Novel convex surrogate for non-modular loss functions.
problem Computational tractability for non-modular loss functions.
method Submodular-supermodular decomposition, slack-rescaling, Lov{á}sz hinge.
result First tractable solution for non-modular loss functions.
A new convex loss function optimizes set predictions with balanced size and coverage.
problem Optimizing set predictions with balanced size and coverage.
method Proposes a convex loss function using Choquet integrals for nondecreasing subset-valued functions.
result Optimal trade-offs between conditional probabilistic coverage and set size.
LOV model calibrates European and American options with path-dependent volatility.
problem Calibrating European and American options with path-dependent volatility.
method Designing a local volatility model that incorporates path-dependent shocks through an occupation sensitivity function.
result LOV model successfully calibrates options chains with automatic European vanilla option calibration and path-dependent flexibility.
Deep CNN classifies EEG-based brain connectivity in schizophrenia.
problem Classifying neuropsychiatric disorders using EEG connectivity.
method Multi-domain connectome CNN framework integrating time and frequency-domain metrics.
result MDC-CNN achieves 93.06% accuracy in schizophrenia classification. In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …
Sz\H ucs proved in 2000 that the r-tuple-point manifold of a generic immersion is cobordant to the Σ1r−1-point manifold of its generic projection. Here we slightly extend this by showing that the natural mappings of these manifolds are bordant to each other. The main novelty of our approach is that we constru…
Random Hinge Forests are a new decision forest method that can be integrated into neural networks.
problem Training and optimizing neural networks efficiently and effectively.
method Random Hinge Forests are a novel variant of decision forests that can be integrated into neural networks and optimized end-to-end.
result Random Hinge Forests can be efficiently optimized end-to-end with stochastic gradient descent.
Motivated by the hinge structure present in protein chains and other molecular conformations, we study the singularities of certain maps associated to body-and-hinge and panel-and-hinge chains. These are sequentially articulated systems where two consecutive rigid pieces are connected by a hinge, that is, a codimension…
Hinge-FM2I fills missing data in time series with high accuracy.
problem Handling missing data in univariate time series.
method Inspired by door hinges, Hinge-FM2I imputes missing data using FM2I and selects the best imputed gap.
result Hinge-FM2I significantly outperforms other methods in sMAPE scores.
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.
This paper provides an explicit formula for complex structures in embeddings of manifolds.
problem Finding explicit formulas for complex structures in embeddings of manifolds.
method Recursive expression and fiberwise Taylor expansion of the canonical complex structure.
result Evidence of canonical vanishing of integrability equations in general settings.
We introduce cylindrical projections to simulate infinite-dimensional occupation flows of diffusions.
problem Computational intractability of infinite-dimensional occupation flows of diffusions.
method Introduce cylindrical projections to approximate the occupation flow via a finite-dimensional system.
result Strong convergence of cylindrical projections to the initial process with derived rates.
The purpose of this paper is to study gradient estimate of Hamilton - Souplet - Zhang type for the general heat equation ut=ΔVu+aulogu+bu on noncompact Riemannian manifolds. As its application, we show a Harnak inequality for the heat solution and a Liouville type theorem for a nonlinear elliptic equation.…
Support vector machines (SVMs) naturally embody sparseness due to their use of hinge loss functions. However, SVMs can not directly estimate conditional class probabilities. In this paper we propose and study a family of coherence functions, which are convex and differentiable, as surrogates of the hinge function. The …
Improves GANs by incorporating class information with a multi-hinge loss.
problem Improving GANs to better respect class information.
method Proposes a multi-class generalization of the Hinge loss for GANs.
result Improves Inception Scores and Frechet Inception Distance on Imagenet.
O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two refinements of Plamenevskaya's invariant, one valued in Bar-Natan's deformation of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum. We show that the first of these…
New loss function calibrates WW-hinge loss for multiclass SVM.
problem WW-hinge loss not calibrated with 0-1 loss.
method Introduced ordered partition loss and proved WW-hinge loss is calibrated.
result WW-hinge loss is calibrated with ordered partition loss.
Logitron combines Perceptron and logistic loss for improved classification.
problem Non-convex and non-smooth zero-one loss function in classification models.
method Introduces a Perceptron-augmented convex classification framework with an extended logistic loss function.
result Hinge-Logitron outperforms logistic regression and SVM in classification accuracy.
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. MAGAN improves GANs stability and performance with adaptive hinge loss.
problem Improving stability and performance of GANs.
method Adaptive hinge loss function with estimated margin based on target distribution energy.
result MAGAN converges to global optimum under certain assumptions.
We study body-and-hinge and panel-and-hinge chains in R^d, with two marked points: one on the first body, the other on the last. For a general chain, the squared distance between the marked points gives a Morse-Bott function on a torus configuration space. Maximal configurations, when the distance between the two marke…
JoVA combines two VAEs to learn user and item representations for better recommendation.
problem Collaborative filtering with implicit feedback.
method Joint Variational Autoencoders (JoVA) with a hinge-based pairwise loss function (JoVA-Hinge).
result JoVA-Hinge outperforms state-of-the-art methods in top-k recommendation.
New method captures multimodal disconnectivity in schizophrenia.
problem Misinterpretation of single modality data in schizophrenia research.
method Gaussian graphical model and modularity-based approach on multimodal data.
result Identifies missing links in schizophrenia's default mode network.
We study general conditions under which the computations of the index of a perturbed Dirac operator Ds=D+sZ localize to the singular set of the bundle endomorphism Z in the semi-classical limit s→∞. We show how to use Witten's method to compute the index of D by doing a combinatorial computation inv…
Paper proposes a boosting method with fast learning rates and early stopping.
problem Missing theoretical guarantees for boosting methods in binary classification.
method Fully-corrective gradient boosting with squared hinge loss and ADMM algorithm.
result Derives fast learning rates of O((m/logm)−1/4) and O((m/logm)−1/2). The paper analyzes top-k classification and proposes consistent loss functions.
problem Understanding consistency of top-k classification in challenging tasks.
method Theoretical analysis, defining top-k calibration, proposing new loss functions.
result Proposes a new consistent hinge loss and a top-k calibrated convex loss.
New approach uses hinge loss for iterative regularization in classification.
problem Improving classification accuracy through regularization.
method Develops an iterative regularization approach based on hinge loss.
result Proves convergence and rates of convergence for classification.
New robust metric learning method improves performance in noisy data.
problem Label noise and outliers in training data degrade metric learning performance.
method Rescaled Hinge loss function and HQ algorithm.
result New method outperforms state-of-the-art methods in noisy data.
Proposes hinge-Wasserstein to improve uncertainty estimation in regression tasks.
problem Estimating multimodal aleatoric uncertainty in regression tasks from images.
method Regression-by-classification paradigm with hinge-Wasserstein loss.
result Hinge-Wasserstein loss improves uncertainty estimation on challenging tasks.
Novel convex surrogate for submodular losses with tractable computation.
problem Learning with non-modular losses for set prediction.
method Proposed Lovász hinge loss function for submodular losses.
result First tractable convex surrogates for submodular losses.
The paper studies consistency of surrogate loss procedures under constrained classifiers.
problem Consistency of surrogate loss approaches under constrained classifiers without correct specification.
method The paper develops theoretical results and hinge loss based procedures for a constrained classification problem.
result Hinge losses are the only surrogate losses that preserve consistency in second-best scenarios.
New framework enhances neural network robustness against adversarial attacks.
problem Vulnerability of deep neural networks to small perturbations.
method Integrates Lipschitz constraint using optimal transport and hinge regularization.
result Proposes a new loss function that certifies adversarial robustness.
We prove a conjecture due to M. Kazarian, connecting two classifying spaces in singularity theory. These spaces are: - Kazarian's space (generalizing Vassiliev's algebraic complex and) showing which cohomology classes are represented by singularity strata. - Author's space Xτ giving homotopy representation of cobord…
Efficient algorithms for large-scale multiclass classification with linear classifiers.
problem Training ℓ1-regularized linear classifiers with high dimensionality and many classes. method Combines quasi-bilinear objective, stochastic mirror descent, and non-uniform sampling.
result Proposes a sublinear algorithm for multiclass hinge loss.
A new procedure for learning cost-sensitive SVM(CS-SVM) classifiers is proposed. The SVM hinge loss is extended to the cost sensitive setting, and the CS-SVM is derived as the minimizer of the associated risk. The extension of the hinge loss draws on recent connections between risk minimization and probability elicitat…
Deep neural networks converge quickly for classification tasks.
problem Classifying data with smooth decision boundaries, probabilities, or margins.
method Hinge loss and cross-entropy for training; analysis of convergence rates.
result DNNs achieve fast convergence rates under various conditions.
Study efficient learning of halfspaces with constant noise tolerance.
problem Learning halfspaces in the presence of both instance and label corruption.
method Develops an algorithm to minimize reweighted hinge loss for robustness.
result Achieves constant noise tolerance for halfspace learning.
New IRLS algorithms for SVM fitting via MM approach.
problem Fitting support vector machines (SVMs) via quadratic programming.
method Majorization--Minimization (MM) paradigm for iteratively-reweighted least-squares (IRLS) algorithms.
result IRLS algorithms for SVM risk minimization problems with various losses and penalties.
New loss functions improve extreme classification with missing labels.
problem Large number of infrequent labels and missing labels in XMC.
method Derive unbiased loss functions for XMC, incorporating them into existing algorithms.
result Significant improvement in extreme classification performance (up to 20%) over existing methods.
Introduces Soft-SVM for binary classification bridging logistic and SVM.
problem Data separability issues in binary classification.
method Soft-SVM regression using convex relaxation of hinge loss with softness and class-separation parameters.
result Soft-SVM performs well in classification and prediction errors.
Neural networks for binary classification have zero training error at all local minima under certain conditions.
problem Understanding the loss surface of neural networks for binary classification.
method Analyzing single-layered neural networks with smooth hinge loss function, providing conditions for zero training error at all local minima.
result Zero training error at all local minima is achieved under specific conditions (strict convexity of neurons and smooth hinge loss).
Partial monitoring is a general model for sequential learning with limited feedback formalized as a game between two players. In this game, the learner chooses an action and at the same time the opponent chooses an outcome, then the learner suffers a loss and receives a feedback signal. The goal of the learner is to mi…
Gradient penalty improves GAN performance by inducing a large-margin classifier.
problem Improving GAN performance and addressing vanishing gradients.
method A unifying framework of expected margin maximization, showing gradient penalties induce large-margin classifiers.
result Gradient penalties reduce vanishing gradients and produce better generated outputs.
New algorithms and bounds for contextual bandits using surrogate losses.
problem Efficiently solving contextual bandit problems with margin-based regret bounds.
method Use of surrogate losses (ramp and hinge) to derive new regret bounds and algorithms.
result Derives new margin-based regret bounds and efficient algorithms for contextual bandits.
New method learns distances and similarities robustly from noisy data.
problem Scalability and robustness in metric learning for large datasets.
method Robust online Distance-Similarity learning with Rescaled hinge loss.
result Significantly outperforms state-of-the-art methods in noisy data.
AUC (area under ROC curve) is an important evaluation criterion, which has been popularly used in many learning tasks such as class-imbalance learning, cost-sensitive learning, learning to rank, etc. Many learning approaches try to optimize AUC, while owing to the non-convexity and discontinuousness of AUC, almost all …
We give elementary constructions for Satake-Furstenberg, Martin and Karpelevich boundaries of symmetric spaces. We also consruct some "new" boundaries
The paper analyzes the dynamics of a simple neural network using a mean-field approach.
problem Understanding the training dynamics of neural networks, especially in classification tasks.
method Developed an analytic theory using a mean-field limit for a simple neural network.
result Explicitly solved the dynamics of a linearly separable dataset with a linear hinge loss.