Study on scheduling jobs with unknown types, achieving sublinear excess cost.
problem Optimizing job scheduling with unknown job types and varying durations.
method Design of algorithms for non-preemptive and preemptive scenarios, proving lower bounds.
result Preemptive algorithms can significantly outperform non-preemptive ones when job types have distinct durations.
Study nonstationary data learning under β-mixing processes.
problem Learning from nonstationary data with varying distributions.
method Proposed a learning method for β-mixing processes.
result Cumulative excess risk grows sublinearly in the number of predictions.
In statistical learning theory, convex surrogates of the 0-1 loss are highly preferred because of the computational and theoretical virtues that convexity brings in. This is of more importance if we consider smooth surrogates as witnessed by the fact that the smoothness is further beneficial both computationally- by at…
The paper explores the information-theoretic nature of excess risk in machine learning.
problem Understanding the excess risk in machine learning models.
method Formulates the minimax excess risk as a zero-sum game and modifies it to allow swapping of the order of play.
result Proves that under certain conditions, the duality gap is zero, allowing for the application of Bayesian results to provide bounds on minimax excess risk.
New tool detects 'fleeting modes' causing excess risk in financial markets.
problem Detecting portfolios with statistically significant excess risk in financial markets.
method Random Matrix Theory to identify 'fleeting modes' independent of underlying correlation structure.
result Fleeting modes exist in both futures and equity markets, and momentum is a source of excess risk.
The paper analyzes the excess risk of PCA and provides a precise characterization.
problem Understanding the excess risk of principal component analysis (PCA).
method Established a central limit theorem for PCA error and derived the excess risk distribution.
result Obtained a non-asymptotic upper bound on the excess risk of PCA.
Study excess risk in statistical inference with transformations.
problem Excess risk in estimating random variables from feature vectors and transformations.
method Characterize lossless transformations, develop test statistics, and information-theoretic bounds.
result Strongly consistent partitioning test statistic for lossless transformations.
Study non-asymptotic bounds for robust estimators under misspecified models.
problem Evaluate performance of robust estimators under adversarial conditions.
method Propose a general approach to adversarial risk analysis, including investigations on generalization and approximation errors.
result Establish non-asymptotic upper bounds for adversarial excess risk under Lipschitz loss functions.
Paper introduces R-conditioning for risk-averse valuation in financial markets.
problem Risk-averse valuation in incomplete financial markets.
method Introduces R-conditioning as a new operator between conditional expectation and sublinear expectation.
result R-conditioning can approximate sublinear expectations and is used to compute risk-averse values.
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.
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.
Paper improves clustering risk bounds for kernel k-means.
problem Improving clustering risk bounds for kernel k-means.
method Analyzes kernel k-means and Nyström approximation.
result Achieves nearly optimal excess clustering risk bound.
Paper studies portfolio investment under volatility uncertainty and short-sale constraints, improving risk-adjusted returns.
problem Investment portfolio optimization under volatility uncertainty and short-sale constraints.
method Sublinear expectation model to handle volatility uncertainty, constructing SLE-MUV model.
result Pareto frontier of SLE-MUV model is a continuous convex curve with polynomial analytical expression.
New method estimates model risk without knowing function class.
problem Evaluating model risk for complex, opaque models.
method Wild refitting with Bregman losses and randomized symmetrization.
result Valid upper bound on excess risk for opaque models.
Local SGD proves efficient in overparameterized linear regression.
problem Efficiently learning overparameterized linear models in distributed settings.
method Distributed SGD (DSGD) with overparameterized models.
result Excess risk of SGD is smaller than ridge regression in the same sample complexity.
Study finds high cyber risk stocks generate significant excess returns.
problem Understanding and quantifying cyber risk's impact on stock returns.
method Machine learning algorithm measuring cyber risk proximity to a corpus.
result High cyber risk stocks generate an excess return of 18.72% p.a.
The paper analyzes the performance of empirical risk minimization for p p p -norm linear regression.
problem Empirical risk minimization on p p 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.
Study uses spectral risk for learning with heavy-tailed data.
problem Learning with heavy-tailed loss distributions.
method Spectral risk with Lipschitz-continuous density, derivative-free learning.
result Excess risk guarantees and improved performance over traditional methods.
