A new method detects long-range cross correlations in complex systems.
problem Detecting long-range cross correlations in complex systems.
method Joint multifractal analysis based on wavelet leaders (MF-X-WL).
result MF-X-WL detects cross correlations in synthetic and real-world data.
Bitcoin volatility shows multifractal structure, contradicting rough volatility models.
problem Applying rough volatility models to Bitcoin volatility data.
method Normalised p-variation framework, multifractal Detrended Fluctuation Analysis, log-log moment scaling, wavelet leaders.
result Bitcoin volatility exhibits multifractal structure, violating rough volatility model assumptions.
Wavelet analysis reveals limitations in detecting multifractality in signals with isolated singularities.
problem Detecting multifractality in signals with isolated singularities using detrended fluctuation analysis and wavelet leaders.
method Comparison of detrended fluctuation analysis and wavelet leaders on signals with isolated singularities.
result Signals with isolated singularities can artefactually give rise to broad multifractal spectra, leading to incorrect inference of multifractality.
Characterizes preferences for decision-making under uncertainty using a leader-follower game model.
problem Decision-making under uncertainty and ambiguity aversion.
method Characterizes niveloidal preferences through a leader-follower game model, satisfying specific axioms.
result The leader's strategy space can serve as an ambiguity aversion index.
A new algorithm reduces online eigenvector computation time while maintaining optimal performance.
problem Online learning of top eigenvectors in both adversarial and stochastic settings.
method Follow the Compressed Leader (FTCL) framework, compressing the matrix strategy to dimensions 3 (adversarial) and 1 (stochastic).
result Achieves optimal regret without sacrificing running time, resolving open questions.
We introduce CSE for MLSF games and devise online learning algorithms for achieving no-external Stackelberg-regret.
problem Learning equilibrium in leader-follower games with noisy bandit feedback.
method Proposed Correlated Stackelberg Equilibrium (CSE) and online learning algorithms balancing exploration and exploitation.
result Achieves no-external Stackelberg-regret, converging to approximate CSE.
Investors with asymmetric information play a game to optimize their portfolios.
problem Two investors with different information levels compete in portfolio selection.
method Modelled as a Stackelberg game with entropy-regularized mean-variance objectives.
result Equilibria exist where follower's strategy depends on leader's actions.
Proposes a neural network method to learn wavelet filters from data.
problem Learning structured wavelet filters from raw data.
method Formulates discrete wavelet transform as a neural network, trains with gradient descent.
result Trained model produces wavelets similar to traditional Fourier-derived ones.
Wavelets help compress neural networks efficiently.
problem Efficiently compressing linear layers in neural networks.
method Learnable wavelet transforms to compress RNNs.
result Wavelet compressed RNNs have fewer parameters and perform competitively.
Improved wavelet filters enhance neural network performance.
problem Enhancing wavelet transform for better neural network representations.
method Extending gradient-based filter learning to dual-tree wavelet transform.
result Directional filters improve dual-tree wavelet transform performance.
A new algorithm for deep learning training reduces communication costs and improves convergence.
problem Training deep learning models efficiently with limited communication.
method Leader Stochastic Gradient Descent (LSGD) combines local and global leaders' gradients to update workers.
result LSGD outperforms existing methods in distributed training of convolutional neural networks.
Paper introduces rational Gaussian wavelets for efficient signal approximation.
problem Efficiently approximating complex signals with few coefficients.
method Continuous wavelet transform using rational Gaussian wavelets with adjustable parameters.
result Proposed rational Gaussian wavelets provide accurate signal approximations.
MODWST improves classification tasks with wavelet scattering.
problem Signal classification challenges.
method Combines MODWT and WST for feature extraction.
result MODWST outperforms CNNs in limited data scenarios.
New RL algorithms learn QSE from strategic feedbacks with sample efficiency.
problem Learning QSE in Markov games with strategic feedbacks.
method Proposes sample-efficient algorithms for online and offline settings, combining quantal response model learning and RL.
result Achieves sublinear regret bounds and quantifies model uncertainty.
