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.
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 present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex optimization, the sample complexity of our algorithms depends only on the margin of…
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
COMET Flows model multivariate extremes with heavy tails and asymmetric dependence.
problem Normalizing flows struggle with multivariate extremes and asymmetric tail dependence.
method COMET Flows decomposes modeling into marginal and copula parts; uses tail belief and kernel density for marginals, and low-dimensional manifold for tail dependence.
result COMET Flows outperform other models in capturing heavy-tailed marginals and asymmetric tail dependence.
This paper proposes a new method to improve domain adaptation by distinguishing between marginal and dependence structure differences.
problem Existing domain adaptation methods fail to differentiate between marginal and dependence structure differences, leading to suboptimal transferability.
method The paper introduces a new approach that measures and optimizes the differences in internal dependence structure separately from marginals.
result The new method significantly improves transferability and robustness compared to existing benchmarks on real-world datasets.
Generative models often fail to preserve joint structure despite matching marginals.
problem Generative models fail to capture complex dependencies beyond univariate marginals.
method Introduced D_Sigma(P,Q) = ||Sigma_P - Sigma_Q||_F to measure covariance-level dependence fidelity.
result Covariance-level divergence can lead to structural instability in downstream inference.
The paper explores the relationship between joint mixability and negative dependence structures.
problem Understanding the connection between joint mixability and various negative dependence concepts.
method Analyzes the properties of joint mixes and their relation to negative dependence structures.
result Derives necessary and sufficient conditions for a joint mix to be negatively dependent.
mGRN improves multivariate time series prediction by managing marginal and joint memories.
problem Extracting dependencies in multivariate sequential data with strong serial and cross-sectional dependencies.
method Developed a novel recurrent network architecture, Memory-Gated Recurrent Networks (mGRN), with gates for marginal and joint memories.
result mGRN consistently outperforms state-of-the-art architectures on various public datasets.
Estimates marginal independence structure of Bayesian networks from data.
problem Learning the marginal independence structure of Bayesian networks from observational data.
method Using Gröbner basis and MCMC method (GrUES) to connect and recover the true structure.
result GrUES recovers the true marginal independence structure at a higher rate than simple independence tests.
CMRFs extend PGMs for topological data, capturing both conditional and marginal dependencies.
problem Limited expressiveness of PGMs for topological data.
method Introducing Colored Markov Random Fields (CMRFs) that model Gaussian edge variables on topological spaces.
result CMRFs improve distributed estimation over physical networks compared to baselines.
DCC separates marginal estimation from dependence modeling for improved classification accuracy.
problem Classifying with strong dependence between features.
method Deep Copula Classifier using neural copula densities.
result Achieves excess-risk O(n−r/(2r+d)) for r-smooth copulas. The paper examines how heavy-tailed risks behave under Gaussian copula models.
problem Understanding tail risk probabilities with heavy-tailed marginal risks and Gaussian dependence.
method Modeling heavy-tailed risks using regular variation and analyzing tail probabilities under Gaussian copula.
result The rate of decay of tail set probabilities varies with the type of tail sets and Gaussian correlation matrix.
Researchers expand on best subset selection theory, identifying key complexities.
problem Understanding model selection performance in high-dimensional sparse linear regression.
method Analyzing residualized signals, orthogonality, and spurious projections to establish margin conditions.
result Established necessary and sufficient margin conditions for BSS model consistency.
We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of d…
One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical point of view, the theoretical analysis of generalization performance contribut…
DIET tests conditional independence using marginal dependence measures of residual information.
problem Computational intractability of conditional randomization tests (CRTs).
method DIET avoids fitting large models by leveraging marginal independence statistics of information residuals.
result DIET achieves higher power than other tractable CRTs on synthetic and real benchmarks.
We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We develop our copula for first order Markov series, and extend it to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence…
Introduces joint exclusivity (JE), a new form of negative dependence.
problem Negative dependence structures in probability distributions.
method Defines JE by exclusion of the interior of the non-negative orthant, establishes necessary and sufficient conditions for existence, proposes a canonical construction.
result Sharp necessary and sufficient condition for existence of JE random vectors with prescribed marginals.
