Kernel Quantile Embeddings and Associated Probability Metrics
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings to represent distributions as mean functions in RKHS. However, it remains unclear if the mean function is the only meaningful RKHS representation. Inspired by generalised quantiles, we introduce the notion of kernel quantile embeddings (KQEs). We then use KQEs to construct a family of distances that: (i) are probability metrics under weaker kernel conditions than MMD; (ii) recover a kernelised form of the sliced Wasserstein distance; and (iii) can be efficiently estimated with near-linear cost. Through hypothesis testing, we show that these distances offer a competitive alternative to MMD and its fast approximations.
Code (1)
Similar Papers 제목 키워드 기반
Scalable Kernel-Based Distances for Statistical Inference and Integration
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine pro…
Crop yield probability density forecasting via quantile random forest and Epanechnikov Kernel function
A reliable and accurate forecasting model for crop yields is of crucial importance for efficient decision-making process in the agricultural sector. However, due to weather extremes and uncertainties, most forecasting mo…
Decision MakingDensity EstimationFeature ImportancePrediction+3Hilbert space embeddings and metrics on probability measures
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probabilit…
Dimensionality ReductionDeterministic Fokker-Planck Transport -- With Applications to Sampling, Variational Inference, Kernel Mean Embeddings & Sequential Monte Carlo
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting probability flow ODE offers appealing pr…
Density EstimationVariational InferenceFixing the Pitfalls of Probabilistic Time-Series Forecasting Evaluation by Kernel Quadrature
Despite the significance of probabilistic time-series forecasting models, their evaluation metrics often involve intractable integrations. The most widely used metric, the continuous ranked probability score (CRPS), is a…
Probabilistic Time Series ForecastingTime SeriesTime Series Forecasting