Related papers: Ekeland's Variational Principle for An $\bar{L}^{0…

We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The…

The Maurey-Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some L_p(\nu) which satisfies a certain vector-valued inequality even allows a weighted norm inequality. Continuing the work of…

We generalize Lindeberg's proof of the central limit theorem to an invariance principle for arbitrary smooth functions of independent and weakly dependent random variables. The result is applied to get a similar theorem for smooth functions…

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

We develop a pseudo-likelihood theory for rank one matrix estimation problems in the high dimensional limit. We prove a variational principle for the limiting pseudo-maximum likelihood which also characterizes the performance of the…

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $\left(\varphi_1, \varphi_2\right)-$convex function $g, $ with arbitrarily small norm, such that $f + g…

We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least action principle and Noether's theorem to this generalized…

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…

We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…

Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures.…

In this paper, we first introduce the notion of the Laplace transform for an abstract-valued function from $[0, \infty)$ to a $\mathcal{T}_{\varepsilon, \lambda}$-complete random normed module $S$. Then, combining respective advantages of…

E-variables are a relatively new approach for testing statistical hypotheses that has been experiencing major development during the last several years. In this paper we introduce the method of e-variable-approximability and use it to…

We consider Borwein-Preiss and Ekeland variational principles using distance functions that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced…

Let $\k$ be a global function field in 1-variable over a finite extension of $\Fp$, $p$ prime, $\infty$ a fixed place of $\k$, and $\A$ the ring of functions of $\k$ regular outside of $\infty$. Let $E$ be a Drinfeld module or $T$-module.…

The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…

Let $M$ be smooth $n$-dimensional manifold, fibered over a $k$-dimensional submanifold $B$ as $\pi:M \to B$, and $\vartheta \in \Lambda^k (M)$; one can consider the functional on sections $\phi$ of the bundle $\pi$ defined by $\int_D \phi^*…

We develop E-variables for testing whether two or more data streams come from the same source or not, and more generally, whether the difference between the sources is larger than some minimal effect size. These E-variables lead to exact,…

We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation…

Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form \[ \langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0. \] Here…

The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…