Paper extends Lévy models with memory to better price FX double barrier options.
problem Efficiently pricing double barrier options in complex FX models.
method Introduces regime-switching Lévy models with memory and a modified numerical method.
result New models and method improve accuracy of option pricing.
Least squares regression shows unexpected double descent in under-parameterized models.
problem Understanding the generalization of under-parameterized models in regression.
method Analyzing the spectrum and eigenvectors of the sample covariance matrix.
result Least squares regression can exhibit a peak in generalization in the under-parameterized regime, contrary to previous explanations.
We study a phenomenological model for the continuous double auction, equivalent to two independent M / M / 1 M/M/1 M / M /1 queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the auction are derived and, as a consequence, three possible regimes in the behavior …
New statistical models capture double power-law behavior in data.
problem Capturing two-regime power-law behavior in datasets.
method Introducing completely random measures with double power-law behavior.
result Proposed models provide a better fit than Pitman-Yor process.
More data can actually hurt linear regression performance in certain conditions.
problem The test risk of linear regression estimators increases with additional samples in overparameterized settings.
method An analysis of linear regression with isotropic Gaussian covariates using gradient descent.
result The bias decreases with more samples, but variance increases, leading to a surprising increase in test risk.
Quantum models show improved performance in overparameterized regimes.
problem Overfitting in quantum machine learning models.
method Analytical demonstration and numerical experiments on quantum kernel methods.
result Quantum models can operate in the modern, overparameterized regime without overfitting.
The paper analyzes how over-parameterization affects reinforcement learning performance.
problem Understanding the impact of over-parameterization in reinforcement learning.
method Theoretical analysis of Least-Square Temporal Difference (LSTD) algorithm with random features and asymptotic regime.
result Identification of a double descent phenomenon in reinforcement learning performance.
Double descent observed in tree-based models for genomic prediction.
problem Understanding the generalization behavior of tree-based models in machine learning.
method Systematic variation of model complexity in a genomic prediction task using whole-genome sequencing data.
result Double descent emerges only when complexity is scaled jointly across learner capacity and ensemble size.
We analyze kernel matrices in polynomial high-dimensional settings and explain double descent in KRR.
problem Understanding the spectrum of kernel matrices in polynomial high-dimensional settings and its implications for KRR risk.
method Generalized decomposition of kernel matrices into low-rank spike matrix, identity, and Gegenbauer matrix.
result The test error in KRR can exhibit double descent behavior, depending on effective regularization and signal-to-noise ratio.
More training data can hurt the generalization of adversarially robust models.
problem The challenge of balancing adversarial robustness and generalization in machine learning models.
method Investigation of three regimes based on adversary strength and empirical studies on various models.
result More training data can hurt the generalization of adversarially robust models in different regimes.
Deep learning models can initially degrade in performance as they grow larger, then improve.
problem Performance degradation of larger models and more data.
method Defined effective model complexity and identified double descent phenomenon.
result Increasing model size and data can initially hurt performance, contrary to intuition.
Proposes pT-Learning for optimal dynamic treatment regimes in mHealth.
problem Challenges in learning optimal dynamic treatment regimes with large intervention options and infinite time horizon.
method Proximal Temporal consistency Learning (pT-Learning) framework for adaptively adjusting between deterministic and stochastic policies.
result Minimax estimator avoids double sampling issue and can incorporate off-policy data.
Double descent phenomenon explained in simple terms.
problem Understanding the surprising drop in test error in overparameterized models.
method Informal explanation using linear algebra and probability, visual intuition with polynomial regression, mathematical analysis with ordinary linear regression.
result Three factors create double descent: data undersampling, model size, and parameter count. Ablating any one of these factors prevents double descent.
This paper explains double descent using VC theory.
problem Understanding the generalization of overfitting neural networks.
method VC-theoretical analysis of double descent.
result Double descent can be explained by classical VC-generalization bounds.
New findings challenge the traditional U-shaped curve of model complexity and error, revealing a second descent in error as model size increases.
problem The traditional U-shaped curve of model complexity and prediction error is incomplete, with recent work suggesting a second descent in error as model size increases.
method Careful consideration of multiple complexity axes and a nonparametric statistics perspective were used to interpret the observed double descent curves.
result The observed double descent curves in classical statistical machine learning methods fold back into traditional convex shapes, resolving tensions with statistical intuition.
The paper explores how model complexity affects OOD detection performance.
problem Ensuring reliability and safety of machine learning systems through OOD detection.
method Investigates the relationship between model capacity and OOD detection performance using empirical and theoretical analysis.
result The Double Descent phenomenon is observed in post-hoc OOD detection, indicating that overparameterization can enhance OOD detection.
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading strategies, we analyze the timings and sequences of the investor's market participation,…
Model shows loss curve with two distinct exponents due to sparse activations.
problem Sparse activations impact neural network scaling laws.
method Introduced a model for neural scaling laws under sparse activations, derived asymptotic population loss, and analyzed gradient-descent dynamics.
result Loss curve exhibits double-descent peak near interpolation threshold with two distinct scaling exponents.
We analyze double descent in finite-width neural networks using influence functions.
problem Understanding double descent in finite-width neural networks.
method Using influence functions to derive population loss bounds and investigate loss function effects.
result Derived bounds exhibit double descent behavior at the interpolation threshold.
Study shows label noise impacts neural representations' information content, revealing double descent behavior.
problem Impact of label noise on neural network hidden representations.
method Information Imbalance proxy of conditional mutual information to compare hidden representations.
result Representations learned with noisy labels are more informative than those with clean labels in the underparameterized regime, and equally informative in the overparameterized regime.
The study provides precise asymptotic theory for in-context learning by Transformers.
problem Understanding the sample complexity, pretraining task diversity, and context length for successful in-context learning.
method An exactly solvable model of linear regression task by linear attention, deriving sharp asymptotics.
result Double-descent learning curve with increasing pretraining examples, phase transition between low and high task diversity regimes.
Paper connects neural networks to Gaussian processes for understanding double-descent.
problem Understanding the double-descent phenomenon in neural networks.
method Uses techniques from random matrix theory and Gaussian processes.
result Establishes a connection between NNGP and random matrix theory for neural networks.
Study on RF regression with SGD shows double descent phenomenon.
problem Understanding generalization in RF models trained with SGD.
method Precise non-asymptotic error bounds derived for RF regression under constant and polynomial-decay step-size SGD.
result RF regression generalizes well for interpolation learning and exhibits double descent behavior.
Study CMC hypersurfaces in H 2 i m e s H 2 \mathbb{H}^2 imes\mathbb{H}^2 H 2 im es H 2 with a specific symmetry.
problem Constant mean curvature hypersurfaces with double horocyclic symmetry in H 2 i m e s H 2 \mathbb{H}^2 imes\mathbb{H}^2 H 2 im es H 2 . method Reduction to a single ODE, solving explicitly, classifying solutions.
result Existence and uniqueness of double horocyclic CMC hypersurfaces.
Deep networks generalize well even when they fit training data perfectly, thanks to overparametrization.
problem Understanding generalization in overparametrized deep networks.
method Random features regression, asymptotic analysis, ensemble averaging.
result Bias remains constant beyond the interpolation threshold, while variance components decay with overparametrization.
The paper analyzes the effectiveness of principal component regression with varying numbers of features.
problem The study examines the performance of principal component regression with different numbers of selected features.
method The analysis considers the least squares linear regression over uncorrelated Gaussian features selected in decreasing variance order. It also analyzes the prediction error in the average-case setting as the number of features and samples grow.
result The prediction error shows a 'double descent' shape as the number of features increases, and conditions are established for achieving minimum risk in the interpolating regime.
New method for efficient pricing of double barrier options in Lévy models.
problem Difficulties in accurately and quickly calculating prices of double barrier options in jump models.
method GWR-SINH method based on Gaver-Wynn-Rho acceleration applied to Bromwich integral.
result Accurate and fast calculations of prices of double barrier options in jump models achieved.
The paper analyzes the generalization error of random features regression, revealing a double descent curve.
problem Analyzing the generalization error of random features regression.
method Performing ridge regression on N random features of the form σ(wa^T x), where wa are random weights.
result The test error follows a double descent curve, with a global minimum above the interpolation threshold.
Exact expressions for double descent and implicit regularization in over-parameterized models.
problem Understanding the generalization error of over-parameterized models like deep neural networks.
method Surrogate random design to replace standard i.i.d. design, leading to exact expressions for mean squared error and implicit regularization.
result Exact non-asymptotic expressions for double descent and implicit regularization in over-parameterized models.
Overparameterization aids in model pruning, leading to improved test accuracy.
problem Improving lightweight model performance through pruning.
method Theoretical analysis and high-dimensional asymptotics of model pruning in overparameterized neural networks.
result Even with known informative features, training a large model and then pruning leads to better test accuracy.
The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.
problem Characterizing generalization properties of high-dimensional kernel ridge regression.
method Bias-variance decomposition of the expected excess risk, considering different regularization schemes and data eigen-profiles.
result The risk curve of kernel regression can be double-descent-like, bell-shaped, or monotonic, depending on n, d, and regularization level.
The study examines denoising and noisy-input regression under distribution shift, revealing double descent behavior and insights for data augmentation.
problem Understanding denoising in machine learning, especially under noisy inputs and distribution shift.
method Theoretical analysis of supervised denoising and noisy-input regression, considering low-rank data and proportional regime.
result The test error exhibits double descent under general distribution shift, indicating that overfitting the noise can be benign, tempered, or catastrophic.