Currency volatility shocks predict lower excess returns, and buying weak transmitters outperforms selling strong ones.
problem Predicting currency returns using volatility shocks.
method Constructed a dynamic, directed network of volatility connections using option-implied volatilities.
result Currencies that transmit more volatility shocks earn lower excess returns.
New algorithm achieves optimal privacy and efficiency in non-Euclidean convex optimization.
problem Optimizing convex functions while maintaining privacy in non-Euclidean settings.
method Developed a linear-time algorithm for ℓ p \ell_p ℓ p -setups, leveraging geometric properties. result Optimal excess risk achieved in linear time for 1 < p ≤ 2 1 < p \leq 2 1 < p ≤ 2 . Excessive leverage, i.e. the abuse of debt financing, is considered one of the primary factors in the default of financial institutions. Systemic risk results from correlations between individual default probabilities that cannot be considered independent. Based on the structural framework by Merton (1974), we discuss …
This paper analyzes multi-pass SGD for least squares, improving generalization bounds.
problem Improving generalization bounds for multi-pass SGD in the least squares problem.
method Develops an instance-dependent excess risk bound for least squares in the interpolation regime.
result SGD performs worse than GD instance-wise but saves computational time.
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strate…
The paper bounds the excess risk of deep neural networks for weakly dependent processes.
problem Learning with weakly dependent data using deep neural networks.
method Approximation of smooth functions by deep neural networks and a bound on excess risk.
result The excess risk bound for deep learning under weak dependence is close to O ( n − 1 / 2 ) \mathcal{O}(n^{-1/2}) O ( n − 1/2 ) for sufficiently smooth functions. Early stopping improves gradient descent's performance in Gaussian mixture classification.
problem Gradient descent's implicit bias can be suboptimal in overparameterised classification.
method Early stopping combined with sharp upper and matching lower bounds.
result Early-stopped GD achieves minimax-optimal risk for Gaussian mixture models.
Study tests if equity factors explain Bitcoin's risk and returns.
problem Explaining Bitcoin's risk and return with equity factors.
method Applied statistical methods to test Fama-French factors on Bitcoin's excess returns.
result Fama-French factors have explanatory power on Bitcoin's risk and returns.
New method for unbiased regression reduces excess risk.
problem Least squares regression with optimal solution and Hessian matrix.
method Averaged stochastic gradient descent with time-average estimator.
result Unbiased estimator with O(1/k) expected excess risk.
New inequality for regression risk with random design and noise.
problem Excess risk in least-squares regression with random design and heteroscedastic noise.
method Proved a new concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise, separating linearized and quadratic processes.
result Generalized the approach to quadratic contrasts and random design.
Optimal reinsurance strategy for risk models influenced by stochastic factors.
problem Optimal excess-of-loss reinsurance under stochastic risk factors.
method Stochastic control theory and Hamilton-Jacobi-Bellman equation.
result Optimal reinsurance strategy maximizing expected utility of terminal wealth.
Deep linear networks can closely approximate interpolants without improving risk.
problem Understanding the risk bounds of deep linear networks compared to minimum ℓ 2 \ell_2 ℓ 2 -norm solutions. method Bounding excess risk of interpolating deep linear networks trained using gradient flow.
result Deep linear networks can closely approximate or match minimum ℓ 2 \ell_2 ℓ 2 -norm solutions in terms of risk. SMP estimator improves density and logistic regression under misspecification.
problem Improper estimator for optimal excess risk in misspecified models.
method SMP minimizes a new excess risk bound for statistical learning.
result SMP achieves optimal excess risk of O ( ( d + B 2 R 2 ) / n ) O((d + B^2R^2)/n) O (( d + B 2 R 2 ) / n ) for logistic regression. New method refines model-free evaluation of complex machine learning models.
problem Evaluating the excess risk of opaque machine learning predictors.
method Perturbing derivatives to create pseudo-outcomes and refitting the model twice.
result Upper bound on excess risk derived efficiently without prior function class knowledge.
Paper improves privacy in SGD with low noise, achieving optimal risk rates.
problem Privacy-preserving machine learning with good performance.
method Differentially private SGD with low-noise analysis.
result Achieves optimal excess risk rates for non-smooth losses.
