Related papers: Isotonic conditional laws
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
We introduce a basic intuitionistic conditional logic $\mathsf{IntCK}$ that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that…
The recent years have seen interest into the possibility for (classical as well as quantum) causal structures that, while remaining logically consistent, feature a cyclic causal order between events, opening intriguing possibilities for new…
In-context learning (ICL) is a recent advancement in the capabilities of large language models (LLMs). This feature allows users to perform a new task without updating the model. Concretely, users can address tasks during the inference time…
In-context learning (ICL) i.e. showing LLMs only a few task-specific demonstrations has led to downstream gains with no task-specific fine-tuning required. However, LLMs are sensitive to the choice of prompts, and therefore a crucial…
Conformal predictors are machine learning algorithms that output prediction sets that have a guarantee of marginal validity for finite samples with minimal distributional assumptions. This is a property that makes conformal predictors…
In-context learning (ICL) has emerged as a powerful paradigm for adapting large language models (LLMs) to new and data-scarce tasks using only a few carefully selected task-specific examples presented in the prompt. However, given the…
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…
In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…
Inverse Constraint Learning (ICL) is the problem of inferring constraints from safe (i.e., constraint-satisfying) demonstrations. The hope is that these inferred constraints can then be used downstream to search for safe policies for new…
In standard classification, we typically treat class categories as independent of one-another. In many problems, however, we would be neglecting the natural relations that exist between categories, which are often dictated by an underlying…
In this paper, we establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of sample correlation matrix $R$, constructed from a $p\times n$ data matrix $X$ with independent and identically distributed (i.i.d.)…
Motivated by recent development of mean-field systems with common noise, this paper establishes Ito's formula for flows of conditional probability measures under a common filtration associated with general semimartingales. This generalizes…
Inferring causal relationships from dynamical systems is the central interest of many scientific inquiries. Conditional local independence, which describes whether the evolution of one process is influenced by another process given…
A new version of a Strong Law of Large Numbers is proposed in this note for pairwise independent random variables. The main goal is to relax the assumption on a finite expectation for each term.
Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…
State-of-the-art SAT solvers are nowadays able to handle huge real-world instances. The key to this success is the so-called Conflict-Driven Clause-Learning (CDCL) scheme, which encompasses a number of techniques that exploit the conflicts…
Real-world applications of large language models (LLMs) in computational social science (CSS) tasks primarily depend on the effectiveness of instruction tuning (IT) or in-context learning (ICL). While IT has shown highly effective at…
Forecasts for uncertain future events should be probabilistic. Probabilistic forecasts are commonly issued as prediction intervals, which provide a measure of uncertainty in the unknown outcome whilst being easier to understand and…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…