Related papers: Inference From Visible Information And Background …
The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
Counterfactuals -- expressing what might have been true under different circumstances -- have been widely applied in statistics and machine learning to help understand causal relationships. More recently, counterfactuals have begun to…
It is claimed that a variety of facts concerning ellipsis, event reference, and interclausal coherence can be explained by two features of the linguistic form in question: (1) whether the form leaves behind an empty constituent in the…
Many practical problems can be understood as the search for a state of affairs that extends a fixed partial state of affairs, the \emph{environment}, while satisfying certain conditions that are formally specified. Such problems are found…
Identifying causal relationships from observation data is difficult, in large part, due to the presence of hidden common causes. In some cases, where just the right patterns of conditional independence and dependence lie in the data---for…
Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…
Counterfactual inference considers a hypothetical intervention in a parallel world that shares some evidence with the factual world. If the evidence specifies a conditional distribution on a manifold, counterfactuals may be analytically…
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
The field of query-by-example aims at inferring queries from output examples given by non-expert users, by finding the underlying logic that binds the examples. However, for a very small set of examples, it is difficult to correctly infer…
It is often said that the fundamental problem of causal inference is a missing data problem -- the comparison of responses to two hypothetical treatment assignments is made difficult because for every experimental unit only one potential…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…
We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the \emph{use criterion}, according to which in order for some premises to have some…
The question of \emph{knowledge}, \emph{truth} and \emph{trust} is explored via a mathematical formulation of claims and sources. We define truth as the reproducibly perceived subset of knowledge, formalize sources as having both generative…
A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for…
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…
We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any…