Related papers: Another look at Second order condition in Extreme …
This paper provides a theorem to compare the minimum total cost of two different Euclidean Random Assignment Problems with the same number of points, using the stochastic order of the costs of one of the pairs in these two problems. The…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
In this paper we investigate the Burr distributions family which contains twelve members. Second order expansions of quantiles of the Burr's distributions are provided on which may be based statistical methods, in particular in extreme…
The effective application of representation learning to real-world problems requires both techniques for learning useful representations, and also robust ways to evaluate properties of representations. Recent work in disentangled…
In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of…
This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under certain constraint qualifications. A particular focus is put…
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
An intriguing connection between extreme value statistics and traveling fronts has been found recently in a number of diverse problems. In this brief review we outline a few such problems and consider their various applications.
Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from…
The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal problems on open subsets of Euclidean space in this setting we…
We consider the second-order cone function (SOCF) $f: {\mathbb R}^n \to \mathbb R$ defined by $f(x)= c^T x + d -\|A x + b \|$. Every SOCF is concave. We give necessary and sufficient conditions for strict concavity of $f$. The parameters $A…
Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt…
Second-price auctions with reserve play a critical role for modern search engine and popular online sites since the revenue of these companies often directly de- pends on the outcome of such auctions. The choice of the reserve price is the…
In this note the author uses order statistics to estimate WCRE and WCE in terms of empirical and survival functions. An example in both cases normal and exponential WFs is analyzed.
Counterfactual explanations (CE) are the de facto method for providing insights into black-box decision-making models by identifying alternative inputs that lead to different outcomes. However, existing CE approaches, including group and…