Related papers: Parameter estimation for second-order SPDEs in mul…
In this article we focus on dynamic network data which describe interactions among a fixed population through time. We model this data using the latent space framework, in which the probability of a connection forming is expressed as a…
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
The method to design exponentially stable adaptive observers is proposed for linear time-invariant systems parameterized by unknown physical parameters. Unlike existing adaptive solutions, the system state-space matrices A, B are not…
One of the unspoken challenges of tractography is choosing the right parameters for a given dataset or bundle. In order to tackle this challenge, we explore the multi-dimensional parameter space of tractography using streamline-specific…
This paper is concerned with inference about low-dimensional components of a high-dimensional parameter vector $\beta^0$ which is identified through instrumental variables. We allow for eigenvalues of the expected outer product of included…
The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is…
Probabilistic values, including Shapley values and semivalues, provide a model-agnostic framework to attribute the behavior of a black-box model to data points or features, with a wide range of applications including explainable artificial…
We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a…
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order model, such as a deep neural network, to approximate the…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
We analyze multivariate ordered discrete response models with a lattice structure, modeling decision makers who narrowly bracket choices across multiple dimensions. These models map latent continuous processes into discrete responses using…
We consider learning high-dimensional multi-response linear models with structured parameters. By exploiting the noise correlations among responses, we propose an alternating estimation (AltEst) procedure to estimate the model parameters…
In recent years, addressing the challenges posed by massive datasets has led researchers to explore aggregated data, particularly leveraging interval-valued data, akin to traditional symbolic data analysis. While much recent research, with…
We consider likelihood-based two-step estimation of latent variable models, in which just the measurement model is estimated in the first step and the measurement parameters are then fixed at their estimated values in the second step where…
Partial differential equations (PDEs) with spatially-varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional PDE solvers struggle with the immense complexity found in…