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Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…

Graph convolutional networks (GCNs) have been employed as a kind of significant tool on many graph-based applications recently. Inspired by convolutional neural networks (CNNs), GCNs generate the embeddings of nodes by aggregating the…

We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…

Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…

Finite mixture models, typically Gaussian mixtures, are well known and widely used as model-based clustering. In practical situations, there are many non-Gaussian data that are heavy-tailed and/or asymmetric. Normal inverse Gaussian (NIG)…

Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue…

While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…

Rapid development of big data and high-performance computing have encouraged explosive studies of deep learning in geoscience. However, most studies only take single-type data as input, frittering away invaluable multisource, multi-scale…

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's…

Understanding and interpreting how machine learning (ML) models make decisions have been a big challenge. While recent research has proposed various technical approaches to provide some clues as to how an ML model makes individual…

Embeddings are now used to underpin a wide variety of data management tasks, including entity resolution, dataset search and semantic type detection. Such applications often involve datasets with numerical columns, but there has been more…

We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD…

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…

The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…

Mistakes/uncertainties in object detection could lead to catastrophes when deploying robots in the real world. In this paper, we measure the uncertainties of object localization to minimize this kind of risk. Uncertainties emerge upon…

For many types of machine learning algorithms, one can compute the statistically `optimal' way to select training data. In this paper, we review how optimal data selection techniques have been used with feedforward neural networks. We then…

Data-driven approaches such as deep learning can result in predictive models for material properties with exceptional accuracy and efficiency. However, in many applications, data is sparse, severely limiting their accuracy and…

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…

Uncertainty awareness is crucial to develop reliable machine learning models. In this work, we propose the Natural Posterior Network (NatPN) for fast and high-quality uncertainty estimation for any task where the target distribution belongs…

We propose the Gaussian Gated Linear Network (G-GLN), an extension to the recently proposed GLN family of deep neural networks. Instead of using backpropagation to learn features, GLNs have a distributed and local credit assignment…