3MSBM learns smooth trajectories from multiple snapshots.
problem Capturing long-range temporal dependencies in complex systems.
method Lifts dynamics to phase space, generalizes stochastic bridges to multi-marginal conditional problems, learns transport maps preserving intermediate marginals.
result Significantly improves convergence and scalability in capturing complex dynamics.
Study shows how steepest descent algorithms' geometric margin increases during training.
problem Understanding implicit bias in steepest descent algorithms for neural networks.
method Analysis of steepest descent algorithms with infinitesimal learning rates in homogeneous neural networks.
result Limit points of training trajectories correspond to KKT points of margin-maximization problems.
This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize…
New SVM margin bound improves generalization in machine learning.
problem Improving SVM margin bounds for better generalization.
method Stable sample compression schemes to derive new data-dependent generalization bounds.
result Proves a new optimal SVM margin bound with a log factor improvement.
Bayesian models use hyperparameters to indirectly assign priors, and this work shows how these priors can be derived from maximum entropy principles.
problem Understanding the assumptions and dependencies in Bayesian hierarchical models.
method Demonstrates how canonical distributions and maximum entropy principles can be used to derive marginal priors in hierarchical models.
result Marginal priors in hierarchical models derived from maximum entropy principles have different constraints compared to the original priors.
This paper assesses tail risk and systemic risk in cryptocurrencies using expectiles and MES.
problem Quantifying tail risk and systemic risk in cryptocurrencies.
method The study uses expectiles and Marginal Expected Shortfall (MES) to assess tail risk and systemic risk of cryptocurrencies.
result The expectile-based approach and MES provide a dynamic method to evaluate the impact of single assets on systemic risk.
Study bounds financial path expectations using martingale distributions.
problem Bounding path-dependent financial expectations over martingale distributions.
method Relaxed martingale optimal transport problem, approximated via linear programming.
result Empirical relaxation can be approximated within O(n^(-1/2)) error.
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.
Paper proves tight lower bounds for online multicalibration, separating it from marginal calibration.
problem Proving lower bounds for online multicalibration in relation to marginal calibration.
method Information-theoretic approach, constructing group families from orthonormal bases.
result Establishes tight lower bounds for online multicalibration, matching upper bounds up to logarithmic factors.
Identifies interpretable generative model for multivariate data.
problem Black-box architectures of deep generative models are often unidentified and difficult to interpret.
method Introduces Deep Discrete Encoder (DDE) Copula, a hierarchical binary latent variable model inside a copula framework.
result Establishes conditions for identification of DDE copula parameters and proves posterior consistency.
The paper addresses portfolio allocation with uncertain covariance matrices, finding a logarithmic risk dependence.
problem Portfolio allocation with uncertain covariance matrices.
method Calculates the expected value of CARA utility function over a distribution of covariance matrices, considering uncertainty in future returns and covariances.
result Marginalization introduces a logarithmic dependence on risk, leading to lower allocation levels for higher uncertainties.
The paper examines risk aggregation under mixtures of marginals, finding that more homogeneous distributions lead to larger uncertainty.
problem Investigating the impact of mixing on risk aggregation uncertainty.
method Analyzes ordering relations and inequalities for aggregation sets under distribution and quantile mixtures.
result More homogeneous marginals result in larger aggregation sets, indicating greater model uncertainty.
Enhanced consistency bounds derived for classification under a new noise condition.
problem Enhanced consistency bounds for classification under a new noise condition.
method Model Margin Noise (MM noise) assumption, derived enhanced H-consistency bounds.
result Enhanced H-consistency bounds under MM noise condition, interpolates between linear and square-root regimes.
A new copula, the checkerboard copula, maximizes entropy and preserves dependence.
problem Choosing copula for non-continuous marginal distributions.
method Introducing the checkerboard copula, maximizing Shannon entropy.
result Checkerboard copula maximizes entropy and preserves dependence.
