Extends online learning to metric spaces using exponential weights.
problem Online learning in metric spaces.
method Exponentially weighted average forecaster, barycenters, Jensen's inequality, measure contraction property.
result Results in a statistical learning framework.
We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate…
A new method for exponentially weighted moving models using approximations.
problem Efficiently updating moving averages for time series data.
method Approximates EWMM using a fixed window and quadratic term, solving non-growing problems.
result Approximation produces estimates similar to exact EWMM.
Introduces Exponentially Weighted Signature for better path representation.
problem Uniform treatment of historical information in signatures.
method Generalizes EFM signature to bounded linear operators, enabling contextualised temporal weighting.
result EWS is the unique solution to a linear controlled differential equation and generalizes state-space models.
Researchers extend asymptotic analysis to Bergman projections with Gevrey weights.
problem Analyzing Bergman projections with Gevrey weights.
method Extending direct approach to semiclassical asymptotics to Gevrey weights using Fourier integral operators.
result Gevrey symbol amplitude of asymptotic Bergman projection with Gevrey weights and Gevrey-type growth rate.
The study analyzes how neural reward models learn features for policy optimization in a Gaussian single-index model.
problem Reward modeling in policy optimization and its impact on downstream value.
method Two-stage neural reward model: first learns hidden direction, then fits readout layer.
result For any feature-learning temperature above a dimension-free threshold, a constant fraction of neurons recover the hidden direction.
Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.
problem Exact recovery of communities in weighted graphs with Gaussian and exponential distributions.
method Introduces a new semi-metric to describe conditions for exact recovery and analyzes conditions for both complete and incomplete graphs.
result Necessary and sufficient conditions for exact recovery are asymptotically tight and applicable to both complete and incomplete graphs.
A new accelerated method with simpler momentum update rules.
problem Optimizing parameters in machine learning models.
method Proposes a novel accelerated stochastic gradient method with simpler momentum update rules.
result The method outperforms Sgdm and Adam in practical problems.
Paper analyzes sparse aggregation in GLMs with Kullback-Leibler risk bounds.
problem Sparse aggregation in GLMs for parameter approximation.
method Exponential weighted aggregation scheme with Kullback-Leibler risk bounds.
result Sharp oracle inequality for Kullback-Leibler risk with leading constant 1 and minimax-optimal rate of aggregation.
Decentralized algorithm reduces regret and converges to Nash equilibrium in online congestion games.
problem Online congestion games with exponential action sets and strict Nash equilibria.
method CongestEXP algorithm using exponential weights method.
result CongestEXP achieves O ( k F T ) O(kF\sqrt{T}) O ( k F T ) regret bound and almost exponential convergence to strict Nash equilibrium. We improve deep threshold networks' memorization capacity exponentially.
problem Memorizing datasets with randomized labels using deep neural networks.
method Using Gaussian random weights in the first layer and binary or integer weights in subsequent layers, we prove a new dependence on minimum distance.
result We show that O ~ ( 1 δ + n ) \widetilde{\mathcal{O}}(\frac{1}{\delta} + \sqrt{n}) O ( δ 1 + n ) neurons and O ~ ( d δ + n ) \widetilde{\mathcal{O}}(\frac{d}{\delta} + n) O ( δ d + n ) weights are sufficient. Abstract result on correlations of pairs in exponentially growing discrete subsets.
problem Pair correlations in exponentially growing discrete subsets with weight functions.
method Proved abstract result on correlations of pairs of elements in an exponentially growing discrete subset with a weight function.
result Distribution function of unscaled differences is t ↦ δ 2 e − ∣ t ∣ t\mapsto\fracδ2\,e^{-|t|} t ↦ 2 δ e − ∣ t ∣ , and pair correlation exhibits Poissonian behavior under certain conditions. New algorithm optimizes online network resource allocation with long-term constraints.
problem Optimal resource reservation in communication networks with job transfers and budget limits.
method Randomized exponentially weighted method for long-term constraints.
result Upper bound for regret and cumulative constraint violations established.
Nonuniform tubular neighborhoods of curves in Euclidean n-space are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but injective exponential maps. A generalization of the thickness formula is obtaine…
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
Improved averaging method for noisy observations converges strongly.
problem Noisy observations from random dynamical systems require stable estimates.
method Introduced p p p -EMA, a modified exponential moving average with subharmonic weight decay. result Stochastic convergence guarantees for p p p -EMA under mild assumptions. New aggregation strategy handles unbounded losses with regret bounds.
problem Online optimization with unbounded loss functions.
method Follow The Regularized Leader (FTRL) with φ-divergence.
result Worst regret bound for unbounded losses with alternative divergences.
