SRMD uses random features for efficient time-frequency analysis.
problem Efficiently analyzing time-series data with low computational cost.
method Sparse Random Mode Decomposition (SRMD) constructs a sparse approximation to the spectrogram.
result SRMD outperforms other methods in signal representation, outlier removal, and mode decomposition.
New MHSNs extract multiscale features from complex data for robust classification.
problem Signal classification and domain classification on complex data.
method Layered structure with multiscale basis dictionaries, pooling operations, and invariant features.
result High-accuracy classification with fewer parameters than traditional graph neural networks.
Combining neural networks and multiscale decomposition for financial market analysis.
problem Financial markets' complexity and mainstream models' limitations in capturing non-linear structures.
method Neural networks for non-linear associations combined with multiscale decomposition.
result Improved understanding of financial market data substructures.
New algorithm learns switching dynamics from multiple neural signals.
problem Learning accurate switching dynamical system models from multimodal neural data.
method Unsupervised learning algorithm for multiscale switching dynamical system models.
result Switching multiscale dynamical system models outperform single-scale models in behavior decoding.
New methods detect continuous variation in single-cell data.
problem Continuous variation within and between cell types not detected by discrete analyses.
method Three topologically motivated mathematical methods for unsupervised feature selection.
result Detect additional biologically meaningful genes with coherent expression patterns.
Event detection has been one of the most important research topics in social media analysis. Most of the traditional approaches detect events based on fixed temporal and spatial resolutions, while in reality events of different scales usually occur simultaneously, namely, they span different intervals in time and space…
New approach combines PCA and t-sne for better data analysis.
problem Multiscale complexity in high-dimensional data.
method Multiscale joint characterization using PCA and t-sne.
result Joint characterization detects signals not seen by PCA or t-sne alone.
New method analyzes knots and links using multiscale Gauss link integral.
problem Lack of localization and quantization in knot theory applications.
method Integrates curve segmentation and multiscale analysis into the Gauss link integral.
result Significantly outperforms other methods in protein flexibility analysis.
Proposes a new algorithm for non-stationary bandits.
problem Non-stationary reward distributions in contextual bandits.
method Multiscale changepoint detection for adaptive learning.
result Regret bound analysis and superior performance in experiments.
The Weyl transform is introduced as a rich framework for data representation. Transform coefficients are connected to the Walsh-Hadamard transform of multiscale autocorrelations, and different forms of dyadic periodicity in a signal are shown to appear as different features in its Weyl coefficients. The Weyl transform …
MELD model clusters data at multiple scales, improving understanding of latent structure.
problem Understanding latent multiscale structure in datasets.
method Multiscale Learning by Unsupervised Nonlinear Diffusion (M-LUND) algorithm.
result M-LUND detects latent structure in synthetic and real datasets.
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable function…
Paper proposes multiscale self-attentive convolutions for vision and language.
problem Improving language and vision understanding models using self-attention.
method Developed 1D and 2D Self Attentive Convolutions (SAC), multiscale SAC (MSAC).
result MSAC enhances model performance for vision and language tasks.
Study compares Bitcoin, gold, and gas price complexity using multifractal and multiscale entropy methods.
problem Quantifying complexity of financial time series for market analysis.
method Employed MF-DFA and RCMSE to analyze Bitcoin, GBP/USD, gold, and natural gas price log-return time series.
result Bitcoin shows higher complexity compared to other markets, linked to higher nonlinear correlations.
The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional represen…
We perform a scaling analysis on NYSE daily returns. We show that volatility correlations are power-laws on a time range from one day to one year and, more important, that they exhibit a multiscale behaviour.
