Related papers: Positivity: Identifiability and Estimability
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
Existing preference optimization methods often assume scenarios where paired preference feedback (preferred/positive vs. dis-preferred/negative examples) is available. This requirement limits their applicability in scenarios where only…
Classification is the task of predicting the class labels of objects based on the observation of their features. In contrast, quantification has been defined as the task of determining the prevalences of the different sorts of class labels…
In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item. Specifically, we assume that there are multiple disjoint \emph{semi-defective…
We present a novel, input-output data-driven approach to uncertainty model identification. As the true bounds and distributions of system uncertainties ultimately remain unknown, we depart from the goal of identifying the uncertainty model…
Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…
Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs. This idea has been extended to quantum mechanics through a completely…
Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for…
How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences.…
We introduce the notion of a stochastic probabilistic program and present a reference implementation of a probabilistic programming facility supporting specification of stochastic probabilistic programs and inference in them. Stochastic…
When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…
Statistical matching methods are widely used in the social and health sciences to estimate causal effects using observational data. Often the objective is to find comparable groups with similar covariate distributions in a dataset, with the…
Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…
We provide the first formal definition of reward hacking, a phenomenon where optimizing an imperfect proxy reward function leads to poor performance according to the true reward function. We say that a proxy is unhackable if increasing the…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…
Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and…
The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the…