Annealed Entropic Allocation improves ranking and selection by mitigating hard switching and improving finite-budget discrimination.
problem Sequential budget allocation in ranking and selection
method Annealed weighted soft-min framework
result Surrogate converges uniformly to the hard minimum, soft-min weights concentrate on active challengers, and target allocation map is continuous.
Study addresses RTB model performance drops due to distribution shifts.
problem Distribution shifts between training and target environments in RTB markets.
method Applies Exponential Tilt Reweighting Alignment (ExTRA) algorithm to estimate and correct model weights.
result Demonstrates improved RTB model performance using ExTRA algorithm.
Guyon-Lekeufack model accurately predicts market volatility.
problem Modeling and predicting market volatility accurately.
method Path-dependent volatility model with weighted past price returns and squared volatility.
result Wellposedness of the coupled system of stochastic differential equations for all parameter values.
Develops a new fuzzy model using QPs and ewl2 regularization to improve local region behavior.
problem Inability of constant and linear functions to accurately describe local regions in fuzzy models.
method Applied Fuzzy C-Means for structure identification, used QPs as consequents, introduced ewl2 regularization.
result Improved model's ability to describe local regions without overfitting.
AEW estimator achieves optimal risk in expectation for large enough temperatures.
problem Understanding minimax-rate optimality of AEW estimator in model selection aggregation.
method Analyzing AEW estimator with exponential weights for squared loss under random design.
result AEW achieves excess risk T log ( M ) / ( n + 1 ) T \log (M) / (n+1) T log ( M ) / ( n + 1 ) in expectation for large enough temperatures. Researchers prove constant solutions for a specific Finslerian equation.
problem Investigating exponentially harmonic functions on Finslerian spaces.
method Analyzing the exponential energy functional and using nonnegative Ricci curvature conditions.
result Any bounded solution to the Finslerian equation is constant.
This work improves polynomial approximations for functions with asymmetric behavior.
problem Efficiently approximating functions with asymmetric behavior, especially those growing unbounded on one side.
method Introduces weighted deep polynomial approximants that combine learnable deep polynomials with one-sided weights.
result Weighted deep polynomial approximants outperform existing methods in approximating functions with asymmetric behavior.
Efficiently optimizes boolean functions using multilinear polynomials and exponential weight updates.
problem Optimizing boolean functions over the boolean hypercube with high computational cost.
method Proposes a computationally efficient algorithm using multilinear polynomials and exponential weight updates.
result Improves computational time up to several orders of magnitude compared to state-of-the-art algorithms.
This paper addresses the problem of prediction with expert advice for outcomes in a geodesic space with non-positive curvature in the sense of Alexandrov. Via geometric considerations, and in particular the notion of barycenters, we extend to this setting the definition and analysis of the classical exponentially weigh…
Paper introduces kernel deformed exponential families for sparse continuous attention.
problem Creating efficient attention mechanisms for sparse data.
method Developed kernel deformed exponential families, theoretically and experimentally.
result Kernel deformed exponential families can attend to multiple compact regions of data.
Gradient descent on normalized networks reveals sparsity preferences.
problem Understanding the inductive bias of gradient descent on normalized neural nets.
method Analysis of gradient descent on weight-normalized smooth homogeneous neural nets, focusing on SWN and EWN.
result EWN causes weights to be updated in a way that prefers asymptotic relative sparsity.
Two new PCA variants improve financial data analysis.
problem Numerical instability and nonstationarity in PCA for finance.
method Iterated and exponentially weighted moving PCA variants using Ogita-Aishima iteration.
result Improved stability and adaptability in financial data analysis.
CDEFs reduce model complexity and uncover time correlations.
problem Model complexity and data efficiency in probabilistic modeling.
method Builds on deep exponential families, ties weights for reduced parameters.
result CDEFs uncover time correlations with fewer parameters.
WildWood improves Random Forest predictions using bootstrap out-of-bag samples.
problem Improving Random Forest predictions for supervised learning.
method Uses bootstrap out-of-bag samples to compute improved predictions by aggregating all possible subtrees with exponential weights.
result WildWood produces faster and more competitive predictions compared to other ensemble methods.