Characterizes RFF regression in large n , p , N n,p,N n , p , N setting, providing precise learning phases and double descent curve.
problem Characterizes RFF regression in large n , p , N n,p,N n , p , N setting. method Characterizes the exact asymptotics of random Fourier feature (RFF) regression in the realistic setting of large n , p , N n,p,N n , p , N . result Characterizes two qualitatively different phases of learning and the corresponding double descent test error curve.
Study shows minimizing the norm of the ERM solution stabilizes kernel ridge-less regression.
problem Stability of kernel ridge-less regression.
method Minimizing the norm of the ERM solution to minimize CV stability.
result Interpolating solution with minimum norm minimizes CV stability.
Kernel methods and MLPs perform similarly to linear models in high dimensions.
problem Understanding the performance of kernel methods and MLPs in high-dimensional settings.
method Analysis of kernel methods and MLPs in a high-dimensional regime with proportional asymptotics.
result Linear models are optimal in high-dimensional settings when data is generated by kernel models with nonlinear relationships.
Improved estimators for causal inference using cross-fitting and undersmoothing.
problem Estimating expected conditional covariance in causal inference.
method Double cross-fit doubly robust (DCDR) estimators with undersmoothing for non-smooth nuisance functions.
result DCDR estimators achieve n \sqrt{n} n -consistency and asymptotic normality under minimal conditions. Neural networks generalize well despite overfitting due to high capacity.
problem Understanding why deep neural networks generalize well in overparameterized settings.
method High-dimensional asymptotic analysis of generalization under kernel regression with Neural Tangent Kernel.
result Test error exhibits non-monotonic behavior and can have additional peaks and descents in the overparameterized regime.
Study on ridge regression in convolutional models shows double descent error behavior.
problem Understanding generalization and estimation error in over-parameterized convolutional models.
method Analysis of ridge estimators for convolutional linear models, derivation of exact error formulae.
result Ridge estimators exhibit double descent error behavior in high-dimensional convolutional models.
Study on test risk dynamics in learning theory with stochastic gradient flow.
problem Understanding test risk in stochastic gradient flow dynamics.
method Path integral formulation for small learning rates, explicit computation for weak features.
result Explicit corrections due to stochastic term in dynamics, good agreement with simulations.
BP, a method for sparse recovery, shows generalization error decreases with more features.
problem Understanding the generalization error of overfitting solutions in linear regression.
method Study of Basis Pursuit (BP) for sparse recovery of linear regression models.
result BP's model error decreases with more features, showing double-descent behavior.
A study on a surprising phase transition in model generalization error as parameters approach sample size.
problem Understanding the generalization error of overparametrized ridge models.
method Finite sample analysis using continuous Newton method and ℓ 2 \ell_2 ℓ 2 -norm solution performance. result The generalization error decreases after the threshold p = n p=n p = n for ridge models. Paper proposes DG-ETC for online submodular maximization with stochastic bandit feedback.
problem Online unconstrained submodular maximization with stochastic bandit feedback.
method Double-Greedy - Explore-then-Commit (DG-ETC) approach.
result DG-ETC achieves logarithmic regret O ( d log ( d T ) ) O(d\log(dT)) O ( d log ( d T )) for 1 / 2 1/2 1/2 -approximate pseudo-regret. Study shows overparameterization helps in generalizing from smooth interpolants.
problem Understanding generalization in overparameterized linear models.
method Analysis of random Fourier series model with weighted trigonometric interpolation.
result Weighted trigonometric interpolation leads to lower generalization error in overparameterized scenarios.
This study shows ESG ratings reduce equity crash risk during market downturns.
problem Decoupling of alpha from tail risk resilience in traditional models.
method Double Machine Learning for structural deconfounding, state-dependent analysis.
result High ESG ratings reduce crash incidence during systemic drawdowns.
The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.
problem Numerical integration challenges in SV models, especially with high precision and low computational time.
method Proposes a fast regime switching algorithm to determine when higher precision arithmetic is needed.
result Shows that numerical quadratures need to be carefully chosen based on model parameters and parameter values.
Deep linear networks oscillate beyond the edge of stability in a predictable manner.
problem Understanding oscillations in deep linear networks beyond the edge of stability.
method Theoretical analysis of loss oscillations in deep matrix factorization loss.
result Loss oscillations in deep linear networks follow a period-doubling route to chaos and occur within a small subspace.
Study on generalisation in random feature learning and hidden manifold models.
problem Generalisation in high-dimensional learning problems.
method Replica method from statistical physics for asymptotic generalisation performance.
result Closed-form expression for generalisation performance in various high-dimensional settings.
The paper studies PCA of probability measures with varying sample sizes and finds optimal convergence rates.
problem PCA of multiple probability measures with varying sample sizes.
method Double asymptotic regime analysis with convergence rates n − 1 / 2 + m − α n^{-1/2} + m^{-α} n − 1/2 + m − α for empirical covariance and PCA risk. result Optimal convergence rates for empirical covariance and PCA risk in the dense regime are proven.