Related papers: Identification of unknown parameters and predictio…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Gradient-based solvers risk convergence to local optima, leading to incorrect researcher inference. Heuristic-based algorithms are able to ``break free" of these local optima to eventually converge to the true global optimum. However, given…

We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…

Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a…

Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…

This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…

The Baum-Welsh algorithm together with its derivatives and variations has been the main technique for learning Hidden Markov Models (HMM) from observational data. We present an HMM learning algorithm based on the non-negative matrix…

The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis. One of the key reasons for this versatility is the ability of HMM to deal with missing data. However, standard HMM learning…

We reinvigorate maximum likelihood estimation (MLE) for macroeconomic density forecasting through a novel neural network architecture with dedicated mean and variance hemispheres. Our architecture features several key ingredients making MLE…

When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…

We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…

We present novel Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods to determine the unbiased covariance of random variables using h-statistics. The advantage of this procedure lies in the unbiased construction of the estimator's…

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

Machine learning can provide deep insights into data, allowing machines to make high-quality predictions and having been widely used in real-world applications, such as text mining, visual classification, and recommender systems. However,…

We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training a deep neural network (DNN) model for the unknown system using its trajectory data. A key…

We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…

Knowledge present in a domain is well expressed as relationships between corresponding concepts. For example, in zoology, animal species form complex hierarchies; in genomics, the different (parts of) molecules are organized in groups and…

Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements…

Machine learning models are increasingly used to predict material properties and accelerate atomistic simulations, but the reliability of their predictions depends on the representativeness of the training data. We present a scalable,…