This work proposes SDI regularization to improve adversarial robustness.
problem Improving adversarial robustness of deep neural networks.
method SDI regularization term to complement adversarial training.
result Combining SDI with AT variants enhances robustness and generalization.
Simplifies risk minimization combining mean and standard deviation.
problem Minimizing mean and standard deviation under heavy-tailed losses.
method Adapting robust mean estimation technique to include standard deviation.
result Simple approach performs as well or better than alternative risk criteria.
Deviation inequalities for stochastic approximation methods.
problem Establishing bounds on the deviation of stochastic approximation methods.
method Martingale approximation method for separately Lipschitz functions.
result Established various deviation inequalities for stochastic approximation by averaging and minimization.
SAM improves generalization in overparameterized models, but its behavior in tensorized models is less understood.
problem Understanding the implicit regularization of SAM in tensorized models.
method Scale-invariance analysis and gradient flow analysis to derive Norm Deviation as a measure of core norm imbalance, and propose Deviation-Aware Scaling (DAS).
result DAS achieves competitive or improved performance over SAM, while offering reduced computational overhead.
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
New Gini indices capture more nuanced income inequality.
problem Measuring joint dispersion across multiple observations.
method Axiomatic approach to define and characterize n-th order Gini deviations.
result Higher-order Gini coefficients reveal more extreme income disparities.
A new method to break down insurance costs into risk and uncertainty.
problem Understanding and quantifying insurance costs in uncertain environments.
method An axiomatic approach to decompose premium principles into risk and deviation measures.
result Maximal risk and minimal deviation measures can be uniquely identified in decompositions.
Study minimizes market inefficiency in systemic economies.
problem Minimizing deviations of market prices from fundamental values.
method Characterized market inefficiency and developed a matrix of holdings to minimize it.
result Portfolio holdings should deviate more from diversification if banks have similar systemic significance.
Optimal learning via moderate deviations theory improves statistical accuracy.
problem Statistical estimation of expected loss in various models.
method Develops confidence intervals using moderate deviation principle.
result Proposed confidence intervals are statistically optimal.
Unified proof for various bandit algorithms with logarithmic regret.
problem Achieving logarithmic regret in stochastic bandit algorithms.
method Minimal high-probability concentration condition and two deterministic lemmas.
result Unified proofs for classical and contemporary bandit algorithms.
SVR analyzed within RQ framework for risk management.
problem Risk management in stochastic optimization.
method Risk Quadrangle (RQ) theory applied to SVR.
result SVR formulations as minimization of Vapnik error and CVaR norm.
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from their true values are almost surely diverse, which makes each data point not equal…
New model tackles real-world distribution mismatches in machine learning.
problem Real-world applications often have training and test distributions that differ.
method Developed a learning model based on information theory using importance sampling.
result The model performs better under large distribution deviations.
Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…
We propose a robust risk measurement approach that minimizes the expectation of overestimation plus underestimation costs. We consider uncertainty by taking the supremum over a collection of probability measures, relating our approach to dual sets in the representation of coherent risk measures. We provide results that…
Improved adaptive algorithms for identifying the best arm in MABs with fixed budget.
problem Identifying the best arm in stochastic Multi-Armed Bandits with a fixed sampling budget.
method Established a connection between Large Deviation Principles and adaptive algorithms, improving error probability bounds and devising new algorithms.
result The \sred algorithm outperforms existing algorithms in identifying the best arm.
Introduces Star-Shaped deviation measures for risk analysis.
problem Risk measurement and analysis in finance.
method Characterizes Star-Shaped deviation measures through acceptance sets and convex deviation measures.
result Exposes the relationship between Star-Shaped risk measures and deviation measures.
New method uses Coulomb gases for Monte Carlo integration with reduced errors.
problem Reducing integration errors in numerical algorithms.
method Using Gibbs measures with a large deviations approach.
result Preserves large deviation principle for improved integration.
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently l…
We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization problem on a suitably constructed compact manifold and is based on the spectral t…
Proposes ITISC for clustering with minimized worst-case expected distortions.
problem Real-world clustering data distribution mismatch.
method Information theoretical importance sampling, constrained minimax optimization, Lagrange method.
result Validation of ITISC on synthetic and real-world datasets.
New framework embeds generalization in learning dynamics using large deviation theory.
problem Improving generalization and robustness in learning problems.
method Gradient methods from continuous-time perspective with Freidlin-Wentzell theory of large deviations.
result Asymptotic probability estimate for rare events in learning dynamics.
Paper characterizes monotonic mean-deviation risk measures.
problem Developing consistent risk measures from mean-deviation models.
method Applying a risk-weighting function to the deviation part of a mean-deviation model.
result Characterizes monotonic mean-deviation measures as consistent risk measures.
