Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Data
problem Improving prediction intervals for non-exchangeable time-indexed datasets
method Spectral adaptive conformal prediction
result Improves on fixed spectral weighting while monitoring uncertainty changes
Proposes a Gaussian process for graph signals using adaptive spectral kernels.
problem Predicting signals on graph nodes with various structures.
method Spectral kernel learning approach that incorporates a polynomial function in the graph spectral domain.
result The model accurately recovers ground truth spectral filters and outperforms in real-world graph data.
Study cryptocurrency price dynamics using adaptive EMD and spectral analysis.
problem Analyze the time-varying volatility of cryptocurrency prices.
method Adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis.
result Reveal the properties of various timescales in cryptocurrency price dynamics.
ARFF reduces spectral bias in SGD-trained neural networks.
problem Spectral bias in two-layer neural networks.
method Comparison of SGD and ARFF on spectral bias and robustness.
result ARFF yields a closer to zero spectral bias compared to SGD.
New bounds adaptively control spectral complexity of trained Transformers.
problem Understanding why Transformers generalize well in machine learning.
method Spectrum-adaptive post hoc generalization bounds for multi-layer Transformers.
result Bounds adaptively trade off spectral complexity against dimension and depth factors.
Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the objective. For this purpose it is important to have an adjusted, adapted and eff…
Adaptive spectral RL method enhances RL performance and interpretability.
problem Balancing interpretability and performance in reinforcement learning.
method Spectral based linear RL approach with adaptive regularization.
result Near-optimal bounds for parameter estimation and generalization error.
SASE improves attributed graph clustering for large graphs with linear time and space complexity.
problem Challenges in clustering large attributed graphs due to high computational and memory costs.
method SASE combines node features smoothing, scalable spectral clustering, and adaptive order selection.
result SASE achieves a 6.9% improvement in ACC and a 5.87x speedup on the ArXiv dataset.
New spectral clustering method for multi-layer networks improves accuracy.
problem Detecting community structure in multi-layer networks.
method Integrative spectral clustering based on adaptive layer aggregation.
result Our methods minimize mis-clustering error and outperform existing methods.
Improves regression models' performance on covariate shift.
problem Out-of-distribution generalization for regression.
method Spectrally adapting the weights of a pre-trained neural regression model.
result Spectral adaptation improves out-of-distribution performance.
Improved spectral gap for MwG with adaptive RWM proposals.
problem Improving mixing efficiency of MwG for log-concave distributions.
method Using adaptive RWM proposals tuned to match conditional variances of log-concave target distributions.
result Established a spectral gap lower bound of order O(1/κd) for MwG. New Hermite approximations accelerate convergence with adaptive coordinate transformations.
problem Accelerating convergence of spectral approximations for Hermite expansions.
method Using normalizing flows for adaptive coordinate transformations and deriving error estimates.
result Error estimates for Hermite expansions under adaptive coordinate transformations.
Paper develops Riemannian geometry for SPSD matrices with DA applications.
problem Riemannian geometry of SPSD matrices for DA.
method Closed-form expressions, approximations of geodesic path, PT, canonical representation.
result Proposes an algorithm for DA with improved performance.
Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
problem Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
method Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
result Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
Spectral clustering adapted for mixed data types without preprocessing.
problem Clustering mixed data types (numerical and categorical).
method Adding extra nodes for categories, leading to a linear-time algorithm.
result Linear-time spectral clustering for categorical-only data.
SpecGrad improves neural vocoder sound quality by adapting diffusion noise to log-mel spectrogram.
problem Improving neural vocoder sound quality, especially in high-frequency bands.
method Adapting the diffusion noise distribution to the conditioning log-mel spectrogram through time-varying filtering.
result SpecGrad generates higher-fidelity speech waveform than conventional DDPM-based neural vocoders.
