Paper connects risk consistency to L_p consistency for broader loss functions.
problem Establishing risk consistency for a wider class of loss functions.
method Analyzes the connection between risk consistency and L_p-consistency for various loss functions.
result Shifted loss functions do not reduce assumptions as much as other results.
New method synthesizes and analyzes probability measures using entropy-regularized optimal transport.
problem Synthesize and analyze probability measures with entropy-regularized optimal transport.
method Entropy-regularized Wasserstein-2 cost and Sinkhorn divergence for synthesis and analysis.
result Computed barycentric coefficients and their stability for classification of corrupted point cloud data.
The abstract proves the existence and regularity of Brakke flows starting from a given set.
problem Existence and regularity of Brakke flows starting from a given set.
method Proves the existence and regularity of Brakke flows using a closed countably 1-rectifiable set in R^2.
result For almost all time, the flow locally consists of a finite number of embedded curves of class W^{2,2} whose endpoints meet at junctions with angles of 0, 60, or 120 degrees.
Theoretical analysis of MCR for improving imputation quality in partially observed data.
problem Improving model generalization in partially observed settings.
method Theoretical analysis of Measure Consistency Regularization (MCR) for neural network distance.
result MCR's generalization advantage is not always guaranteed and can be monitored through a duality gap.
Machine learning forecasts show bias at long horizons, contrary to standard tests.
problem Forecast efficiency tests misinterpret machine learning performance.
method Theoretical and empirical analysis of regularization and measurement noise.
result Machine learning forecasts exhibit overreaction at longer horizons, not bias.
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force solutions of variational problems to belong to a low-dimensional manifold (the so…
Scalable algorithm for computing Wasserstein-2 barycenters without bias.
problem Computing Wasserstein-2 barycenters efficiently and accurately.
method Input convex neural networks and cycle-consistency regularization.
result Our approach avoids introducing bias and does not require minimax optimization.
The paper quantifies the regularity of attention operations.
problem Quantifying the regularity of attention operations.
method Proposes a new mathematical framework using measure theory and integral operators.
result Proves attention operation is Lipschitz continuous on compact domains and provides an estimate of its Lipschitz constant.
Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of prediction accuracy. We assume only that the densities have a convex parametrization …
The paper proposes a new method to estimate interest rates consistently under both risk-neutral and real-world measures.
problem Consistent estimation of interest rates under both risk-neutral and real-world measures.
method Proposes a framework using progressive and square-integrable functions to specify the change of measure, and introduces two time-dependent candidates: step and linear functions.
result The proposed methods produce more stable and realistic long-term interest rate forecasts compared to using a constant function.
New method for scalable barycenter computation using Wasserstein gradient flows.
problem Scalability and integration of label information in barycenter computation.
method Gradient flows in Wasserstein space, time discretization, mini-batch optimal transport, modular regularization, task-aware functions, supervised information integration.
result Empirically validated new state-of-the-art barycenter solver with labeled barycenters outperforming unlabeled ones.
Dynamic risk measures follow law invariance principles over time.
problem Tackles dynamic risk measurement principles.
method Shows equivalence between adapted law invariance and recursive one-step conditional-law representation for time-consistent risk measures.
result Identifies adapted law invariance as the dynamic counterpart of ordinary law invariance.
Study shows consistency of shallow GCNNs on sampled point clouds under manifold assumption.
problem Consistency of shallow GCNNs on sampled point clouds under manifold assumption.
method Functional analysis perspective, weakly compact product of unit balls, Sobolev regularity, frequency cutoff.
result Proves Γ-convergence of regularized empirical risk minimization functionals and convergence of their global minimizers. Risk contagion concerns any entity dealing with large scale risks. Suppose (X,Y) denotes a risk vector pertaining to two components in some system. A relevant measurement of risk contagion would be to quantify the amount of influence of high values of Y on X. This can be measured in a variety of ways. In this paper, we…
Improves GAN-based semi-supervised learning with consistency regularization.
problem Lack of consistency in class probability predictions under local perturbations.
method Introduces consistency regularization to GANs, leveraging both local and interpolation consistency.
result Significantly improves performance and achieves new state-of-the-art results.
New algorithm improves OT map estimation for semi-discrete settings.
problem Improving estimation of OT maps in semi-discrete settings.
method Stochastic Gradient Descent with adaptive entropic regularization and averaging acceleration.
result Achieves nearly minimax rate of O(t−1) for OT map estimation. Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.
problem Multi-view clustering where views have both consistent and complementary information.
method Consistent and complementary graph-regularized multi-view subspace clustering (GRMSC).
result The proposed method outperforms state-of-the-art methods on benchmark datasets.
We study a transformation of metric measure spaces introduced by Gigli and Mantegazza consisting in replacing the original distance with the length distance induced by the transport distance between heat kernel measures. We study the smoothing effect of this procedure in two important examples. Firstly, we show that in…
Consistency regularization improves robustness to noisy labels.
problem Improving model robustness to noisy labels in machine learning.
method Empirical study of consistency regularization on noisy datasets.
result Consistency regularization improves model robustness to label noise.
As AI systems develop in complexity it is becoming increasingly hard to ensure non-discrimination on the basis of protected attributes such as gender, age, and race. Many recent methods have been developed for dealing with this issue as long as the protected attribute is explicitly available for the algorithm. We addre…
Develop a comprehensive theory for regularized M-estimation in reproducing kernel Hilbert spaces.
problem Regularized M-estimation in reproducing kernel Hilbert spaces
method Existence and measurability of the estimator, sharp rates of convergence
result New rates for tensor product Sobolev spaces
Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters in some low-dimensional model subspace. In such settings, it is desirable for est…
Enhances GANs by improving consistency regularization.
problem Improving the artifacts introduced by consistency regularization in GANs.
method Proposed modifications to consistency regularization to fix artifacts and improve performance.
result Significant improvement in FID scores on various GAN architectures.
