Related papers: From Multisets over Distributions to Distributions…
We present a development of norms and discuss their relationship to factorization. In earlier work, the first named author introduced the notion of a normset, which is the image of the norm map. A normset is a monoid with its own…
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the…
A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…
Containers are used to carve out a class of strictly positive data types in terms of shapes and positions. They can be interpreted via a fully-faithful functor into endofunctors on Set. Monadic containers are those containers whose…
Arguing for the need to combine declarative and probabilistic programming, B\'ar\'any et al. (TODS 2017) recently introduced a probabilistic extension of Datalog as a "purely declarative probabilistic programming language." We revisit this…
The Poisson multinomial distribution (PMD) describes the distribution of the sum of $n$ independent but non-identically distributed random vectors, in which each random vector is of length $m$ with 0/1 valued elements and only one of its…
We study a relaxation of the problem of coupling probability distributions -- a list of samples is generated from one distribution and an accept is declared if any one of these samples is identical to the sample generated from the other…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
In this work, we study the following basic question: "How much parallelism does a distributed task permit?" Our definition of parallelism (or symmetry) here is not in terms of speed, but in terms of identical roles that processes have at…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
A central tenet of probabilistic programming is that a model is specified exactly once in a canonical representation which is usable by inference algorithms. We describe JointDistributions, a family of declarative representations of…
A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…
In traditional Distributional Semantic Models (DSMs) the multiple senses of a polysemous word are conflated into a single vector space representation. In this work, we propose a DSM that learns multiple distributional representations of a…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
Unlabeled multigraphs have diverse applications across scientific fields, from transportation and social networks to polymer physics. In particular, multigraphs are essential for studying the relationship between the spatial organization…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…