Related papers: Analytic Subordination for Free Compression
This paper proves that homology equivalences of cogenerating complexes induce homology equivalences of the cofree coalgebras in many interesting cases. We show that the underlying chain complex of any cofree coalgebra is naturally a direct…
This report presents adaptive artificial compression methods in which the time-step and artificial compression parameter $\varepsilon $ are independently adapted. The resulting algorithms are supported by analysis and numerical tests. The…
We study conjugate and Lagrange dualities for composite optimization problems within the framework of abstract convexity. We provide conditions for zero duality gap in conjugate duality. For Lagrange duality, intersection property is…
In the talk we investigate the question of commutation of the whole-partial derivatives, which should be considered when the function, which is subjected to differentiation, has both explicit and implicit dependence. We apply the results to…
The purpose of this paper is to extend some useful results, such as the multiplication being open, previously known for suitable finitely generated relatively free profinite semigroups, to relatively free profinite semigroupoids over…
Let $f_1, f_2, ..., f_n$ be a family of independent copies of a given random variable f in a probability space $(\Omega, \mathcal{F}, \mu)$. Then, the following equivalence of norms holds whenever $1 \le q \le p < \infty$…
This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
We consider a general class of empirical-type likelihoods and develop higher order asymptotics with a view to characterizing members thereof that allow the existence of possibly data-dependent probability matching priors ensuring…
In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its…
In this paper we examine how the notion of algebra of quotients for Lie algebras ties up with the corresponding well-known concept in the associative case. Specifically, we completely characterize when a Lie algebra $Q$ is an algebra of…
We extend the refined asymptotics of analytic torsion associated to congruence subgroups of $\operatorname{SL}(n)$ in previous work, to congruence subgroups in a large family of reductive groups. This is applied to give new asymptotics and…
Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a…
Given a simple Lie algebra $\mathfrak{g}$ and an element $\mu\in\mathfrak{g}^*$, the corresponding shift of argument subalgebra of $\text{S}(\mathfrak{g})$ is Poisson commutative. In the case where $\mu$ is regular, this subalgebra is known…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
Algebraic contraction is proposed to realize mappings between models Hamiltonians. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic $XXZ$ Heisenberg…
An analytic formula is proposed to characterize the variance propagation from correlated input variables to the model response, by using multi-variate Taylor series. With the formula, partial variance contributions to the model response are…
We prove an expansion for densities in the free CLT and apply this result to an expansion in the entropic free central limit theorem assuming a moment condition of order 8 for the free summands.
We establish the existence and uniqueness of finite free resolutions - and their attendant Betti numbers - for graded commuting d-tuples of Hilbert space operators. Our approach is based on the notion of free cover of a (perhaps…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…