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Many current applications use recommendations in order to modify the natural user behavior, such as to increase the number of sales or the time spent on a website. This results in a gap between the final recommendation objective and the…
Multivariate categorical data are common in many fields. We are motivated by election polls studies assessing evidence of changes in voters opinions with their candidates preferences in the 2016 United States Presidential primaries or…
Duda, Hart, and Nilsson have set forth a method for rule-based inference systems to use in updating the probabilities of hypotheses on the basis of multiple items of new evidence. Pednault, Zucker, and Muresan claimed to give conditions…
We study the interpretability of conditional probability estimates for binary classification under the agnostic setting or scenario. Under the agnostic setting, conditional probability estimates do not necessarily reflect the true…
A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore…
Many ideas in modern control and reinforcement learning treat decision-making as inference: start from a baseline distribution and update it when a signal arrives. We ask when this can be made literal rather than metaphorical. We study the…
Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
Conformal predictors are set predictors that are automatically valid in the sense of having coverage probability equal to or exceeding a given confidence level. Inductive conformal predictors are a computationally efficient version of…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
Before we combine actions and probabilities two very obvious questions should be asked. Firstly, what does "the probability of an action" mean? Secondly, how does probability interact with nondeterminism? Neither question has a single…
Bayesian optimization is a class of data efficient model based algorithms typically focused on global optimization. We consider the more general case where a user is faced with multiple problems that each need to be optimized conditional on…
Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…
We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively…