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.
We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP…
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 uncovers hierarchical block structure in large matrices.
problem Uncovering hierarchical block structure in symmetric matrices.
method Incremental multiresolution matrix factorization.
result Algorithm scales well to large matrices and uncovers structure one feature at a time.
Extends MMF to nonsymmetric matrices for hierarchical structure.
problem Capturing hierarchical structure in nonsymmetric matrices.
method Multiresolution Matrix Factorization (MMF) extended to nonsymmetric matrices.
result Effective for matrix compression tasks, outperforming low-rank methods.
MRTL learns interpretable spatial patterns efficiently.
problem Efficient and interpretable spatial analysis in various fields.
method Multiresolution Tensor Learning (MRTL) algorithm.
result 4~5x speedup with accurate and interpretable latent factors.
In this letter we exhibit the relation between the isometries of a Riemannian contraction of a sub-Riemannian manifold and those of the sub-Riemannian metric, for to use this relation with two goals: establishing a result about the existence of fixed points of isometries groups; and the other, defining a Multiresolutio…
MathNet uses wavelets for graph representation and learning.
problem Graph Neural Networks (GNNs) for graph classification and regression.
method Multiresolution Haar-like wavelets, graph convolution, and pooling.
result MathNet achieves notable accuracy gains on graph classification and regression tasks.
New model captures long-range patterns in sequences efficiently.
problem Efficiently capturing long-range patterns in sequential data.
method Inspired by wavelet multiresolution analysis, introduces MultiresLayer with multiresolution convolution.
result State-of-the-art performance on sequence classification and autoregressive density estimation tasks.
This paper approximates scattered data using samplet coordinates with sparsity constraints.
problem Scattered data approximation with sparsity constraints.
method Samplet basis pursuit with ℓ1-regularization, multiresolution techniques, and semi-smooth Newton method. result The proposed method provides faster convergence and better signal sparsity compared to existing methods.
We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/multiresolution method for PDEs with rough (L∞) coefficients with rigorous a-priori accuracy and performance estimates. The method is discovered through a decision/game theory formulation of the problems of (1) identifying restri…
Cisco introduces a new time series model for better forecasting.
problem Improving time series forecasting accuracy.
method Developed a new multiresolution decoder-only model trained on large datasets.
result The new model achieves superior performance on observability datasets.
NAOMI improves imputation accuracy for long-range sequences.
problem Missing value imputation in spatiotemporal data.
method Non-autoregressive deep generative model exploiting multiresolution structure.
result Significant improvement in imputation accuracy (60% reduction in average prediction error).
AV-ASR system improves speech recognition with visual context.
problem Improving speech recognition accuracy with visual information.
method Transformer-based architecture with multiresolution and multimodal training.
result Multiresolution training speeds up convergence and improves WER by 18%.
MKA improves Gaussian process regression for large datasets.
problem Gaussian process regression struggles with large datasets.
method MKA is a memory-efficient, direct kernel approximation method.
result MKA achieves better performance with small kernel length scales.
Adaptive GMRA approximates high-dimensional data with low-dimensional geometric structures.
problem Efficiently approximating high-dimensional data from a nearly low-dimensional manifold.
method Adaptive GMRA with thresholding of geometric wavelet coefficients.
result Adaptive GMRA approximations perform well on various measures with different regularity.
Automated robust solvers for arbitrary operators using game theory and Gaussian fields.
problem Developing scalable numerical solvers for any bounded linear operator.
method Formulating the problem as a game theory problem and using Gaussian fields to find optimal strategies.
result Introducing the Fast Gamblet Transform (FGT) for efficient linear system solving and eigenspace analysis.
Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for spa…
The study develops methods to summarize team passing strategies from soccer data.
problem Modeling spatial passing networks across multiple games with varying positions.
method Multiresolution tensor decomposition and Poisson nonnegative block term decomposition.
result Automatic production of network motifs at different levels of detail.
New model improves GP approximations by relaxing independence across resolutions.
problem Overfitting and non-smooth predictions in multiresolution GPs.
method Conditional independence among GPs across resolutions.
result Improved robustness against overfitting and smoother predictions.
Optimizes over flag manifolds for numerical PDE and statistics.
problem Optimizing over flag manifolds for numerical PDE and statistics.
method Develops tools for Riemannian optimization on flag manifolds, deriving analytic expressions and parameterizations.
result Closed-form analytic expressions and parameterizations for various geometric objects on flag manifolds.
We introduce the multiresolution recurrent neural network, which extends the sequence-to-sequence framework to model natural language generation as two parallel discrete stochastic processes: a sequence of high-level coarse tokens, and a sequence of natural language tokens. There are many ways to estimate or learn the …
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.
New method avoids surface self-collision in geometric optimization.
problem Avoiding self-collision in surface optimization.
method Developed a numerical framework using tangent-point energy and fractional Sobolev inner product.
result Successfully accelerated collision avoidance scheme for triangle meshes.
A new autoencoder architecture captures multiscale data.
problem Multiscale spatio-temporal data representation.
method Integrates multigrid methods, convolutional autoencoders, and transfer learning.
result Adaptive, hierarchical architecture captures different scaled features dynamically.
