Related papers: Uncertain Data in Initial Boundary Value Problems:…
We investigate the problem of determining the predictive confidence (or, conversely, uncertainty) of a neural classifier through the lens of low-resource languages. By training models on sub-sampled datasets in three different languages, we…
The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…
Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…
A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting…
We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…
We establish existence and uniqueness results for initial boundary value problems with nearly incompressible vector fields. We then apply our results to establish well-posedness of the initial-boundary value problem for the Keyfitz and…
In the first of two papers, we study the initial boundary-value problem that underlies the theory of the Boltzmann equation for general non-spherical hard particles. In this work, for two congruent ellipses and for a large class of…
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system,…
When inferring the causal effect of one variable on another from correlational data, a common practice by professional researchers as well as lay decision makers is to control for some set of exogenous confounding variables. Choosing an…
For multiple reasons -- such as avoiding overtraining from one data set or because of having received numerical estimates for some parameters in a model from an alternative source -- it is sometimes useful to divide a model's parameters…
Energy demand prediction is critical for grid operators, industrial energy consumers, and service providers. Energy demand is influenced by multiple factors, including weather conditions (e.g. temperature, humidity, wind speed, solar…
The Oxygen Depletion problem is an implicit free boundary value problem. The dynamics allow topological changes in the free boundary. We show several mathematical formulations of this model from the literature and give a new formulation…
Predictive models are often introduced to decision-making tasks under the rationale that they improve performance over an existing decision-making policy. However, it is challenging to compare predictive performance against an existing…
We study the large fluctuations of the work injected by the random force into a Brownian particle under the action of a confining harmonic potential. In particular, we compute analytically the rate function for generic uncorrelated initial…
In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…
In experimental and observational data settings, researchers often have limited knowledge of the reasons for missing outcomes. To address this uncertainty, we propose bounds on causal effects for missing outcomes, accommodating the scenario…
This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…
Scientific applications typically generate large volumes of floating-point data, making lossy compression one of the most effective methods for data reduction, thereby lowering storage requirements and improving performance in large-scale…
In this paper, we have defined the free boundary formulation for two extended Blasius problems. These problems are of interest in boundary layer theory and are deduced from the governing partial differential equations by using appropriate…