In this paper, we prove a classification for complete embedded constant weighted mean curvature hypersurfaces Σ ⊂ R n + 1 Σ\subset\mathbb{R}^{n+1} Σ ⊂ R n + 1 . We characterize the hyperplanes and generalized round cylinders by using an intrinsic property on the norm of the second fundamental form. Furthermore, we prove an equivalence of pro…
Introduces a new theoretical framework for exponential smoothing.
problem Theoretical foundation and robustness of simple exponential smoothing.
method Stochastic gradient ascent to optimize Gaussian log-likelihood functions.
result Simple exponential smoothing converges to the trend of a trend-stationary process.
New algorithm for learning mixtures with mostly uniform weights, improving on previous bounds.
problem Learning mixtures of Gaussians with uniform weights and mostly uniform component weights.
method Statistical Query (SQ) lower bound and quasi-polynomial upper bound for testing.
result Quasi-polynomial upper bound for testing mixtures with mostly uniform weights.
Book covers tools for zeroth-order convex optimisation.
problem Zeroth-order convex optimisation.
method Cutting plane methods, interior point methods, continuous exponential weights, gradient descent, online Newton step.
result Improved existing bounds and algorithms.
Improved algorithm reduces excess risk in selective learning.
problem Selective learning with windowed model selection.
method Hybrid Exponential Weights Algorithm and bounded-recall ERM.
result Achieves expected excess risk of O((log log |L| + log log n) / log n).
Solves constant mean curvature Dirichlet problem on catenoids with improved estimates.
problem Solving constant mean curvature Dirichlet problem on catenoidal necks.
method Found solutions in exponentially weighted Hölder spaces with non-integer weight.
result Improved estimate to γ=1 by comparing solutions with their limits on the disk.
New stability theory for Sinkhorn semigroups with explicit decay rates.
problem Stability and convergence of Sinkhorn iterations for various divergences.
method Operator-theoretic framework based on Lyapunov techniques.
result Explicit exponential decay rates for Sinkhorn iterates.
Novel Bayesian method for high-dimensional count data prediction.
problem Count data in high-dimensional settings requires feature selection.
method Pseudo-Bayesian framework with scaled Student prior and exponential weights.
result Strong performance compared to Lasso in various settings.
We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X' \to X. The completion of this complex in exponentially weighted L^2-norms is Fredholm for all but finitely many exceptional weights determined by the eigenvalues of the covering translation map H_*(X') \to H_*(X…
New loss function restores importance weighting in overparameterized models.
problem Restoring importance weighting in overparameterized neural networks.
method Introduced polynomially-tailed losses to restore effects of importance weighting.
result Polynomially-tailed losses improve performance in correcting distribution shift.
New research explores using exponential activation functions in neural networks, achieving convergence with over-parameterization.
problem Achieving neural network convergence with over-parameterization using exponential activation functions.
method Defined a neural function using an exponential activation function, initialized weights with random Gaussian distributions, and used gradient descent to find optimal weights.
result Gradient descent can find a weight matrix such that the neural function's output is within ε of the labels with high probability.
Reweighting training data to better represent new tasks.
problem Deploying machine learning models to new tasks is challenging due to training data distribution.
method Formulate an exponential tilt distribution shift model and learn train data importance weights to minimize KL divergence.
result The learned train data weights improve target performance evaluation, fine-tuning, and model selection.
Paper develops a new weighted low-rank matrix approximation technique.
problem Matrix completion with missing data.
method Element-wise weighted generalization of low-rank matrix approximation.
result Proposes an algorithm and acceleration techniques for solving the weighted problem.
Article provides Bernstein gradient estimates for heat equations with potential terms.
problem Gradient estimates for heat equations with potential terms on weighted Riemannian manifolds.
method Derived Bernstein type gradient estimates for two systems of heat equations with linear, exponential, and combined potentials.
result Resolves part of the problem raised by Bhattacharyya et al. in \cite{SB-1}.
New method improves covariance estimation for weighted samples.
problem Improving covariance estimation for weighted sample data.
method Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
result Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the exponential weights algorithm and bound its regret in this setting. Under conditions on …
The study analyzes when Bayesian averaging over decision trees is reliable.
problem When do Bayesian model averaging weights over decision trees provide reliable information?
method Closed-form solution for Bayesian decision trees with Catalan-exponential priors.
result Established a complete non-asymptotic theory of rational commitment thresholds.