A novel unsupervised domain adaptation method using hierarchical optimal transport.
problem Unsupervised domain adaptation between source and target domains.
method Hierarchical optimal transport, leveraging class labels for structure formation in the source domain and learning probability measures in the target domain.
result The proposed HOT-DA method outperforms state-of-the-art approaches on various datasets.
The paper validates Stokes' theorem for differential subcomplexes in positively graded Lie groups.
problem Validating Stokes' theorem for differential subcomplexes in positively graded Lie groups.
method Introducing geometric conditions and spectral complexes to recover Stokes' theorem on locally smooth intrinsic graphs.
result Stokes' theorem holds for Rumin complex and new spectral complexes on Carnot groups.
BankGCN improves graph convolution networks by handling multi-channel signals with adaptive filter banks.
problem Handling multi-channel graph signals with limited architectures.
method BankGCN decomposes multi-channel signals into subspaces and uses adapted filters for each subspace.
result BankGCN achieves excellent performance in graph classification on benchmark datasets.
A new method for creating simpler models from complex ones.
problem Creating accurate approximations of complex models at reduced costs.
method Sequential adaptive surrogate modeling based on locally spectral expansions.
result Stochastic spectral embedding (SSE) shows good approximation capabilities and scalability.
Graph Laplacians adapt to different manifold dimensions, while Dirichlet energies converge to a tensorized Dirichlet energy.
problem Understanding machine learning methods for data with varying intrinsic dimensions.
method Γ-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on intersecting manifolds of varying dimensions.
result Normalized Dirichlet energy converges to a tensorized Dirichlet energy that adapts to all dimensions simultaneously.
ACFS optimizes spectral risk under decision-dependent uncertainty using adaptive forest sampling.
problem Minimizing spectral risk with decision-dependent uncertainty.
method ACFS integrates Generalised Random Forests, CEM-guided exploration, rank-weighted augmentation, and multi-start refinement.
result ACFS achieves lowest median oracle spectral risk on both benchmarks.
Paper introduces RAS for robust MTL with contamination.
problem Representation-based multi-task learning struggles with contamination.
method Robust and Adaptive Spectral (RAS) method.
result RAS prevents negative transfer and performs well with up to 80% contamination.
Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we propose a Deviation-based approach to quantify uncertainty. Furthermore, the theory …
Shampoo achieves higher token efficiency than Muon in language models.
problem Understanding the relationship and relative data efficiency of Shampoo and Muon compared to Adam and Signum.
method Extensive experiments on language models, demonstrating Shampoo's higher efficiency and decomposing its updates.
result Shampoo's benefits are attributed to its application to weight matrices, challenging interpretations based on variance adaptation and whitening.
New approach speeds up DNA sequence alignment.
problem Efficiently estimating alignment scores for large sets of reads.
method Rank-one crowdsourcing models and multi-armed bandit algorithm.
result Adaptive algorithm identifies pairs with large alignment scores.
New accelerators for EM improve convergence speed in complex mixture models.
problem Improving the convergence speed of the EM algorithm for complex mixture models.
method Derive a new operator connecting global descent and local convergence, and use it to develop two acceleration strategies.
result Two new acceleration strategies (G-Accelerator and Geo-Adaptive) significantly improve EM algorithm performance.
We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the theta functions and monopole data of the genus 4 curve to be given in terms of g…
New method efficiently learns positive-definite curvature for neural nets.
problem Efficiently learn positive-definite curvature for neural net training.
method Spectral-factorized positive-definite curvature learning approach.
result Efficiently applies arbitrary matrix roots and generic curvature learning.
The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This paper proposes a practical approach to learn spectral clustering based on adaptive…
Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network defined in the vertex domain. We provi…
The paper computes an approximation to the sample Frechet mean of graph sets using spectral information.
problem Characterizing the location of a set of graphs in a metric space.
method The Frechet mean is computed for sets of large graphs using the pseudometric defined by the norm between eigenvalues of adjacency matrices.
result An algorithm to approximate the sample Frechet mean of undirected unweighted graphs is described.