VDWs enhance graph neural networks for analyzing complex data.
problem Analyzing data on non-Euclidean geometries.
method Incorporating vector diffusion wavelets into geometric graph neural networks.
result VDW-GNNs effectively analyze synthetic and real-world data.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
Study leader-follower games with terminal state constraints using McKean-Vlasov SDEs.
problem Leader-follower games with terminal state constraints.
method Linear McKean-Vlasov forward-backward SDEs, existence and uniqueness results, convergence results.
result Existence and uniqueness of solutions for leader-follower games with constraints.
New method selects diffusion scales for graph wavelets.
problem Choosing optimal diffusion scales for graph wavelets.
method Proposes an unsupervised method using information theory.
result Method selects diffusion scales for graph wavelets.
New wavelets use Monte Carlo for efficient discretization.
problem Efficiently discretizing continuous wavelets on general domains.
method Defined continuous wavelets via spectral calculus and proposed a Monte Carlo discretization.
result Convergence of Monte Carlo wavelets under natural regularity assumptions.
Wavelet Kolmogorov-Arnold Networks improve federated learning performance.
problem Improving performance in federated learning with heterogeneous data.
method Implemented Wav-KAN with CWT and DWT for multiresolution capability, integrating wavelet-based activation functions.
result Significant improvements in computational efficiency, robustness, and accuracy in federated learning.
Wavelet boosts gradient boosting, improving accuracy, especially in imbalanced data.
problem Improving gradient boosting performance, especially in imbalanced data.
method Wavelet decomposition of trees in gradient boosting.
result Wavelet-based gradient boosting outperforms existing methods, especially in imbalanced data.
Wavelet Networks learn from raw time-series data, outperforming conventional CNNs.
problem Learning from raw time-series data efficiently and effectively.
method Constructing scale-translation equivariant neural networks based on wavelet symmetries.
result Wavelet Networks outperform conventional CNNs on raw waveforms and spectrograms.
Wavelet features improve image clustering and segmentation accuracy.
problem Noise and lack of spatial context in pixel intensity-based methods.
method Modified K-means, Fuzzy c-means, and ACWE algorithms incorporating Wavelet features.
result Wavelet-based algorithms converge to different segmentation results based on frequency information.
This paper proposes the use of wavelet methods to estimate U.S. core inflation. It explains wavelet methods and suggests they are ideally suited to this task. Comparisons are made with traditional CPI-based and regression-based measures for their performance in following trend inflation and predicting future inflation.…
Wavelets improve VAE image quality.
problem VAEs produce blurry images due to lack of high-frequency detail emphasis.
method Wavelet space VAE that emphasizes high-frequency components.
result Wavelet-based VAE generates higher quality images.
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
problem Graph classification with geometric properties encoded in persistence diagrams.
method Optimizes spectral wavelets for graph datasets to capture best-suited features for classification.
result Competitive performance in graph classification problems compared to other persistence-based architectures.
Revisits SWIFT method for option pricing using Shannon wavelets.
problem Improving option pricing under known characteristic functions.
method SWIFT method based on Shannon wavelets.
result Exposes drawbacks and discusses improvements.
Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
problem Improving texture synthesis quality using wavelet representations.
method Proposes a family of statistics based on non-linear wavelet representations with a generalized rectifier non-linearity.
result Significantly improves visual quality of texture synthesis compared to classical wavelet-based models.
Using a two-point correlation technique, we study emergence of market efficiency in the emergent Russian futures market by focusing on lagged correlations. The correlation strength of leader-follower effects in the lagged inter-market correlations on the hourly time frame is seen to be significant initially (2009-2011)…
Cake wavelets minimize orientation score uncertainty.
problem Minimizing uncertainty in orientation scores.
method Axiomatically derived wavelets for orientation score lifting.
result Uncertainty gap of cake wavelets is less than 1.1.
Wavelets improve accuracy in solving backward SDEs.
problem Solving backward stochastic differential equations (SDEs) with high accuracy and simplicity.
method Time discretization combined with trigonometric wavelets, enhanced by antireflective boundary technique.
result Improved numerical algorithm for SDEs with enhanced accuracy and ease of implementation.
Wavelet SGM accelerates generative modeling with linear time complexity.
problem High computational cost in SGMs.
method Factorizing data distribution into wavelet coefficients.
result WSGM synthesizes wavelet coefficients with linear time complexity.