New theorem for generalized group sparsity improves consistency and convergence rates.
problem Improving statistical inference in high-dimensional data with element-wise and group-wise sparsity.
method Developed a generalized version of Sparse-Group Lasso and proved a universal theorem for consistency and convergence rates.
result Obtained results on consistency and convergence rates for different forms of double sparsity regularization.
New solver SR2 tackles deep neural network training with nonsmooth regularization.
problem Training deep neural networks with nonsmooth regularization to achieve sparsity and efficiency.
method Combines adaptive quadratic regularization with proximal stochastic gradient principles.
result Established worst-case iteration complexity of O(ε^−2) for SR2.
Study reveals learning curves and benign overfitting in spectral algorithms for large dimensions.
problem Understanding learning curves and benign overfitting in spectral algorithms for large-dimensional data.
method Analysis of learning curves and benign overfitting in spectral algorithms for inner-product kernels on the sphere and general domains.
result Characterization of three distinct regimes: over-regularized, under-regularized, and interpolation regimes, revealing benign overfitting across both under-regularized and interpolation regimes.
This work extends entropic optimal transport to non-product reference couplings, focusing on Gaussian cases.
problem Finding a diffuse coupling between two measures with non-product reference couplings.
method Reduction of the entropic optimal transport problem to a matrix optimization problem.
result Complete description of the solution for non-product reference couplings, including primal and dual variables.
In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded neural networks have been reported to achieve state-of-the-art results with respec…
Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized that even without training, convolutional networks can function as concise imag…
ε-Consistent Mixup improves semi-supervised classification accuracy.
problem Improving semi-supervised classification accuracy with limited labeled data.
method Combines Mixup's linear interpolation with consistency regularization, using an adaptive tradeoff between the two.
result ε-Consistent Mixup yields the largest gains in low label-availability scenarios.
TPBS models improve robustness to overfitting with localized Dirichlet energy regularization.
problem Global Dirichlet energy-based regularization fails for TPBS models due to perfect interpolation.
method Propose local Dirichlet energy regularization and two inference estimators.
result TPBS models outperform neural networks in overfitting regimes and maintain competitive performance otherwise.
A new algorithm computes Wasserstein barycenters without entropic regularization.
problem Computing Wasserstein barycenters efficiently and accurately.
method Free-support algorithm based on particle flow and Riemannian geometry.
result The algorithm avoids entropic regularization and is computationally tractable.
Wasserstein archetypal analysis finds optimal data summaries using Wasserstein metric.
problem Finding optimal data summaries using Wasserstein metric.
method Alternative formulation of archetypal analysis based on Wasserstein metric, with regularization and gradient-based computational approach.
result Existence and consistency of solutions for the regularized problem.
Study optimizes option pricing with robust strategies, ensuring consistency with vanilla option prices.
problem Optimizing exotic option pricing with robust strategies.
method Introduces semistatic strategies and robust convex integral functionals on bounded continuous functions.
result Consistent indifference prices with observed vanilla option prices.
We conduct an axiomatic study of the problem of estimating the strength of a known causal relationship between a pair of variables. We propose that an estimate of causal strength should be based on the conditional distribution of the effect given the cause (and not on the driving distribution of the cause), and study d…
In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variabl…
VOLARE provides standardized realized volatility measures from financial data.
problem Lack of standardized realized volatility measures from ultra-high-frequency data.
method Asset-specific pipeline for cleaning and sampling data, providing a wide range of realized estimators.
result Comprehensive set of realized estimators for equities, exchange rates, and futures.
In recent years, deep learning has surpassed traditional approaches to the problem of singing voice separation. The Wave-U-Net is a recent deep network architecture that operates directly on the time domain. The standard Wave-U-Net is trained with data augmentation and early stopping to prevent overfitting. Minimum hyp…
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…
Generative Adversarial Networks (GANs) are known to be difficult to train, despite considerable research effort. Several regularization techniques for stabilizing training have been proposed, but they introduce non-trivial computational overheads and interact poorly with existing techniques like spectral normalization.…
In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are fou…
SCR improves GNN training with consistency regularization.
problem Balancing labeled and unlabeled data in GNNs.
method Introduces two consistency regularization strategies: perturbed predictions and Mean Teacher.
result Enhances various GNNs to achieve better performance.
In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the numéraire-based model and work with utility functions only supporting R+. Under the assumption of existence of consistent price sy…
In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main results of this paper on time consistency; namely, an equivalent recursive form…
Deep neural networks without regularization can achieve consistent estimates with good convergence rates.
problem The necessity of regularization in deep neural networks for consistent estimates.
method Gradient descent on an over-parametrized neural network without regularization, with specific initialization, step size, and number of steps.
result An estimate without regularization is universally consistent and achieves good convergence rates.
From the perspective of network analysis, the ubiquitous networks are comprised of regular and irregular components, which makes uncovering the complexity of network structures to be a fundamental challenge. Exploring the regular information and identifying the roles of microscopic elements in network data can help us …
Improves risk and variability measures continuity and consistency.
problem Improving the continuity and consistency of risk and variability measures.
method Analyzes convex and order bounded above functionals on Frechet lattices and Orlicz spaces.
result Order-continuous, law-invariant functionals on Orlicz spaces are strongly consistent everywhere.
Contrastive regularization improves semi-supervised learning by better propagating confident pseudo-labels.
problem Consistency regularization's limitation in high performance and efficiency.
method Proposes contrastive regularization to update model features, pushing confident labels into unlabeled samples.
result Improves semi-supervised learning tasks with fewer training iterations and robust performance.