SC-Net learns interpretable filters for inverse problems, achieving optimal convergence and super-resolution.
problem Solving ill-posed inverse problems with effective regularization and interpretability.
method SC-Net operates in the spectral domain, learning a pointwise adaptive filter function based on signal-to-noise ratio.
result SC-Net achieves optimal convergence rate and zero-shot super-resolution, matching theoretical bounds.
Spectral clustering for directed graphs using likelihood estimation.
problem Clustering directed graphs with edge directions.
method Maximum likelihood estimation on stochastic block models.
result Significant performance gains over existing methods.
Study on discrepancy principle for learning algorithms in nonparametric regression.
problem Determining optimal iteration number in nonparametric regression with unknown optimal iteration.
method Investigates discrepancy principle and modified principles for kernelized spectral filters, using deviation inequalities and change-of-norm arguments.
result Classical discrepancy principle is adaptive for slow rates, while modified principles are adaptive for faster rates.
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, ε-graphs and k-NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based…
Understanding the adaptation process of plants to drought stress is essential in improving management practices, breeding strategies as well as engineering viable crops for a sustainable agriculture in the coming decades. Hyper-spectral imaging provides a particularly promising approach to gain such understanding since…
Optimizes spectral density estimation for stationary and nonstationary processes.
problem Estimating spectral density of time series with complex structure.
method Optimally adaptive Bayesian spectral density estimation using smoothing spline covariance structure.
result Optimal eigendecomposition provides superior performance compared to alternative covariance functions.
Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix construction, low-dimensional embedding, and K-Means clustering as post processing), whi…
Bayesian parametric matrix models provide uncertainty quantification for spectral learning.
problem Uncertainty quantification in spectral learning for safety-critical applications.
method Bayesian parametric matrix models (B-PMMs) that extend PMMs to provide uncertainty estimates.
result B-PMMs achieve exceptional uncertainty calibration (ECE < 0.05) while maintaining favorable scaling.
We study the behavior of the degeneration at the second step of the Frölicher spectral sequence of a C∞ family of compact complex manifolds. Using techniques from deformation theory and adapting them to pseudo-differential operators we prove a result \textit{à la Kodaira-Spencer} for the dimension o…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and dependency of financial time series in a non-parametric fashion assuming that the time…
We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our training objective, based on the Hilbert Schmidt Information Criterion, can be o…
New method reduces uncertainty in high-dimensional circuits by automatically determining tensor rank and adaptive sampling.
problem Uncertainty quantification in high-dimensional circuits due to fabrication process variations.
method Tensor regression with ℓq/ℓ2 group-sparsity regularization for rank determination and adaptive sampling. result Captures uncertainty with only 100-600 simulation samples for 19-100 random variables.
Study ratio-limit boundaries for random walks on hyperbolic groups.
problem Computing ratio-limit boundaries for relatively hyperbolic groups.
method Adapting Woess's strategy to non-hyperbolic groups and analyzing degenerate cases.
result Closure of minimal points in R-Martin boundary is the unique smallest invariant subspace in ratio-limit boundary. We consider the problem of learning from a similarity matrix (such as spectral clustering and lowd imensional embedding), when computing pairwise similarities are costly, and only a limited number of entries can be observed. We provide a theoretical analysis using standard notions of graph approximation, significantly …
CAST improves spectral clustering for multi-scale data by integrating reachability similarity.
problem Applying spectral clustering to multi-scale data where clusters vary in size and density.
method CAST integrates reachability similarity with distance-based similarity to derive a coefficient matrix, then applies trace Lasso regularization.
result CAST provides excellent performance and robustness across various multi-scale data test cases.
Spectral variability is one of the major issue when conducting hyperspectral unmixing. Within a given image composed of some elementary materials (herein referred to as endmember classes), the spectral signature characterizing these classes may spatially vary due to intrinsic component fluctuations or external factors …