A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Gradient methods avoid overfitting on separable data.
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…
Paper corrects Max-Margin loss for multi-label tasks.
We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The result also generalizes to other monotone decreasing loss functions with an inf…
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…
New findings on the max margin problem in neural networks.
This study investigates how gradient-based methods bias neural networks trained on high-dimensional data.
Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, it is relatively insufficient to empower the discriminative ability of DGMs on making accurate predictions. This paper presents max-ma…
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…
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…
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…
Adam's bias shifts from full-batch to max-margin of different norms for separable data.
New insights into when benign overfitting occurs in linear and classification tasks.
We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable dataset. The classifier is described by a nonlinear ReLU model and the objective function adopts the exponential loss function. We first characterize the landscape of the loss function and show th…
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…
GMC benchmark isolates retrieval in Transformers, revealing max-margin alignment.
Max-margin classifiers' behavior is studied in high dimensions with non-Gaussian features.
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…
Structured prediction is a powerful framework for coping with joint prediction of interacting outputs. A central difficulty in using this framework is that often the correct label dependence structure is unknown. At the same time, we would like to avoid an overly complex structure that will lead to intractable predicti…
Paper analyzes GMM for separable data with various parameter structures.
Interpolation hurts robust generalization even without noise.
Max-min margin Markov networks improve consistency in structured prediction.
Existing multi-view learning methods based on kernel function either require the user to select and tune a single predefined kernel or have to compute and store many Gram matrices to perform multiple kernel learning. Apart from the huge consumption of manpower, computation and memory resources, most of these models see…
New loss function improves convergence rate for neural networks.
Paper proposes MDAT to stabilize domain alignment in label-scarce settings.
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-…
GD at EoS edge minimizes logistic loss without monotonic convergence.
With an eye toward understanding complexity control in deep learning, we study how infinitesimal regularization or gradient descent optimization lead to margin maximizing solutions in both homogeneous and non-homogeneous models, extending previous work that focused on infinitesimal regularization only in homogeneous mo…
In unsupervised domain adaptation, it is widely known that the target domain error can be provably reduced by having a shared input representation that makes the source and target domains indistinguishable from each other. Very recently it has been studied that not just matching the marginal input distributions, but th…
We prove a new generalization bound that shows for any class of linear predictors in Gaussian space, the Rademacher complexity of the class and the training error under any continuous loss can control the test error under all Moreau envelopes of the loss . We use our finite-sample bound to directly recover…
Word embeddings provide point representations of words containing useful semantic information. We introduce multimodal word distributions formed from Gaussian mixtures, for multiple word meanings, entailment, and rich uncertainty information. To learn these distributions, we propose an energy-based max-margin objective…
New tensor formulation reveals gradient flow's bias in linear neural networks.
Unified approach for optimizing predictions in linear programming and inverse problems.
We embed KKT points in neural networks of different sizes.
New findings on robust learning with well-separated data.
Theory for soft-margin classifiers on object manifolds.
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…
Improved unsupervised probing for ranking tasks using Contrast-Consistent Ranking.
Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes. Motivated by these phenomena, we revisit high-dimensional maximum margin classification for line…
This work studies the implicit bias of mini-batch SGD in classification.
Algorithm improves SVM classification in non-Euclidean spaces.
The paper analyzes the training dynamics of a transformer for next-token prediction.
Gradient descent is a simple and widely used optimization method for machine learning. For homogeneous linear classifiers applied to separable data, gradient descent has been shown to converge to the maximal margin (or equivalently, the minimal norm) solution for various smooth loss functions. The previous theory does …
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…
The problem of forecasting conditional probabilities of the next event given the past is considered in a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct a single predictor that performs asymptotically as well as the best predictor in C, on any data.…
New bounds explain deterministic non-smooth deep nets without large Lipschitz constants.
Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.
This paper proposes a method to reduce complexity in GLMs with categorical predictors.