The paper analyzes SMOTE for imbalanced classification, providing theoretical bounds and guidelines.
problem The challenge of imbalanced classification problems, especially with minority classes.
method Theoretical analysis of SMOTE and related oversampling techniques for minority classes.
result Derives concentration and excess risk bounds for SMOTE and kernel-based classifiers.
Optimizes differentially private kernel learning with random projection.
problem Privacy-preserving learning algorithms with optimal performance.
method Differentially private kernel ERM algorithm based on random projection in reproducing kernel Hilbert space.
result Achieves minimax-optimal excess risk rates for various loss functions.
We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the sample size n. The bounds lead us to consider sample variance penalization, a nov…
New approach avoids excess empirical risk in domain generalization.
problem Learning models that generalize to unseen distributions from diverse data sets.
method Minimizes penalty under constraint of optimal empirical risk, leveraging rate-distortion theory.
result Significant improvements in domain generalization performance across multiple methods.
A new formula reveals symmetries between mean excess and ES functions.
problem Optimizing risk measures in financial models.
method Established a reverse ES optimization formula.
result Reveals elegant symmetries and relationships between mean excess and ES functions.
The paper analyzes the generalization performance of spectral clustering algorithms and proposes new methods to improve their effectiveness.
problem Theoretical analysis of spectral clustering's generalization performance.
method Theoretical analysis and development of new spectral clustering algorithms.
result The excess risk bounds of spectral clustering algorithms have a O ( 1 / n ) \mathcal{O}(1/\sqrt{n}) O ( 1/ n ) convergence rate. The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, a…
The paper provides guarantees for statistical learning with a nuisance parameter.
problem Statistical learning with an unknown nuisance parameter.
method Two-stage sample splitting meta-algorithm for target and nuisance parameters.
result Nuisance estimation error impacts excess risk bound of second order under Neyman orthogonality.
Lower bounds show OLS outperforms basis pursuit in overparameterized linear regression.
problem Excess risk of sparse interpolating procedures in overparameterized linear regression.
method Proved lower bounds on excess risk for OLS and basis pursuit.
result Excess risk of basis pursuit can converge at an exponentially slower rate than OLS.
Paper introduces robust kernel ridge regression using Cauchy loss for handling various noise types.
problem Developing robust regression methods for noisy data.
method Introduces kernel Cauchy ridge regressor (KCRR) using Cauchy loss function.
result Establishes almost minimax-optimal convergence rate for KCRR in terms of L 2 L_2 L 2 -risk. Investing in high quality firms yields excess returns, contrary to risk or behavioral explanations.
problem Excess returns of quality stocks despite risk and behavioral explanations.
method Investigated two explanations: risk and behavioral views; provided novel evidence for the behavioral view.
result Excess returns of quality stocks are not due to risk, but due to systematic underestimation by analysts.
Full-batch GD achieves generalization close to any stationary point with fewer assumptions.
problem Generalization and excess risk bounds for smooth losses, including non-Lipschitz and nonconvex cases.
method Path-dependent analysis of GD's generalization error, focusing on optimization error and stability.
result Generalization error is tightly bound in terms of optimization error and iteration count, bypassing common assumptions.
Paper proposes ZO-SMD for MERO, achieving optimal convergence rates.
problem Minimizing excess risk across all test distributions.
method Zeroth-order stochastic mirror descent algorithm for both smooth and non-smooth MERO.
result Converges at optimal rates of O ( 1 / t ) \mathcal{O}(1/\sqrt{t}) O ( 1/ t ) for estimates and optimization errors. We present extensive evidence that ``risk premium'' is strongly correlated with tail-risk skewness but very little with volatility. We introduce a new, intuitive definition of skewness and elicit an approximately linear relation between the Sharpe ratio of various risk premium strategies (Equity, Fama-French, FX Carry,…
New G-VaR predictor outperforms existing VaR models under model uncertainty.
problem Predicting VaR under model uncertainty in financial markets.
method G-VaR predictor based on sublinear expectation and worst-case scenario analysis.
result G-VaR predictor outperforms existing benchmarks on NASDAQ and S\&P500 datasets.