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While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
This paper is about the recent notion of computably probably approximately correct learning, which lies between the statistical learning theory where there is no computational requirement on the learner and efficient PAC where the learner…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
Iterated Belief Change is the research area that investigates principles for the dynamics of beliefs over (possibly unlimited) many subsequent belief changes. In this paper, we demonstrate how iterated belief change is connected to…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…
In modern scientific experiments, we frequently encounter data that have large dimensions, and in some experiments, such high dimensional data arrive sequentially rather than full data being available all at a time. We develop multiple…
Claims about recursive self-improvement in AI often slide from repeated internal revision to the possibility of qualitatively stronger capability without clearly distinguishing the underlying computational regimes. This paper gives a formal…
In computerized adaptive testing (CAT), items (questions) are selected in real time based on the already observed responses, so that the ability of the examinee can be estimated as accurately as possible. This is typically formulated as a…
We study the problem of quantifying epistemic predictive uncertainty (EPU) -- that is, uncertainty faced at prediction time due to the existence of multiple plausible predictive models -- within the framework of conformal prediction (CP).…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…
When prospectively developing a new clinical prediction model (CPM), fixed sample size calculations are typically conducted before data collection based on sensible assumptions. But if the assumptions are inaccurate the actual sample size…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
Contextual online decision-making problems with constraints appear in a wide range of real-world applications, such as adaptive experimental design under safety constraints, personalized recommendation with resource limits, and dynamic…
Sequential recommender systems have achieved steady gains in offline accuracy, yet it remains unclear how close current models are to the intrinsic accuracy limit imposed by the data. A reliable, model-agnostic estimate of this ceiling…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…