Related papers: On the Aubin property of solution maps to paramete…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
By using variational methods, the existence of infinitely many solutions for a nonlinear algebraic system with a parameter is established in presence of a perturbed Lipschitz term. Our goal was achieved requiring an appropriate behavior of…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
We develop method that allows to derive reductions and solutions to hyperbolic systems of partial differential equations. The method is based on using functions that are constant in the direction of characteristics of the system. These…
We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
We study the problem of conditional predictive inference on multiple outcomes missing at random (MAR) -- or equivalently, under covariate shift. While the weighted conformal prediction offers a tool for inference under covariate shift with…
We show the existence of nontrivial solutions for a class of highly quasilinear problems in which the governing operators depend on the unknown function. By using a suitable variational setting and a weak version of the Cerami-Palais-Smale…
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
We introduce a new compositional framework for generalized variational inference, clarifying the different parts of a model, how they interact, and how they compose. We explain that both exact Bayesian inference and the loss functions…
Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that…
A system of differential equations of the Okubo normal form containing accessory parameters is considered. A condition for determining special values of the accessory parameters is given. It is shown that the special values give the…
Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in systems that possess this property but their energy functional is unbounded both lower and…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
Probing experiments investigate the extent to which neural representations make properties -- like part-of-speech -- predictable. One suggests that a representation encodes a property if probing that representation produces higher accuracy…
Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…
This paper investigates conditional specifications for multivariate count variables. Recently, the spatial count data literature has proposed several conditional models such that the conditional expectations are linear in the conditioning…