Related papers: Measuring Time-Series Dataset Similarity using Was…
We propose the Wasserstein-Fourier (WF) distance to measure the (dis)similarity between time series by quantifying the displacement of their energy across frequencies. The WF distance operates by calculating the Wasserstein distance between…
Fairness testing evaluates whether a model satisfies a specified fairness criterion across different groups, yet most research has focused on classification models, leaving regression models underexplored. This paper introduces a framework…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
Training time-series forecasting models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach resorts to minimizing the conditional negative…
Missing data can significantly hamper standard time series analysis, yet they occur frequently in applications. In this paper, we introduce temporal Wasserstein imputation, a novel method for imputing missing data in time series. Unlike…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
Scientific datasets often have hierarchical structure: for example, in surveys, individual participants (samples) might be grouped at a higher level (units) such as their geographical region. In these settings, the interest is often in…
Change point detection for time series analysis is a difficult and important problem in applied statistics, for which a variety of approaches have been developed in the past several decades. Here, the Wasserstein metric is employed as a…
Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…
We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…
We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…
We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…
This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
We study statistical inference on the similarity/distance between two time-series under uncertain environment by considering a statistical hypothesis test on the distance obtained from Dynamic Time Warping (DTW) algorithm. The sampling…
We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…