MLShrink integrates machine learning with wavelet shrinkage for denoising.
problem Denoising signals with uncertain magnitudes
method Combines wavelet shrinkage with machine learning
result Preserves simplicity for signal coefficients while allowing data-adaptive decisions for ambiguous coefficients
Study of 2imes2 zero-sum games with noisy observations and commitments.
problem Analyzing 2imes2 zero-sum games with noisy observations and commitments. method Modeling a 2imes2 zero-sum game with a leader committing to a strategy and a follower observing a noisy version of the leader's action. result Observing the leader's action is either beneficial or immaterial for the follower, and the equilibrium payoff is bounded.
Wavelet-based CFC improves EEG seizure classification.
problem Improving accuracy in distinguishing ictal seizures from normal brain activity.
method Wavelet-based cross frequency coupling (CFC) for feature extraction, followed by t-test and QDA for classification.
result Wavelet-based CFC enhances classification accuracy of epileptic EEG signals.
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
Transformers cluster meaningless words around leaders for sentiment analysis.
problem Capturing context in sentiment analysis using transformers.
method Characterized transformers with hardmax self-attention and normalization, showing asymptotic convergence to clustered equilibrium.
result Transformers can effectively capture context by clustering meaningless words around leader words.
Unified method for simultaneous denoising and clustering.
problem Clustering noisy signals.
method Sparse convex wavelet clustering with fusion and group-sparse penalties.
result Unified approach that denoises and clusters simultaneously.
AWD distills neural network info into interpretable wavelets.
problem Imbalanced interpretability and efficiency in deep learning models.
method Adaptive wavelet distillation (AWD) penalizes neural network attributions in wavelet domain.
result AWD yields a concise, efficient, and interpretable model.
Wavelet-based method for sparse data on manifolds.
problem Sparse representation of manifold-valued data.
method Interpolatory wavelet/multiscale transform for sparse regularization.
result Well-posedness of variational models and successful numerical algorithms.
A new WNN framework selects wavelet bases for efficient learning.
problem Challenges in constructing accurate wavelet bases and high computational costs in WNN.
method Introduces a constructive WNN that selects initial bases and trains functions by introducing new bases for predefined accuracy while reducing computational costs.
result Significantly improves computational efficiency through a frequency estimator and wavelet-basis increase mechanism.
Neural operators approximate Stackelberg game solutions.
problem Intractability of follower's best-response operator in dynamic Stackelberg games.
method Used attention-based neural operators to approximate the best-response operator.
result Approximate best-response operator yields close game value.
WaveletGAN improves GANs by homogenizing noise through multi-channel wavelet filtering.
problem Current noise generation models in GANs struggle with homogenizing noise, leading to low-fidelity samples.
method Proposes a multi-channel wavelet-based filtering method to homogenize noise in GANs.
result WaveletGAN generates high-fidelity samples with the smallest FIDs on Fashion-MNIST, KMNIST, and SVHN datasets.
Paper defends iris recognition from adversarial examples using wavelet decomposition.
problem Adversarial examples threaten deep neural networks in biometric applications.
method Wavelet domain denoising of input examples to detect and mitigate adversarial attacks.
result Proposed defense strategies improve recognition accuracy against adversarial attacks.
Wav-KAN improves neural network interpretability and performance.
problem Challenges in interpretability, training speed, robustness, and performance of traditional neural networks.
method Integrates wavelet functions into the Kolmogorov-Arnold network structure for efficient data representation.
result Enhanced accuracy, faster training speeds, and increased robustness compared to existing methods.
3D scattering model predicts lithium-silicon formation energies.
problem Predicting formation energies of amorphous Li-Si materials.
method Steerable wavelet scattering for 3D signals, invariant to translations and rotations.
result State-of-the-art results compared to other machine learning methods.
Game theory approach to predicting and responding to interventions based on causal relationships.
problem Optimizing predictions and interventions in response to observational data.
method Prediction-intervention game framework, focusing on invariant subsets of covariates.
result Stable-blanket predictors are optimal for certain follower objectives and under specific conditions.
Study compares WTT and DWT for FTIR data feature extraction of medicinal plants.
problem Improving machine learning efficiency with FTIR spectra of medicinal plants.
method Comparison of WTT and DWT for feature extraction, varying preprocessing steps.
result WTT and DWT yield similar results, improving clustering and classification accuracy.