributions outperform word2vec and Gaussian embeddings.
Max-margin classifiers' behavior is studied in high dimensions with non-Gaussian features.
problem Understanding the role of featurization maps and high-dimensional misclassification error.
method High-dimensional asymptotics, Gaussian model, support vector representation.
result Asymptotic behavior of max-margin classifiers is determined by feature covariance and label covariance.
Max-margin classifiers can overfit without harming performance in high dimensions.
problem Understanding how max-margin classifiers generalize in high-dimensional settings.
method Stylized setting with Gaussian features and labels, proportional asymptotics, and random neural network features.
result Exact expressions for limiting generalization error and conditions for 'benign overfitting'.
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.
GMC benchmark isolates retrieval in Transformers, revealing max-margin alignment.
problem Understanding how Transformers develop match-and-copy behavior on natural data.
method Introducing Gaussian Match-and-Copy (GMC) as a minimalist benchmark.
result Gradient descent drives parameters to diverge while aligning with max-margin separator.
A deep generative model is developed for representation and analysis of images, based on a hierarchical convolutional dictionary-learning framework. Stochastic {\em unpooling} is employed to link consecutive layers in the model, yielding top-down image generation. A Bayesian support vector machine is linked to the top-…
Paper proposes MDAT to stabilize domain alignment in label-scarce settings.
problem Stable and comprehensive domain alignment in label-scarce settings.
method Max-margin Domain-Adversarial Training (MDAT) with Adversarial Reconstruction Network (ARN).
result MDAT stabilizes gradient reversing and achieves strong robustness to hyper-parameters.
Gradient descent on separable data converges to SVM's max-margin solution.
problem Gradient descent on logistic regression problems with linearly separable data.
method Examination of gradient descent on logistic regression with homogeneous predictors.
result Gradient descent converges to the max-margin solution of SVM.
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.
Interpolation hurts robust generalization even without noise.
problem The challenge of robust generalization in the absence of noise.
method Avoiding interpolation through ridge regularization.
result Ridge regularization improves robust generalization.
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.
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.
Paper tackles multi-label zero-shot learning, improving label embedding projection for unseen classes.
problem Challenges in transferring knowledge from seen to unseen classes in multi-label zero-shot learning.
method Proposes a transfer-aware embedding projection approach to project label embeddings into a low-dimensional space for better inter-label relationships and explicit information transfer.
result Demonstrates the efficacy of the proposed approach through experiments on zero-shot multi-label image classification.
Improved BP on CRBMs yields better structured prediction results.
problem Structured prediction on CRBMs using current methods is suboptimal.
method Matrix-based belief propagation implementation for CRBMs.
result BP on CRBMs provides significantly better results than CD methods.
New loss function improves convergence rate for neural networks.
problem Improving convergence speed of neural networks for classification tasks.
method Proposes a modified hinge loss function with gradients to critical points.
result Margin converges to max-margin at O(1/t) rate, faster than exponential losses. Sparse AUC-maximizing classifier design for imbalanced data.
problem Maximizing AUC performance in imbalanced datasets.
method Max-margin surrogate loss function, online learning, greedy basis function addition.
result Sparse classifiers achieve AUC performance comparable to non-sparse models, with significantly fewer basis functions.
ARLD uses active deep Q-learning to learn faster with expert demonstrations.
problem Efforts required to obtain enough expert demonstrations for RL training.
method ARLD framework with Active Deep Q-Network (ADQN) for active demonstration queries.
result ARLD learns faster and reaches super-expert performance with expert demonstrations.
This paper simplifies deep learning networks by mapping them to a linear function of a feature map.
problem Understanding how weights in deep networks coordinate across layers and generalize.
method Reparameterizes DNNs as a linear function of a feature map, transforming depth-dependencies into tensor products.
result Develops sample compression representation of neural networks in terms of support vectors, showing sample complexity of O(ns/epsilon).
Unified approach for optimizing predictions in linear programming and inverse problems.
problem Optimizing predictions in linear programming and inverse problems.
method Maximum optimality margin approach.
result Unified approach that balances computational efficiency and theoretical properties.
Metric learning is a key problem for many data mining and machine learning applications, and has long been dominated by Mahalanobis methods. Recent advances in nonlinear metric learning have demonstrated the potential power of non-Mahalanobis distance functions, particularly tree-based functions. We propose a novel non…
This study investigates how gradient-based methods bias neural networks trained on high-dimensional data.
problem The implicit biases of gradient-based optimization algorithms in neural networks trained on high-dimensional data.
method Investigation of gradient flow and gradient descent in two-layer fully-connected neural networks with leaky ReLU activations.
result Gradient flow and gradient descent lead to neural networks with low-rank solutions and linear decision boundaries.
New findings on robust learning with well-separated data.
problem Learning robust classifiers with well-separated classes.
method Analyzing sample complexity for linear classifiers with robustness.
result For linear classifiers on well-separated data, robust loss is at least $Ω( rac{d}{n})$.
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.
Model reveals double descent in binary linear classification.
problem Investigating classification error in high-dimensional binary linear classification.
method Gradient descent on logistic loss, maximum-likelihood, max-margin (SVM) solutions, and convex Gaussian min-max theorem.
result Double descent phenomenon observed in classification error for varying overparameterization ratio.
We introduce a graphical framework for multiple instance learning (MIL) based on Markov networks. This framework can be used to model the traditional MIL definition as well as more general MIL definitions. Different levels of ambiguity -- the portion of positive instances in a bag -- can be explored in weakly supervise…
Theory for soft-margin classifiers on object manifolds.
problem Classifying object manifolds with variability.
method Mean-field theory of soft-margin classifiers applied to object manifolds.
result Prediction of classification errors and their dependence on regularization.
Gradient methods avoid overfitting on separable data.
problem Overfitting on separable data with gradient methods.
method Gradient methods (flow, descent, SGD) on separable data.
result Gradient methods asymptotically do not overfit on separable data.
New tensor formulation reveals gradient flow's bias in linear neural networks.
problem Understanding implicit bias in linear neural network training.
method Tensor formulation of neural networks, including fully-connected, diagonal, and convolutional networks.
result Gradient flow on linear tensor networks converges to solutions of specific optimization problems.
The paper analyzes the training dynamics of a transformer for next-token prediction.
problem Understanding the non-asymptotic performance of transformers in next-token prediction.
method Characterizes training dataset properties, designs a two-stage training algorithm, and analyzes attention gradient properties.
result Trained transformers converge sub-linearly to max-margin solutions and exhibit linear convergence in cross-entropy loss.
Many successful applications of computer vision to image or video manipulation are interactive by nature. However, parameters of such systems are often trained neglecting the user. Traditionally, interactive systems have been treated in the same manner as their fully automatic counterparts. Their performance is evaluat…
We embed KKT points in neural networks of different sizes.
problem Classifying data using homogeneous neural networks.
method Introducing KKT point embedding principle and proving it for different network types.
result KKT points of a smaller network can be mapped to those of a larger network via linear transformations.
Improved unsupervised probing for ranking tasks using Contrast-Consistent Ranking.
problem Improving self-consistency in language model rankings.
method Adapting Contrast-Consistent Search (CCS) to Contrast-Consistent Ranking (CCR) for ranking tasks.
result CCR probing outperforms prompting techniques across different models and datasets.
This work studies the implicit bias of mini-batch SGD in classification.
problem Understanding the implicit bias of mini-batch SGD in multi-class classification.
method Characterizes how batch size, momentum, and variance reduction affect convergence and max-margin behavior under different norms.
result Momentum enables small-batch convergence to an approximate max-margin solution, while variance reduction recovers the exact full-batch bias.