Related papers: A Categorical Approach to DIBI Models
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A…
We describe a new, generally applicable strategy for the systematic construction of basis invariants (BIs). Our method allows one to count the number of mutually independent BIs and gives controlled access to the interrelations (syzygies)…
For complex simulation problems, inferring parameters often precludes the use of classical likelihood-based techniques due to intractable likelihoods. Simulation-based inference (SBI) methods offer a likelihood-free approach to directly…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…
Simulation-Based Inference (SBI) is an approach to statistical inference where simulations from an assumed model are used to construct estimators and confidence sets. SBI is often used when the likelihood is intractable and to construct…
Causal Models are like Dependency Graphs and Belief Nets in that they provide a structure and a set of assumptions from which a joint distribution can, in principle, be computed. Unlike Dependency Graphs, Causal Models are models of…
Drawbacks of ignoring the causal mechanisms when performing imitation learning have recently been acknowledged. Several approaches both to assess the feasibility of imitation and to circumvent causal confounding and causal misspecifications…
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning…
The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
We study various notions of dependency in semiring team semantics. Semiring teams are essentially database relations, where each tuple is annotated with some element from a positive semiring. We consider semiring generalizations of several…
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…
Conditional Independence (CI) graph is a special type of a Probabilistic Graphical Model (PGM) where the feature connections are modeled using an undirected graph and the edge weights show the partial correlation strength between the…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
Standard methods of using categorical variables as predictors either endow them with an ordinal structure or assume they have no structure at all. However, categorical variables often possess structure that is more complicated than a linear…
Multilabel classification is a relatively recent subfield of machine learning. Unlike to the classical approach, where instances are labeled with only one category, in multilabel classification, an arbitrary number of categories is chosen…