相关论文: GAP Computations Concerning Probabilistic Generati…
Complex computer codes are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this problem consists in replacing cpu-time expensive…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually…
Generative Artificial Intelligence is emerging as an important technology, promising to be transformative in many areas. At the same time, generative AI techniques are based on sampling from probabilistic models, and by default, they come…
Let G be a finite group. By Riemann's Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic…
Gaussian stochastic process (GaSP) has been widely used as a prior over functions due to its flexibility and tractability in modeling. However, the computational cost in evaluating the likelihood is $O(n^3)$, where $n$ is the number of…
The asymptotic study of the conjugacy classes of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based…
It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case.…
We provide a novel approach to construct generative models for graphs. Instead of using the traditional probabilistic models or deep generative models, we propose to instead find an algorithm that generates the data. We achieve this using…
We present novel understandings of the Gamma-Poisson (GaP) model, a probabilistic matrix factorization model for count data. We show that GaP can be rewritten free of the score/activation matrix. This gives us new insights about the…
A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.
Y haplogroup analyses are an important component of genealogical reconstruction, population genetic analyses, medical genetics and forensics. These fields are increasingly moving towards use of low-coverage, high throughput sequencing.…
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
Computational method for statistical measures of reliability, confidence, and assurance are available for infinite population size. If the population size is finite and small compared to the number of samples tested, these computational…
Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…
A general method to produce uniformly distributed pseudorandom numbers with extended precision by combining two pseudorandom numbers with lower precision is proposed. In particular, this method can be used for pseudorandom number generation…
We describe a deterministic algorithm for finding a generating element of the multiplicative group of the finite field $\mathbb{F}_{p^n}$ where $p$ is a prime. In time polynomial in $p$ and $n$, the algorithm either outputs an element that…