Related papers: On conditional Sibson's $\alpha$-Mutual Informatio…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…
Temporal information conveyed by language describes how the world around us changes through time. Events, durations and times are all temporal elements that can be viewed as intervals. These intervals are sometimes temporally related in…
To date, there has been no formal study of the statistical cost of interpretability in machine learning. As such, the discourse around potential trade-offs is often informal and misconceptions abound. In this work, we aim to initiate a…
The conditional Aalen--Johansen estimator, a general-purpose non-parametric estimator of conditional state occupation probabilities, is introduced. The estimator is applicable for any finite-state jump process and supports conditioning on…
Data-based decisionmaking must account for the manipulation of data by agents who are aware of how decisions are being made and want to affect their allocations. We study a framework in which, due to such manipulation, data becomes less…
Interaction information is one of the multivariate generalizations of mutual information, which expresses the amount information shared among a set of variables, beyond the information, which is shared in any proper subset of those…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic…
The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we…
This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…
In this paper, we define a new velocity having a dimension of $(Length)^{\alpha}/(Time)$ and a new acceleration having a dimension of $(Length)^{\alpha}/(Time)^2$, based on the fractional addition rule. We then discuss the fractional…
A formal theory based on a binary operator of directional associative relation is constructed in the article and an understanding of an associative normal form of image constructions is introduced. A model of a commutative semigroup, which…
In current practice a formal analysis of hybrid system models is assertion-based. The work presented here is based on features that look beyond functional correctness toward a quantitative evaluation of behavioral attributes. A feature…
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…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…
Partial information decompositions (PIDs), which quantify information interactions between three or more variables in terms of uniqueness, redundancy and synergy, are gaining traction in many application domains. However, our understanding…
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
Differential privacy is a precise mathematical constraint meant to ensure privacy of individual pieces of information in a database even while queries are being answered about the aggregate. Intuitively, one must come to terms with what…