Paper introduces MJ distances for better anomaly detection in time series.
problem Anomaly detection in large collections of time series.
method Introduces semi-metric MJ distances for measuring structural breaks.
result MJ distances outperform existing metrics in detecting similarity and anomalies.
New ensemble models classify mouse movement trajectories to assess survey question difficulty.
problem Assessing survey question difficulty based on respondents' interaction data.
method Ensemble models combining semi-metric-based weak learners to classify multivariate functional data.
result Improved survey data quality through better identification of respondent difficulty.
The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining applications. This article converts the dtw-distance to a semi-metric and shows that its…
Study robust covariance estimation in large data with concentrated vectors.
problem Estimating robust covariance in large data with concentrated vectors.
method Fixed point of a contracting function using stable semi-metric and concentration of measure.
result Existence and uniqueness of robust estimator with evaluated limiting spectral distribution.
A new KM clustering algorithm reduces error and scales to large datasets.
problem Traditional KM error analyses suffer from generalization gaps and lack true error bounds.
method Formalized true K-Medoids error, decomposed into ME and MME, provided convergence result, proposed MCPAM algorithm.
result MCPAM achieves true error bounds and scales to 1 billion points.
New algorithm reduces simultaneous asset shocks in financial portfolios.
problem Reducing simultaneous asset shocks in financial portfolios.
method Uses semi-metrics to determine distance between asset structural breaks for portfolio optimization.
result Proposed method outperforms existing metrics in synthetic and real data, reducing volatility and drawdown.
StoSOO optimistically maximizes noisy, locally smooth functions.
problem Global maximization of noisy, locally smooth functions with unknown semi-metric.
method StoSOO uses optimistic upper confidence bounds to iteratively decide on the next evaluation point.
result StoSOO performs almost as well as the best tuned algorithms, even without knowing the semi-metric.
This study improves estimation of locally stationary functional time series using NW method.
problem Accurately capturing time-dependence in locally stationary functional time series with time-varying covariates.
method Nadaraya-Watson (NW) estimation procedure for the conditional distribution of LSFTS.
result Established convergence rates of NW estimator for LSFTS with respect to Wasserstein distance.
Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.
problem Exact recovery of communities in weighted graphs with Gaussian and exponential distributions.
method Introduces a new semi-metric to describe conditions for exact recovery and analyzes conditions for both complete and incomplete graphs.
result Necessary and sufficient conditions for exact recovery are asymptotically tight and applicable to both complete and incomplete graphs.
SAMBA improves safe reinforcement learning with active exploration metrics.
problem Safe reinforcement learning in dynamic systems.
method Combines probabilistic modelling, information theory, and statistics. Uses novel metrics for out-of-sample Gaussian process evaluation.
result Orders of magnitude reduction in samples and violations compared to state-of-the-art methods.
Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the e…
Paper proves collapsing result for orbifolds without curvature bounds.
problem Proving collapsing result for orbifolds without curvature bounds.
method Introduces weak submersions and stratified Riemannian metrics.
result Allows Gromov-Hausdorff limits of orbifolds with strictly lower dimension.
A new warping-invariant distance improves nearest-neighbor classification efficiency.
problem dtw distance inconsistency and inefficiency in nearest-neighbor classification.
method Showed dtw is not warping-invariant, converted to twi distance.
result twi distance equivalent error rates to dtw, more efficient.
Non-parametric method predicts multi-stream longitudinal data evolution.
problem Predicting the evolution of multi-stream longitudinal data for an in-service unit.
method Decomposes each stream into eigenfunctions and FPC scores, uses Gaussian process prior and empirical Bayesian updating.
result Framework outperforms state-of-the-art approaches and achieves high predictive accuracy.
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures μ from some set M to functions in a reproducing kernel Hilbert space (RKHS) with kernel k. The RKHS distance of two mapped measures is a semi-metric dk over M. We study three questions. (I) For a…
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a Gaussian mixture distribution, a fact exploited to softly matc…
A scalable version of MADD improves big-data classification speed.
problem High computational complexity of MADD in big data.
method Selecting a representative set and using Random Fourier Features.
result Achieves similar performance to MADD but at a fraction of the computing time.
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time position follows a Gaussian mixture distribution, a fact exploited to softly …
New null distance bounds confirm Big Bang singularity in cosmological models.
problem Understanding the geometry of spacetime near Big Bang singularities.
method Developed a new null distance metric for temporal functions and applied it to cosmological models.
result Null distance is bounded by a constant multiple of Riemannian distance on level sets with constant gradient norm.
Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.
problem Convergence and approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
method Analysis of convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
result Strictly weaker convergence in 2-Sinkhorn divergence for Gaussian measures compared to exact 2-Wasserstein distance.