Default-ERM shortcut learning persists even without additional information.
problem Default-ERM shortcut learning in perception tasks despite stable feature sufficiency.
method Studied linear perception task; developed margin control (MARG-CTRL) loss functions.
result Margin control mitigates shortcut learning on various tasks.
The paper examines higher moments in insurance, focusing on coskewness and its impact on actuarial quantities.
problem The impact of higher-order moments on actuarial applications, particularly expected shortfall and life annuity valuation.
method Derives analytical bounds for mixed moments under unspecified dependence structure, applies copula-based mixture model.
result Coskewness and odd-order mixed moments exhibit a monotonic relationship with expected shortfall and annuity premiums.
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
Given a matrix A, a linear feasibility problem (of which linear classification is a special case) aims to find a solution to a primal problem w:ATw>0 or a certificate for the dual problem which is a probability distribution p:Ap=0. Inspired by the continued importance of "large-margin cla…
This paper is devoted to the quantification and analysis of marginal risk contribution of a given single financial institution i to the risk of a financial system s. Our work expands on the CoVaR concept proposed by Adrian and Brunnermeier as a tool for the measurement of marginal systemic risk contribution. We first g…
Improved forecasting of financial risk using Diffusion-Copula framework.
problem Capturing complex, asymmetric dependence structures in financial markets.
method Explicitly decouples marginal distribution learning from dependence structure using Mixture Density Networks and Classification-Diffusion Copula.
result Superior performance in forecasting systemic extremes of marginal and joint events.
The paper calibrates geophysical predictions using marginal distributions and machine learning.
problem Sensitivity to initial conditions in geophysical systems leads to large deviations in long-term forecasts.
method The method introduces a calibration algorithm based on normalization and Kernelized Stein Discrepancy (KSD) to enhance ML predictions.
result The method improves the fidelity of ML predictions to known physical distributions, ensuring consistency with non-local statistical structures.
GPDFlow models extreme threshold exceedance with flexible dependence using normalizing flows.
problem Challenges in modeling multivariate threshold exceedance probabilities due to infinite parametrizations.
method GPDFlow uses normalizing flows to flexibly represent dependence without explicit parametric assumptions.
result GPDFlow significantly improves modeling accuracy and flexibility compared to traditional parametric methods.
Generative moment matching networks (GMMNs) are introduced as dependence models for the joint innovation distribution of multivariate time series (MTS). Following the popular copula-GARCH approach for modeling dependent MTS data, a framework based on a GMMN-GARCH approach is presented. First, ARMA-GARCH models are util…
We prove that the marginal densities of a global probability mass function in a primal normal factor graph and the corresponding marginal densities in the dual normal factor graph are related via local mappings. The mapping depends on the Fourier transform of the local factors of the models. Details of the mapping, inc…
New method uncovers zero entropy in dependent observations after finite samples.
problem Understanding uncertainty reduction in dependent observations.
method Minimum list entropy coupling, greedy algorithm.
result Zero entropy achieved with O(log(1/P_min)) samples for dependent observations.
The paper examines how small positive dependence can lead to correlated tail risks.
problem Understanding the impact of dependence uncertainty on tail risk measures.
method Introducing a regular dependence measure and analyzing the aggregation of risks.
result Small positive dependence can result in perfectly correlated tail risks.
New method improves calibration of neural networks by targeting robust margins and local smoothness.
problem Poor calibration of neural networks, leading to unreliable confidence estimates.
method Intervene on training procedure by targeting robust margins and local smoothness.
result Improved out-of-sample calibration without sacrificing accuracy.
Study online learning of neural networks with margin condition.
problem Online learning of neural networks with sign activation function.
method Characterized margin condition for online learnability, proved mistake bounds, constructed counterexamples.
result Proved optimal mistake bounds and lower bounds for neural networks.
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of the data distribution, and show distribution-specific upper and lower bounds on…