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.
A neural network predicts coarse-scale basis functions for efficient uncertainty quantification.
problem Efficiently estimating coarse-scale basis functions for multiscale methods.
method Data-driven approach using neural networks fitted to solution samples.
result Significant computational savings for uncertainty quantification tasks.
Delayed rejection HMC improves sampling efficiency for multiscale distributions.
problem Hamiltonian Monte Carlo struggles with wide-ranging distributions, especially in high-curvature areas.
method Introduces a delayed rejection variant of HMC, using geometrically smaller step sizes for retries.
result Up to five-fold performance gains in effective sample size per gradient evaluation.
We present a probabilistic model for natural images which is based on Gaussian scale mixtures and a simple multiscale representation. In contrast to the dominant approach to modeling whole images focusing on Markov random fields, we formulate our model in terms of a directed graphical model. We show that it is able to …
The paper extends first-order asymptotics for path-dependent derivatives in multiscale stochastic volatility.
problem Analyzing path-dependent derivatives in a multiscale stochastic volatility environment.
method First-order asymptotics analysis using Dupire's functional Ito calculus.
result Market parameters calibrated to vanilla options can price path-dependent derivatives to the same order.
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…
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.
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.
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.
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.
New algorithm reduces GP computation and improves accuracy for large datasets.
problem High computational cost and inaccuracy in GP regression for large datasets and sparse data.
method Hierarchical clustering to partition data into clusters, reducing training set and adapting local covariance.
result Improved prediction accuracy and reduced computational costs for non-uniform data distributions.
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.
Paper proposes a new adaptive multiscale value function approximation for reinforcement learning.
problem Value function approximation in reinforcement learning with varying complexity.
method Adaptive multiscale approximation using multiresolution analysis and tree approximation.
result Convergence rate of the multiscale approximation is independent of basis function regularity.
A new probabilistic model for image segmentation using region trees.
problem Image segmentation, especially multiscale and distributional.
method Probabilistic generative model based on region trees, exact inference via dynamic programming.
result Ability to sample segmentations at various scales and produce a distribution over all possible segmentations.
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…
This work sets lower bounds on the number of score queries needed for diffusion sampling.
problem Establishing information-theoretic limits on the number of score evaluations required for diffusion sampling.
method Proving lower bounds on the number of adaptive score queries needed for sampling.
result Any sampling algorithm requires at least \(\widetilde{\Omega}(\sqrt{d})\) adaptive score queries for \(d\)-dimensional distributions.
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…
New gradient methods solve multiscale optimization problems efficiently.
problem Minimizing functions with multiple non-interacting smooth, strongly convex components.
method Big-Step-Little-Step interleaving of standard methods.
result Complexity bound scales as product of square-roots of condition numbers of components, improving on accelerated gradient methods.
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.
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.
MPRI learns multiscale features for HSI classification.
problem Hyperspectral image classification with limited training samples.
method MPRI combines PRI and regularized LDA for iterative feature learning.
result MPRI outperforms state-of-the-art methods in HSI classification.
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
MsIGN tackles high-dimensional Bayesian inference using multiscale structure.
problem High-dimensional Bayesian inference challenges due to the curse of dimensionality.
method MsIGN generates samples from coarse to fine scale, minimizing Jeffreys divergence.
result MsIGN outperforms previous approaches in posterior approximation and mode capture.
Kernel analog forecasting studied for multiscale systems.
problem Interpreting data-driven predictions in multiscale dynamical systems.
method Kernel analog forecasting methods applied to multiscale systems with varying Markovian closures.
result Guidance provided for interpreting data-driven predictions in practice.
The paper extends entropy maximization to multiscale settings and applies it to neural networks.
problem Achieving optimal risk bounds in neural networks using multiscale entropy.
method Generalizing maximum entropy to multiscale settings and applying it to neural networks.
result The multiscale Gibbs posterior can achieve a smaller excess risk than the single-scale Gibbs posterior in a teacher-student scenario.
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.
