The paper studies generalization bounds for VRM, a variant of ERM.
problem Understanding the generalization performance of VRM.
method Proves generalization bounds for VRM under specific conditions.
result Generalization performance of VRM depends on vicinal function choice and function class quality.
New approach improves model robustness and calibration in latent space.
problem Improving model robustness and calibration under input perturbations.
method VarMixup (Variational Mixup) in latent space of VAEs.
result Models trained with VarMixup in latent space are more robust and calibrated.
Paper explores VRM for PSMLC with partially labeled medical images.
problem Improving PSMLC with limited labeled data.
method Applies VRM to PSMLC for better model performance.
result VRM improves PSMLC performance with partial labels.
Improves speech recognition in noisy environments using robust acoustic models.
problem Adverse environments with significant mismatch between training and test conditions.
method Theoretical analysis of data augmentation as vicinal risk minimization, using mixture of Gaussians to incorporate robust inductive bias.
result Waveform-based approach shows 150% relative improvement in out-of-distribution generalization.
Paper proposes a new method for WDRO with local perturbations, achieving better accuracy.
problem Wasserstein distributionally robust optimization's theoretical understanding needs improvement.
method Develops a new approximation theorem and risk consistency results for WDRO.
result The proposed method achieves significantly higher accuracy on noisy datasets.
We find numerical and empirical evidence for dynamical, structural and topological phase transitions on the (German) Frankfurt Stock Exchange (FSE) in the temporal vicinity of the worldwide financial crash. Using the Minimal Spanning Tree (MST) technique, a particularly useful canonical tool of the graph theory, two tr…
Proposes novel losses for fine-grained categorical domain adaptation.
problem Fine-grained alignment of categories across domains in unsupervised domain adaptation.
method Joint category-domain classifier with adversarial training losses for both domain and category levels, and vicinal domain adaptation.
result Achieves state-of-the-art performance on benchmark datasets.
ALPS improves neural network robustness and generalization.
problem Challenges in designing effective regularization schemes for adversarial robustness.
method Adversarial Labelling of Perturbed Samples (ALPS) using synthetic samples and min-max formulation.
result ALPS achieves state-of-the-art regularization performance and adversarial robustness.
Study on Gibbs-ERM learning, focusing on excess risk bounds and effective dimension.
problem Understanding the interplay between data distribution and learning in large hypothesis spaces.
method Distribution-dependent analysis of Gibbs-ERM, focusing on excess risk and effective dimension.
result Distribution-dependent upper bounds on excess risk, showing effective dimension controls risk.
ML4C uses binary classification to infer causal structures from latent vicinity.
problem Learning causal relations from observational data without ground truth.
method Two-phase paradigm with binary classifier and novel featurization.
result ML4C outperforms state-of-the-art algorithms in causal learning.
Visualizes optimization landscapes to understand FCN performance.
problem Understanding why FCNs perform well empirically.
method Visualizing objective functions in 3D space, comparing networks, investigating skip-layer connections, and analyzing loss surfaces.
result Skip-layer connections in FCNs promote flat optimization landscapes, leading to better generalization.
Paper introduces a novel measure to analyze excess error in classification under covariate shift.
problem Analyzing excess error in classification under covariate shift.
method Utilizes vicinity information to characterize excess error.
result Faster or competitive convergence rates compared to previous techniques.
Study of convergence of point-object configurations to a charged dust continuum.
problem Understanding the convergence of discretized point-object configurations to a charged dust continuum.
method Establishing existence and uniqueness of horizons/minimal surfaces, studying geometries of regions exterior to minimal surfaces, and discussing limits.
result Examples of scalar curvature jumps upon taking Gromov-Hausdorff and intrinsic flat limits.
In many signal detection and classification problems, we have knowledge of the distribution under each hypothesis, but not the prior probabilities. This paper is aimed at providing theory to quantify the performance of detection via estimating prior probabilities from either labeled or unlabeled training data. The erro…
We derive bounds on the distribution function, therefore also on the Value-at-Risk, of φ(X) where φ is an aggregation function and X=(X1,…,Xd) is a random vector with known marginal distributions and partially known dependence structure. More specifically, we analyze three type…
LGV boosts adversarial attacks by improving surrogate models.
problem Improving the transferability of black-box adversarial attacks.
method LGV uses a pretrained surrogate model and multiple weight sets from additional training epochs to generate an effective surrogate ensemble.
result LGV outperforms other test-time transformations by significant margins.
Smooth flow around a helix, extending previous circle solution.
problem Constructing smooth Euler flows near helical shapes.
method Generalization of a previous circle solution approach.
result Smooth flow supported near a helix.
CcGAN tackles conditional image generation for continuous labels.
problem Mathematical challenges in conditioning on continuous, scalar labels.
method Proposes novel empirical losses and label input methods for continuous conditional GANs.
result CcGAN generates diverse, high-quality images from continuous labels.
Generative models such as Variational Auto Encoders (VAEs) and Generative Adversarial Networks (GANs) are typically trained for a fixed prior distribution in the latent space, such as uniform or Gaussian. After a trained model is obtained, one can sample the Generator in various forms for exploration and understanding,…
This paper proves IRM minimizes o.o.d. risk under certain conditions.
problem Deep networks can fail to generalize to new domains with different distributions.
method Proves IRM minimizes o.o.d. risk through a bi-level optimization problem.
result IRM minimizes o.o.d. risk under specific conditions.
The paper analyzes the performance of empirical risk minimization for p-norm linear regression.
problem Empirical risk minimization on p-norm linear regression. method Analyzes performance under various conditions and moment assumptions.
result High probability excess risk bounds for empirical risk minimizer, matching asymptotic rates.
We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extre…
Prove non-asymptotic bounds for minimal risk in statistical learning
problem Estimating minimal risk in statistical learning
method Using concentration inequalities
result Non-asymptotic bounds for minimal risk
Study risk-minimizing insurance investments with taxes and expenses.
problem Determining optimal insurance investments in the presence of taxes and expenses.
method Introduced tax- and expense-modified risk-minimization, derived strategies, linked to decompositions, and established equivalence to artificial market approach.
result Equivalence to artificial market approach and consistency with classic risk-minimization.
Paper shows robust estimators converge to true risk minimizers at optimal rates.
problem Understanding asymptotic properties of robust risk minimizers.
method Investigates robust analogues of empirical risk minimization, focusing on median of means estimator.
result Robust minimizers converge to true minimizers at optimal rates and have similar asymptotic variance.
We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected Shortfall. The minimization problem of a spectral measure is shown to be equivale…
This paper explores portfolio management strategies to maximize alpha and minimize beta.
problem Maximizing returns while minimizing risk in investment portfolios.
method Examines asset allocation, diversification, active management, and risk management strategies.
result Combining these strategies optimizes portfolio performance.
Improved simulation of phase transitions using hierarchical autoregressive networks.
problem Simulating phase transitions in complex systems.
method Hierarchical Autoregressive Neural (HAN) network sampling algorithm.
result Significant improvement in statistical uncertainty compared to the Wolff cluster algorithm.
This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomp…
Solves risk minimization problem with SSD constraints.
problem Finding SSD-minimal quantile function under mixed constraints.
method Explicitly works out SSD-minimal solution and relates to Skorokhod problem.
result Explicit solution to risk minimizing problem.
This paper analyzes privacy-preserving methods for sparse model optimization.
problem Privacy-preserving sparse model optimization with non-differentiable norms.
method Differential privacy techniques applied to Frank-Wolfe and objective perturbation algorithms.
result Excess risk bounds for Frank-Wolfe and objective perturbation algorithms are derived.
Paper tackles heavy-tailed data without finite variance, proposing robust risk minimization.
problem Empirical risk minimization under heavy-tailed data with finite p-th moment. method Minimizes risk values robustly estimated via Catoni's method, using generalized generic chaining.
result Shows better performance of optimizer based on empirical risks via Catoni-style estimation.
In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always resu…
CV outperforms mean-variance for stock returns, minimizing risk and maximizing growth.
problem Traditional risk assessment methods underperform in stock market analysis.
method Derived new CV equation and used it to analyze stock performance.
result Stocks with low but positive CV grow exponentially, outperforming high-risk stocks.
Paper bounds convergence rate of adversarial surrogate risk.
problem Vulnerability of binary classification models to adversarial attacks.
method Characterizes conditions for adversarial consistency and provides surrogate risk bounds.
result Surrogate risk bounds quantify the rate of convergence of adversarial classification risk.
Paper bounds excess risk in robust empirical risk minimization for heavy-tailed distributions.
problem Risk bounds for robust empirical risk minimization in heavy-tailed distributions.
method Proposes robust proxies for expectation to bound excess risk.
result Excess risk of robust estimators can converge to 0 at fast rates.
We study the rates of convergence from empirical surrogate risk minimizers to the Bayes optimal classifier. Specifically, we introduce the notion of \emph{consistency intensity} to characterize a surrogate loss function and exploit this notion to obtain the rate of convergence from an empirical surrogate risk minimizer…
Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.
problem Estimation of normal mean in multivariate settings with correlated observations.
method Approximate risk minimization over a functional class of shrinkage-thresholding rules.
result Unified estimator NOMAD for shrinkage, thresholding, and regularization.
Robust learning method minimizes risk with corrupted data.
problem Statistical learning with unknown corrupted data fraction.
method Develops a robust learning method with specified corrupted data fraction upper bound.
result Optimal weights provide robustness against corrupted data.
New method diversifies risk using complex numbers.
problem Minimizing portfolio risk under constraints.
method Complex valued principal component analysis in risk diversification.
result Outperforms conventional risk parity and diversification methods.
We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Levy processes, Arai and Suzuki (2015) obtained a formula for locally risk-minimiz…
In the present paper, the minimal investment risk for a portfolio optimization problem with imposed budget and investment concentration constraints is considered using replica analysis. Since the minimal investment risk is influenced by the investment concentration constraint (as well as the budget constraint), it is i…
Study minimizes risk in MDPs with spectral measures.
problem Minimizing risk in MDPs with spectral measures.
method Splitting into inner and outer minimization problems; solving inner as MDP; proving existence for outer.
result Existence and solution methods for the outer minimization problem.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
problem Risk-minimization in incomplete markets for exponential additive models.
method Derive explicit mathematical expressions for local risk-minimization strategies in exponential additive models.
result Provide necessary conditions for deriving expressions and confirm integrability conditions for specific models.
MaxRM uses random forests to minimize maximum risk across different environments.
problem Designing methods that generalize better to test environments with different distributions.
method Introducing variants of random forests based on the principle of MaxRM (Maximum Risk Minimization).
result Proved statistical consistency for the proposed method and provided an out-of-sample guarantee for MaxRM with regret.
Investigates optimal portfolios with risk-free assets, minimizing investment risk.
problem Investment risk minimization with budget and return constraints.
method Replica analysis and exploration of implications of a risk-free asset.
result Implications of a risk-free asset on optimal portfolio and investment risk.
New learning algorithm for real analytic functions without gradient descent.
problem Learning real analytic functions without gradient descent.
method Taylor approximation and sampling data distribution.
result Nonuniform learning result for real analytic functions.
TIER uses extended strain data to improve gravitational wave detection sensitivity.
problem Improving gravitational wave detection sensitivity using extended strain data.
method TIER framework using machine learning to capture extended strain data features.
result Up to 20% improvement in sensitive volume time in LIGO-Virgo-Kagra O3 data.