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In uncertainty quantification for parametric partial differential equations (PDEs), it is common to model uncertain random field inputs using countably infinite sequences of independent and identically distributed random variables. The…
Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. In previous work, a Bayesian…
Completely random measures provide a principled approach to creating flexible unsupervised models, where the number of latent features is infinite and the number of features that influence the data grows with the size of the data set. Due…
This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random measures. We propose a truncation method for the mixing distribution by discarding…
In the context of the Dragulescu-Yakovenko (2000) model, we show that empirical income distribution with truncated datasets, cannot be properly modeled by the one-parameter exponential distribution. However, a truncated version…
In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding…
Varying-coefficient functional linear models consider the relationship between a response and a predictor, where the response depends not only the predictor but also an exogenous variable. It then accounts for the relation of the predictors…
Deep neural networks (DNNs) offer significant flexibility and robust performance. This makes them ideal for building not only system models but also advanced neural network controllers (NNCs). However, their high complexity and…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
The deployment of deep neural networks on edge devices is a challenging task due to the increasing complexity of state-of-the-art models, requiring efforts to reduce model size and inference latency. Recent studies explore models operating…
Sampling from multivariate normal distributions, subjected to a variety of restrictions, is a problem that is recurrent in statistics and computing. In the present work, we demonstrate a general framework to efficiently sample a…
We provide efficient algorithms for the problem of distribution learning from high-dimensional Gaussian data where in each sample, some of the variable values are missing. We suppose that the variables are missing not at random (MNAR). The…
We give the first sample complexity characterizations for outcome indistinguishability, a theoretical framework of machine learning recently introduced by Dwork, Kim, Reingold, Rothblum, and Yona (STOC 2021). In outcome…
Balancing between computational efficiency and sample efficiency is an important goal in reinforcement learning. Temporal difference (TD) learning algorithms stochastically update the value function, with a linear time complexity in the…
Data selection is essential for training deep learning models. An effective data sampler assigns proper sampling probability for training data and helps the model converge to a good local minimum with high performance. Previous studies in…
Reduced numerical precision is a common technique to reduce computational cost in many Deep Neural Networks (DNNs). While it has been observed that DNNs are resilient to small errors and noise, no general result exists that is capable of…
We consider the problem of PAC-learning decision trees, i.e., learning a decision tree over the n-dimensional hypercube from independent random labeled examples. Despite significant effort, no polynomial-time algorithm is known for learning…
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important…
While offering a principled framework for uncertainty quantification in deep learning, the employment of Bayesian Neural Networks (BNNs) is still constrained by their increased computational requirements and the convergence difficulties…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…