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Constraint-based structure learning algorithms infer the causal structure of multivariate systems from observational data by determining an equivalent class of causal structures compatible with the conditional independencies in the data.…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
When does society eventually learn the truth, or take the correct action, via observational learning? In a general model of sequential learning over social networks, we identify a simple condition for learning dubbed excludability.…
Estimating causal quantities traditionally relies on bespoke estimators tailored to specific assumptions. Recently proposed Causal Foundation Models (CFMs) promise a more unified approach by amortising causal discovery and inference in a…
We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define…
This paper is devoted to the construction of conditional logic system of {\L}ukasiewicz m-valued propositional logic. We construct conditional logic system {\L}CR based on {\L}ukasiewicz m-valued propositional logic. We construct world…
We study distribution-free predictive inference for data with group symmetries, aiming to establish near-conditional coverage guarantees beyond exchangeability for structured data. While many predictive inference methods achieve a target…
Response-adaptive allocation designs refer to a class of designs where the probability an observation is assigned to a treatment is changed throughout an experiment based on the accrued responses. Such procedures result in random treatment…
The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
The earth system is exceedingly complex and often chaotic in nature, making prediction incredibly challenging: we cannot expect to make perfect predictions all of the time. Instead, we look for specific states of the system that lead to…
Generalization in reinforcement learning (RL) remains a significant challenge, especially when agents encounter novel environments with unseen dynamics. Drawing inspiration from human compositional reasoning -- where known components are…
Conditional Random Fields (CRFs) are undirected graphical models, a special case of which correspond to conditionally-trained finite state machines. A key advantage of these models is their great flexibility to include a wide array of…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images.…
In this paper, we investigate knowledge reasoning within a simple framework called knowledge structure. We use variable forgetting as a basic operation for one agent to reason about its own or other agents\ knowledge. In our framework, two…
The problem of Information Retrieval is, given a set of documents D and a query q, providing an algorithm for retrieving all documents in D relevant to q. However, retrieval should depend and be updated whenever the user is able to provide…
A central problem to understanding intelligence is the concept of generalisation. This allows previously learnt structure to be exploited to solve tasks in novel situations differing in their particularities. We take inspiration from…
The combinatorial basis of entropy by Boltzmann can be written $H= {N}^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy of a system, per unit entity, $N$ is the number of entities and $\mathbb{W}$ is the number of ways in which…
Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among…