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…
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48 results for “Multiscale Representation”
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.
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 …
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.
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…
We introduce a multiscale supervised dimension reduction method for SPatial Interaction Network (SPIN) data, which consist of a collection of spatially coordinated interactions. This type of predictor arises when the sampling unit of data is composed of a collection of primitive variables, each of them being essentiall…
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.
Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales, which do not comply with the nature of dynamical temporal patterns among sequences…
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…
Generative Distribution Embeddings learn multiscale representations of distributions.
problem Learning representations of entire distributions for multiscale reasoning.
method Introducing GDE framework that lifts autoencoders to the space of distributions, using conditional generative models and distributional invariance.
result GDEs learn predictive sufficient statistics embedded in Wasserstein space, recovering distances and trajectories for Gaussian and Gaussian mixture distributions.
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…
Model-data-driven constitutive responses: application to a multiscale computational frameworkstat.ML
A hybrid method combines model-based and data-driven approaches for multiscale constitutive responses.
problem High computational costs and inaccuracies in nonlinear multiscale methods.
method Hybrid methodology combining model-based constitutive laws, data-driven corrections, and computational multiscale approaches.
result Model-data-driven approach improves macroscale simulations with similar accuracy and computational cost.
SAMI learns disentangled representations from data.
problem Learning disentangled representations from data.
method Combines diffusion models and VAEs to learn disentangled representations.
result SAMI learns disentangled representations that are interpretable and useful.
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 …
Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST-equivariant) CNN with joint convolutions across th…
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.
GINNs: Graph-Informed Neural Networks for Multiscale Physicsphysics.comp-ph
GINNs combine deep learning with PGMs for physics-based multiscale systems.
problem Intrinsic computational bottlenecks and lack of sufficient data for QoI estimation.
method Hybrid approach combining deep learning with probabilistic graphical models, informed by structured priors for CVs.
result GINNs produce tight confidence intervals for non-Gaussian QoIs.
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.
Classic contextual bandit algorithms for linear models, such as LinUCB, assume that the reward distribution for an arm is modeled by a stationary linear regression. When the linear regression model is non-stationary over time, the regret of LinUCB can scale linearly with time. In this paper, we propose a novel multisca…
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.
Bayesian multiscale deep generative model for the solution of high-dimensional inverse problemsstat.ML
Bayesian model tackles high-dimensional inverse problems efficiently.
problem Estimating spatially-varying parameters in expensive models.
method Multiscale Bayesian inference with deep generative models and MCMC.
result Efficient estimation of global and local parameter features.
The paper examines how kernel approximations affect Gaussian process regression in large data applications.
problem Effect of kernel approximations on Gaussian process regression in large data applications.
method Unified framework to analyze Gaussian process regression under computational and epistemic misspecification.
result Theoretical analysis of Gaussian process regression under various misspecifications.
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.
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 present a graph-theoretical approach to data clustering, which combines the creation of a graph from the data with Markov Stability, a multiscale community detection framework. We show how the multiscale capabilities of the method allow the estimation of the number of clusters, as well as alleviating the sensitivity…
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.
Unsupervised learning of multiscale switching dynamical system models from multimodal neural datacs.LG
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.
Graph cross network improves graph classification accuracy.
problem Improving graph classification accuracy.
method Graph cross network (GXN) with vertex infomax pooling (VIPool) and feature-crossing layer.
result Improves graph classification accuracy by 2.12% and 1.15%.
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.
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.
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.
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…
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.
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.
On Convergence Rate of Adaptive Multiscale Value Function Approximation For Reinforcement Learningcs.LG
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…
Optimal Dynamic Futures Portfolios Under a Multiscale Central Tendency Ornstein-Uhlenbeck Modelq-fin.MF
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.
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.
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional feature space. To address these challenges, a new multiscale, sparsified GP algorithm…
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.
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.
We study the multiscale simplicial flat norm (MSFN) problem, which computes flat norm at various scales of sets defined as oriented subcomplexes of finite simplicial complexes in arbitrary dimensions. We show that the multiscale simplicial flat norm is NP-complete when homology is defined over integers. We cast the mul…
Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media,…