Optimal multiscale learning of linear operators
problem Statistical and computational limits of learning bounded linear operators between Sobolev spaces
method Reformulate as an infinite-dimensional matrix regression problem with heterogeneous multiscale structure
result Establish minimax rates and construct a finite-resolution blockwise least-squares estimator attaining these rates
Local minimax analysis for Poisson deconvolution of discrete signals.
problem Estimating a discrete uniform signal from Poisson convolutions.
method Local minimax risk analysis of a broad class of kernels.
result Sharp estimation rates as a function of signal clustering.
Extracts causal brain dynamics across multiple scales.
problem Statistical associations do not reflect causal mechanisms in brain dynamics.
method Multiscale causal backbone (MCB) extraction using advanced causal structure learning.
result Sparse MCBs reveal distinct causal roles at different brain frequency bands.
MS-CASTLE learns causal structures across multiple time scales.
problem Inferring causal relationships between time series data at different scales.
method Uses stationary wavelet transform and non-convex optimization to estimate causal structures.
result MS-CASTLE reveals meaningful causal interactions, especially at mid-term time resolutions.
UniPhyNet improves cognitive load classification accuracy using EEG, ECG, and EDA signals.
problem Classifying cognitive load using multimodal physiological data.
method Unified network architecture integrating multiscale parallel convolutional blocks, ResNet-type blocks, and channel block attention module. Uses bidirectional gated recurrent unit for temporal dependencies.
result Improves raw signal classification accuracy from 70% to 80% (binary) and 62% to 74% (ternary) on CL-Drive dataset.
Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.
problem Graphical models in high-dimensional data analysis need to handle clustering and sparsity simultaneously.
method MGLasso combines clustering and graph inference through a convex relaxation of k-means and hierarchical clustering. It uses CONESTA for regularization.
result MGLasso improves network interpretability by estimating graphs at multiple scales.
This paper explores how different audio signal representations affect topological signatures and their predictive power.
problem The impact of different signal representations on topological signatures and their predictive power.
method The study compares three different signal representations (embedding, spectrogram, and spectrogram zeroes) and evaluates their topological signatures for speaker gender, vowel type, and individual prediction.
result Topological signatures from spectrogram zeroes offer the best improvement for gender prediction, and different representations are complementary.
The paper proposes a method to estimate latent structures in multivariate data without assuming their existence.
problem Estimating latent structures in multivariate distributions that are difficult to identify and reflect the data generating mechanism.
method A model-free approach using a multiscale nonparametric maximum likelihood estimator.
result The method captures meaningful discrete structure at different scales and integrates them to yield an interpretable discrete representation.
New knot models analyze local entanglement for robust curve analysis.
problem Lack of local structural information in classical knot theory.
method Proposed multiscale and persistent Jones polynomials.
result Models are stable to small perturbations, robust for real-world applications.
Framework models multiscale dynamics with Bayesian learning for regime changes.
problem Analyzing complex interactions between fast and slow processes.
method Hierarchical state-space modeling with Sequential Monte Carlo.
result Bayesian approach accurately tracks state transitions and identifies switching dynamics.
The art of systematic financial trading evolved with an array of approaches, ranging from simple strategies to complex algorithms all relying, primary, on aspects of time-series analysis. Recently, after visiting the trading floor of a leading financial institution, we noticed that traders always execute their trade or…
This paper proposes a novel architecture, termed multiscale principle of relevant information (MPRI), to learn discriminative spectral-spatial features for hyperspectral image (HSI) classification. MPRI inherits the merits of the principle of relevant information (PRI) to effectively extract multiscale information embe…
The paper analyzes the dynamics of tokens in transformer models at moderate interaction levels.
problem Understanding the evolution of tokens in transformer models at moderate interaction levels.
method Modeling transformer models as a system of particles interacting in a mean-field way and studying the corresponding dynamics.
result Characterization and convergence of the limiting dynamics in different phases of the system.
The paper proves Gorenstein contractions for multiscale differentials on nodal curves.
problem Proving Gorenstein contractions for multiscale differentials on nodal curves.
method Addressing the conjecture by Ranganathan and Wise, showing contractions level by level.
result Multiscale differentials can be contracted to Gorenstein singularities, level by level, from the top down.
