A new method detects small holes in noisy data.
problem Detecting small holes in high-density regions from noise.
method Robust Density-Aware Distance (RDAD) filtration, incorporating distance-to-measure concept.
result The RDAD filtration prolongs the persistences of small holes, making them distinguishable from noise.
NN methods perform well in anomaly detection, especially in high dimensions.
problem Improving anomaly detection methods for high-dimensional data.
method Extensive simulations and theoretical analysis of NN methods for anomaly detection.
result NN methods outperform other state-of-the-art algorithms in anomaly detection.
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a mu…
We consider various notions of strains; quantitative measures for the deviation of a linear transformation from an isometry. The main approach, which is motivated by physical applications and follows the work of Patrizio Neff and co-workers , is to select a Riemannian metric on GLn, and use its induced geodes…
Bayesian DDR models complex multivariate distributions.
problem Modeling relationships between multivariate distributions with differing dimensions.
method Generalized Bayesian framework using sliced Wasserstein distance and MALA for inference.
result Posterior consistency and robust fits demonstrated in simulations and real data.
WRAAC uses Wasserstein distance for robust reinforcement learning.
problem Lack of quantified robustness to system dynamics in existing reinforcement learning algorithms.
method Leverages Wasserstein distance to connect state disturbance to transition kernel disturbance, reducing infinite-dimensional optimization to a finite-dimensional problem.
result Designs a novel algorithm, WRAAC, that achieves robust reinforcement learning.
WEGL embeds graphs in a vector space for faster machine learning.
problem Efficiently embedding graphs for machine learning tasks.
method Wasserstein distance for node embedding similarity, Monge maps for graph representation.
result State-of-the-art classification performance with superior computational efficiency.
We propose a novel method to embed a functional magnetic resonance imaging (fMRI) dataset in a low-dimensional space. The embedding optimally preserves the local functional coupling between fMRI time series and provides a low-dimensional coordinate system for detecting activated voxels. To compute the embedding, we bui…
Paper introduces DP TDA for near-optimal private persistence diagrams.
problem Challenges in privatizing topological data analysis.
method Sensitivity analysis of persistence diagrams, use of exponential mechanism.
result Proposes near-optimal privacy mechanism for TDA.
FedGTEA learns new tasks in federated learning with task embeddings and alignment.
problem Federated class-incremental learning with task-specific knowledge and model uncertainty.
method Cardinality-Agnostic Task Encoder (CATE) for Gaussian task embeddings, 2-Wasserstein distance for inter-task alignment.
result FedGTEA achieves superior classification performance and mitigates forgetting.
A new metric HCP distance for comparing distributions.
problem Comparing high-dimensional probability distributions efficiently.
method Hilbert curve projection to low-dimensional coupling, followed by transport distance calculation.
result HCP distance is a proper metric for probability measures with bounded supports.
New algorithms for efficient matrix profile computation using various Euclidean distances.
problem Efficiently computing matrix profile for all-pairs-similarity search on time series.
method Proposed AAMP, ACAMP, and extended algorithms for p-norm distance.
result AAMP and ACAMP algorithms outperform existing methods for specific Euclidean distances.
New method calibrates deep models for both in-distribution and out-of-distribution samples.
problem Ensuring calibration for deep models in safety-critical applications, especially in OOD regions.
method Geodesic distance and Gaussian kernel to calibrate deep models.
result Proposed KDF and KDN methods achieve well-calibrated posteriors for both in-distribution and out-of-distribution samples.
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation …
A new generalized Statistical Complexity Measure (SCM) was proposed by Rosso et al in 2010. It is a functional that captures the notions of order/disorder and of distance to an equilibrium distribution. The former is computed by a measure of entropy, while the latter depends on the definition of a stochastic divergence…
WF distance measures time series similarity via spectral density displacement.
problem Measuring similarity between time series.
method Wasserstein-Fourier distance between normalised power spectral densities.
result WF establishes as a general-purpose metric for time series.
The paper explores the tradeoff between fairness and accuracy in regression models.
problem Characterizing the tradeoff between fairness and accuracy in regression models.
method Provided a lower bound on the error of any fair regressor and extended the result to joint error using Wasserstein distance.
result Lower bounds on the error of fair regressors and their connection to Wasserstein distance.