相关论文: Wasserstein Measure Coresets

A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…

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…

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…

The primary choice to summarize a finite collection of random objects is by using measures of central tendency, such as mean and median. In the field of optimal transport, the Wasserstein barycenter corresponds to the Fr\'{e}chet or…

Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions.…

Fairness concerns are increasingly critical as machine learning models are deployed in high-stakes applications. While existing fairness-aware methods typically intervene at the model level, they often suffer from high computational costs,…

With the rapid scaling of neural networks, data storage and communication demands have intensified. Dataset distillation has emerged as a promising solution, condensing information from extensive datasets into a compact set of synthetic…

Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…

A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…

Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…

Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…

The Bayesian approach to clustering is often appreciated for its ability to provide uncertainty in the partition structure. However, summarizing the posterior distribution over the clustering structure can be challenging, due the discrete,…

We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset…

Problem definition: A key challenge in supervised learning is data scarcity, which can cause prediction models to overfit to the training data and perform poorly out of sample. A contemporary approach to combat overfitting is offered by…

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…

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…

We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging,…

As deep learning models continue to scale, the growing computational demands have amplified the need for effective coreset selection techniques. Coreset selection aims to accelerate training by identifying small, representative subsets of…

We devise coresets for kernel $k$-Means with a general kernel, and use them to obtain new, more efficient, algorithms. Kernel $k$-Means has superior clustering capability compared to classical $k$-Means, particularly when clusters are…