Develops DSD for analyzing multiscale biological networks.
problem Analyzing multiscale structure in biological networks.
method Data-driven diffusion process with multitemporal analysis.
result Parameter-free inference of intrinsic data structure.
Bayesian model learns multiscale interactions in complex systems.
problem Understanding dynamic interplay between processes at different time scales.
method Bayesian learning framework with Particle Gibbs with Ancestor Sampling (PGAS) algorithm.
result Demonstrated the effectiveness of the proposed approach through simulations.
Graph clustering uses multiscale community detection for improved performance.
problem Improving data clustering accuracy and robustness.
method Graph-theoretical approach combining multiscale community detection.
result Multiscale graph-based clustering achieves better performance than traditional methods.
We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic low dimension structure of the underlying elliptic differential operators. Our method consists of offline and online stages. At the offline stage, a low dimension space and its basis are extracted from th…
DMGNN predicts 3D human motions using adaptive multiscale graphs.
problem Predicting 3D skeleton-based human motions accurately.
method Dynamic multiscale graph neural networks (DMGNN) with adaptive multiscale graphs and MGCU.
result DMGNN outperforms state-of-the-art methods in short and long-term predictions.
Estimates functions on unknown manifolds using multiscale regression.
problem Regression on unknown low-dimensional manifolds embedded in high-dimensional spaces.
method Low-dimensional coordinates at multiple scales, local polynomial fitting, data-driven wavelet thresholding.
result Optimal learning rates for estimating functions with nonuniform regularity.
This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dy…
Neural network approach simplifies multiscale problem homogenization.
problem Homogenizing multiscale problems with varying microscale structures.
method Derivative-free neural network with Brownian walkers.
result Neural network method is computationally efficient and robust.
Very few K-nearest-neighbor (KNN) ensembles exist, despite the efficacy of this approach in regression, classification, and outlier detection. Those that do exist focus on bagging features, rather than varying k or bagging observations; it is unknown whether varying k or bagging observations can improve prediction. Giv…
Entropy-based model for hierarchical learning from multiscale data.
problem Learning from data with auxiliary information and multiscale target functions.
method Entropy-based hierarchical learning model with multiscale entropies.
result Entropy-based model yields stronger guarantees than uniform convergence bounds.
Structural equation models and Bayesian networks have been widely used to study causal relationships between continuous variables. Recently, a non-Gaussian method called LiNGAM was proposed to discover such causal models and has been extended in various directions. An important problem with LiNGAM is that the results a…
Deep neural network approximates flow averages for rough walls in multiscale simulations.
problem Approximating flow averages in rough-wall Stokes flow simulations.
method Fourier neural operator for local averages, parameterized by local wall geometry.
result Stable and accurate HMM solution with reduced micro problem solving cost.
When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold) of lower dimension than the ambient space. This question can be phrased as a (mu…
The paper corrects biases in estimating intrinsic dimension and differential entropy.
problem Systematic bias in estimating intrinsic dimension and differential entropy.
method A bias-corrected estimator for both measures is proposed, highlighting shared steps and useful consequences.
result Simultaneous estimation of differential entropy and intrinsic dimension provides complementary perspectives on underlying manifolds.
This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process, in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented frequency-by-frequency and the concept of the multiscale ratio is introduced to quantify t…
We discuss multiscale representations of discrete manifold-valued data. As it turns out that we cannot expect general manifold-analogues of biorthogonal wavelets to possess perfect reconstruction, we focus our attention on those constructions which are based on upscaling operators which are either interpolating or midp…
The paper (in French) exemplifies graphically a solution of the heat equation which is a 1-dimensional unfolding of an elliptic umbilic catastrophe. The example is due to James Damon and adapts Thom-Mather's singularity theory to multiscale models of scale-space analysis in image processing.
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry…