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In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
Supervised machine learning and predictive models have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction,…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…
A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a…
Uncertainty in machine learning refers to the degree of confidence or lack thereof in a model's predictions. While uncertainty quantification methods exist, explanations of uncertainty, especially in high-dimensional settings, remain an…
This paper examines the quantities used by MYCIN to reason with uncertainty, called certainty factors. It is shown that the original definition of certainty factors is inconsistent with the functions used in MYCIN to combine the quantities.…
When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…
With the rise of increasingly powerful and user-facing NLP systems, there is growing interest in assessing whether they have a good representation of uncertainty by evaluating the quality of their predictive distribution over outcomes. We…
Model uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…
Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…
Transfer learning is a powerful technique for knowledge-sharing between different tasks. Recent work has found that the representations of models with certain invariances, such as to adversarial input perturbations, achieve higher…
Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…
Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the…
The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…