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This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model.…

Generative models can now produce photorealistic synthetic data which is virtually indistinguishable from the real data used to train it. This is a significant evolution over previous models which could produce reasonable facsimiles of the…

Seismic full waveform inversion (FWI) is a powerful technique to generate high resolution images of the Earth's interior. However, significant uncertainty exists in all FWI solutions due to imperfect acquisition geometries, inherent noise…

The infrequent occurrence of overfitting in deep neural networks is perplexing: contrary to theoretical expectations, increasing model size often enhances performance in practice. But what if overfitting does occur, though restricted to…

We propose two new evaluation metrics to assess realness of generated images based on normalizing flows: a simpler and efficient flow-based likelihood distance (FLD) and a more exact dual-flow based likelihood distance (D-FLD). Because…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Generative models aim to learn the distribution of observed data by generating new instances. With the advent of neural networks, deep generative models, including variational autoencoders (VAEs), generative adversarial networks (GANs), and…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

This paper discusses difference-in-differences (DID) estimation when there exist many control variables, potentially more than the sample size. In this case, traditional estimation methods, which require a limited number of variables, do…

In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weighted sums of $2\times 2$ configuration counts. For Boolean models with balls as grains,…

Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing…

Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…

Variational inference provides a powerful tool for approximate probabilistic in- ference on complex, structured models. Typical variational inference methods, however, require to use inference networks with computationally tractable proba-…

Joint machine learning models that allow synthesizing and classifying data often offer uneven performance between those tasks or are unstable to train. In this work, we depart from a set of empirical observations that indicate the…

This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…

The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…

Model-based offline reinforcement learning approaches generally rely on bounds of model error. Estimating these bounds is usually achieved through uncertainty estimation methods. In this work, we combine parametric and nonparametric methods…

Machine learning models encounter Out-of-Distribution (OoD) errors when the data seen at test time are generated from a different stochastic generator than the one used to generate the training data. One proposal to scale OoD detection to…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…