The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.
problem Pricing path-dependent derivatives under multiscale stochastic volatility models.
method Derives a Malliavin representation for the first-order approximation of the price of path-dependent derivatives.
result An efficient Monte Carlo approximation for pricing path-dependent derivatives is derived.
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.
ASRNN adapts scales dynamically for better sequence modeling.
problem Fixed scales in multiscale RNNs don't match temporal patterns.
method Adaptively learns and adjusts scales based on temporal contexts.
result ASRNNs yield better performances with dynamical scaling.
Novel graph network learns hierarchical network structure.
problem Lack of information in hierarchical network topology.
method Hierarchical clustering for multiscale decomposition, graph convolutional layers.
result Competitive performance on citation network benchmark.
Reduced model helps estimate parameters from partially observed multiscale data.
problem Estimating parameters from high-dimensional partially observed multiscale data.
method Established convergence of filter from high-dimensional to reduced dimension model.
result Statistical estimation of parameters is possible in lower dimensions.
The study offers a multiscale model for SPX and VIX options pricing.
problem Capturing the multiscale volatility of financial markets.
method Derives approximate analytic pricing formulas under a multiscale stochastic volatility model.
result The model reduces errors on SPX and VIX option pricing by 9.9% and 13.2% respectively.
New algorithm clusters hyperspectral images at multiple scales.
problem Clustering hyperspectral images at various scales.
method M-SRDL algorithm using spectral-spatial diffusion distances.
result More accurate clustering labels achieved with spatial regularization.
Data-driven method solves multiscale elliptic PDEs with random coefficients.
problem Solving multiscale elliptic PDEs with random coefficients.
method Data-driven approach based on intrinsic dimension reduction.
result Efficient solution of multiscale elliptic PDEs with random coefficients.
iLED framework offers interpretable dynamics for multiscale systems.
problem Modeling high-dimensional multiscale systems is challenging.
method Interpretable Learning Effective Dynamics (iLED) framework based on Mori-Zwanzig and Koopman operator theory.
result Comparable accuracy to state-of-the-art approaches with added interpretability.
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.
Study shows increased precipitation variability in Paris area over years.
problem Evaluating the evolution of precipitation variability over time.
method Shape-based Dynamic Time Warping (IMS-DTW) for clustering rainfall time series.
result Precipitation variability increased in Paris area over years.
Improved VAE model for discrete data through augmented training and multiscale approach.
problem Limited capability of VAE in capturing field correlations in structured data.
method Augmented training with generated variants and multiscale VAE with multiple β values.
result Improved generation quality of VAE models through these methods.
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.
Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challen…
Study optimal futures trading strategies for assets with multiscale central tendency price model.
problem Optimal dynamic trading of futures with multiscale central tendency price model.
method Derive no-arbitrage futures prices, solve HJB equations for optimal strategies.
result Optimal trading strategies depend on asset parameters and futures risk premia.
MER algorithm speeds up VI solving with Markovian data.
problem Solving stochastic variational inequalities with Markovian data.
method MER algorithm using multi-scale sampling from a Markovian buffer.
result Achieves faster convergence without knowing Markov chain mixing time.
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.
Scattering transform improves note onset detection and instrument recognition in music transcription.
problem Note onset detection and instrument recognition in music transcription.
method Multiscale scattering operators applied to MIDI-driven datasets and real musical pieces.
result Scattering transform outperforms other sound representations for note onset detection and instrument recognition.
Deterministic GD can behave stochastically in large learning rates for multiscale functions.
problem Understanding deterministic GD's stochastic behavior in large learning rates for multiscale objectives.
method Established a sufficient condition for deterministic GD to converge to a rescaled Gibbs distribution in large learning rates for multiscale functions.
result Deterministic GD can converge to a statistical distribution in large learning rates for multiscale functions.
A new sampling method estimates scores without training or nested MCMC.
problem Efficient sampling from complex, unnormalised distributions.
method Multiscale averaging in SDEs for score estimation.
result Empirical results show competitive accuracy and efficiency.
Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach for these challenging problems. Deriving an algebraic representation allows us to…
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.