The paper proves deep learning can be robust with certain loss functions.
problem The robustness of deep learning models under flawed data.
method Empirical-risk minimization with unbounded, Lipschitz-continuous loss functions.
result These loss functions provide efficient prediction under minimal data assumptions.
We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the Gärtner-Ellis theorem and sharp large deviations tools.
Paper proves large deviation principle for stochastic approximations.
problem Asymptotic estimates of learning algorithm deviations.
method Weak convergence approach to large deviations.
result Identifies appropriate scaling sequence and new representation for rate function.
In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition,…
Suppose k centers are fit to m points by heuristically minimizing the k-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with p≥4 bounded moments; in particular, the difference between the sample cost and distribution cost decays with $…
Study large deviations in life insurance portfolios without identical distributions.
problem Large deviations in life insurance portfolios with bounded losses and variances.
method Upper bound from standard large deviations, counterexample for full large deviation principle.
result Exponential bound for average loss exceeding a threshold.
SRFE clarifies KL divergences without unifying learning frameworks.
problem Inductive biases of KL divergences and their limitations.
method Introducing SRFE, a log-moment-based functional of the likelihood ratio.
result SRFE recovers KL divergences as limits and reveals a mean-variance tradeoff.
Study large deviations for hypoelliptic diffusion on sub-Riemannian manifolds.
problem Large deviations for hypoelliptic diffusion measures on sub-Riemannian manifolds.
method Rough path theory and manifold-valued Malliavin calculus.
result Proved a large deviation principle for pinned hypoelliptic diffusion measures.
Proposes new deviation measures using Minkowski gauges.
problem Lack of suitable acceptance sets for deviation measures.
method Derives deviation measures through Minkowski gauges of acceptable sets.
result Any positive homogeneous deviation measure can be accommodated in the framework.
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance. We also solve the problem of optimal risk-sha…
Vertex distortion measures how far lattice knots deviate from straight lines.
problem Measuring how much lattice knots deviate from straight paths.
method Analogous to smooth knots, study vertex distortion in lattice knots.
result Vertex distortion is 1 only for the unknot and can be arbitrarily high.
We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and tail asymptotics for diffusions, as well as for option prices and realised vari…
Study rolling dynamics with random slipping and twisting using large deviation principles.
problem Analyzing the stability of a rolling model with random slipping and twisting.
method Modelled as a stochastic differential equation on the orthonormal frame bundle, examined via large deviations.
result Proved large deviation principles for projection curves and their horizontal lifts on the base manifold.
Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a way to speed up computations. This paper considers moderate deviations for the wei…
We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short with respect to the size of the portfolio. We also study the noise sensitivity o…
Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained on this base. This is done via imposing certain conditions on the Lie derivative…
Unified approach to stochastic Volterra systems' deviations.
problem Large and moderate deviations for stochastic Volterra systems.
method Weak convergence approach by Budhijara, Dupuis and Ellis.
result Unified treatment of deviations for a broad class of stochastic Volterra equations.
Study large deviations in random walks on Lie groups.
problem Large deviations in sub-Riemannian random walks.
method Prove large deviation principle for random walks on stratified Lie groups.
result Proved a large deviation principle with a rate function adapted to sub-Riemannian geometry.
BONSAI optimizes parameters while respecting a default configuration, reducing unnecessary changes.
problem Standard BO pushes weakly relevant parameters to the boundary, making it hard to distinguish between important and spurious changes.
method BONSAI is a default-aware BO policy that prunes low-impact deviations from a default configuration while controlling acquisition value loss.
result BONSAI matches the GP-UCB regret rate while recovering the minimal-ℓ0 solution, reducing the number of non-default parameters in recommended configurations. Deviation inequalities and limit laws for random walks on metric spaces.
problem Understanding random walks on metric spaces with contracting isometries.
method Adapting Gouëzel's pivotal time construction to establish deviation inequalities.
result Exponential bounds and limit laws for random walks on mapping class groups and CAT(0) spaces.
Let M be a smooth manifold and S a semi-spray defined on a sub-bundle C of the tangent bundle TM. In this work it is proved that the only non-trivial k-jet approximation to the exact geodesic deviation equation of S, linear on the deviation functions and invariant under an spec…
Optimizes variance reduction in Heston model using large and moderate deviations.
problem Improving variance reduction in stochastic volatility models.
method Large and moderate deviations theory applied to Heston model.
result Derives closed-form solutions for optimal change of measure.
Large deviations theory applied to policy gradient methods.
problem Understanding convergence of policy gradient methods in reinforcement learning.
method Large deviation rate function and contraction principle from large deviations theory.
result Convergence properties of policy gradient methods can be extended to various policy parametrizations.
Study examines large deviations in random walks on hyperbolic spaces.
problem Large deviations in random walks on Gromov-hyperbolic spaces.
method Established large deviations results for distance and translation length of random walks.
result Deduced a special case of a conjecture regarding spectral radii of random matrix products.
This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as l…