The study explores various localized bases and their duals for scattered data approximation.
problem Scattered data approximation using radial basis functions.
method Examines different localized bases including Lagrange, Newton, and multiresolution versions, and their duals.
result Localized orthogonal bases, such as the Newton basis, offer symmetric preconditioners and are feasible for scattered data approximation.
In this work we consider the problem of detecting anomalous spatio-temporal behavior in videos. Our approach is to learn the normative multiframe pixel joint distribution and detect deviations from it using a likelihood based approach. Due to the extreme lack of available training samples relative to the dimension of t…
Transformer models outperform recurrent ones in modeling hierarchical data.
problem Modeling hierarchical structure in data.
method Introducing Multiresolution Transformer Networks leveraging self-attention.
result Multiresolution Transformer Networks significantly outperform state-of-the-art models on query suggestion datasets.
CGNNs use wavelets for continuous function generation in infinite-dimensional spaces.
problem Generating continuous functions in infinite-dimensional spaces for applications like inverse problems.
method Inspired by DCGAN, CGNNs use wavelet multiresolution analysis with convolutional and nonlinear layers.
result CGNNs can be injective under certain conditions on filters and nonlinearity, leading to Lipschitz stability estimates.
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…
A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson sequence and Normal sequence. A neighborhood variability measure is defined to …
In this paper we construct a learning architecture for high dimensional time series sampled by sensor arrangements. Using a redundant wavelet decomposition on a graph constructed over the sensor locations, our algorithm is able to construct discriminative features that exploit the mutual information between the sensors…
We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second the idea that one should be able to compare the results of clustering algorithm…
We present a new method for articulating scale-dependent topological descriptions of the network structure inherent in many complex systems. The technique is based on "Partition Decoupled Null Models,'' a new class of null models that incorporate the interaction of clustered partitions into a random model and generaliz…
Implicit schemes are popular methods for the integration of time dependent PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve corresponding linear systems at each time step constitutes a complexity bottleneck in their application to PDEs with rough coefficients. We present a generalization of ga…
Combines topological and geometric approaches to data analysis.
problem Understanding when and how geometric objects intersect.
method Connects topological and geometric concepts of curvature.
result Reconceptualizes curvature and links it to hyperconvexity.
This paper presents the Speech Technology Center (STC) systems submitted to Automatic Speaker Verification Spoofing and Countermeasures (ASVspoof) Challenge 2015. In this work we investigate different acoustic feature spaces to determine reliable and robust countermeasures against spoofing attacks. In addition to the c…
Finite element method for SABR model pricing under various interest rates.
problem Pricing vanilla and barrier options under the SABR stochastic volatility model.
method Finite element discretization of non-symmetric Dirichlet forms for degenerate parabolic equations.
result Well-posedness of the variational formulation and error analysis for finite element discretization.
The paper explains how microlocal analysis solves geometric inverse problems.
problem Recovering geometric information from boundary measurements.
method Microlocal analysis applied to three inverse problems.
result Microlocal techniques solve specific inverse problems in Riemannian geometry.
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kd-trees (Moore, 1999). In thi…
Survey on Finsler manifolds with weighted Ricci curvature, focusing on geometric analysis.
problem Analysis of Finsler manifolds with weighted Ricci curvature.
method Nonlinear geometric analysis based on the Bochner inequality.
result Gradient estimates, functional inequalities, and isoperimetric inequalities.
Three geometric analysis results on curve flows and Lie groups.
problem Analyzing geometric flows and Lie groups.
method Curve-shortening flow, point-wise curvature preserving flow, Lie group analysis.
result Interpolation between Sol and hyperbolic space in Lie groups.
Workshop on shape analysis discusses new research directions.
problem No specific problem stated; focus on new directions in shape analysis.
method Discussion and collaboration among researchers.
result Promising new directions in shape analysis were discussed.
This is a guided tour through some selected topics in geometric analysis. We have chosen to illustrate many of the basic ideas as they apply to the theory of minimal surfaces. This is, in part, because minimal surfaces is, if not the oldest, then certainly one of the oldest areas of geometric analysis dating back to Eu…
Survey on manifold ends with new heat kernel estimates.
problem Analyzing geometric properties on manifolds with ends.
method Constructing manifolds with ends and analyzing their heat kernel estimates.
result Found manifolds with ends that have different heat kernel estimates.
Survey of de Casteljau's algorithm's applications in geometric data analysis.
problem No specific problem stated; focuses on algorithm applications.
method Constructive approach to generalize parametric smooth curves to manifolds.
result Algorithm provides principled way to analyze geometric data.
This paper reviews discrete curvature models for geometric data analysis.
problem Capturing intrinsic geometric structure in diverse data representations.
method Comprehensive review of discrete curvature models from Riemannian and metric geometry perspectives.
result Systematic pipeline for curvature-driven data analysis and learning.
Geometric analysis improves convergence of variational inference.
problem Challenges in analyzing convergence of variational inference due to non-convexity and non-smoothness.
method Exploits exponential family structure and Bregman divergences to geometrically analyze the optimization landscape.
result Establishes non-asymptotic convergence rates for gradient descent algorithms.