Related papers: A Representation Theorem for Finite Best-Worst Ran…
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the…
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…
The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The…
We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…
Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…
Quantum experiments yield random data. We show that the most efficient way to store this empirical information by a finite number of bits is by means of the vector of square roots of observed relative frequencies. This vector has the unique…
We prove a PCP theorem for the existential theory of the reals, showing that MAX-ETR-INV is $\exists\mathbb{R}$-hard to approximate to within some constant factor. The existential theory of the reals (ETR) is a decision problem asking if…
A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially…
Postulated by Pauli to explain the electronic structure of atoms and molecules, the exclusion principle establishes an upper bound of 1 for the fermionic natural occupation numbers $\{n_i\}$. A recent analysis of the pure…
We obtain a necessary and sufficient condition under which random-coefficient discrete choice models, such as mixed-logit models, are rich enough to approximate any nonparametric random utility models arbitrarily well across choice sets.…
A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a…
The promise of least-privilege learning -- to find feature representations that are useful for a learning task but prevent inference of any sensitive information unrelated to this task -- is highly appealing. However, so far this concept…
Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require…
Representation theory of finite groups portrays a marvelous crossroad of group theory, algebraic combinatorics, and probability. In particular the Plancherel measure is a probability that arises naturally from representation theory, and in…
In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that…
A weak bialgebra is known to be a special case of a bialgebroid. In this paper we study the relationship of this fact with the Tannaka theory of bialgebroids as developed in [4]. We obtain a Tannaka representation theorem with respect to a…
In the late 19th century, Swedish mathematician Lars Edvard Phragm\'{e}n proposed a load-balancing approach for selecting committees based on approval ballots. We consider three committee voting rules resulting from this approach: two…
For arbitrary nontrivial linear combinations of a finite number of Poisson kernels, the fulfillment of the Nagy condition is established for all numbers n, starting from some number. It is also proved for any n the existence of linear…
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…