Related papers: On Probability Leakage
The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many…
Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability…
It is shown that under reasonable assumptions a Drake-style equation can be obtained for the probability that our universe is the result of a deliberate simulation. Evaluating loose bounds for certain terms in the equation shows that the…
Privacy and transparency are two key foundations of trustworthy machine learning. Model explanations offer insights into a model's decisions on input data, whereas privacy is primarily concerned with protecting information about the…
A central concern of network operators is to estimate the probability of an incident that affects a significant part and thus may yield to a breakdown. We answer this question by modeling how a failure of either a node or an edge will…
A concrete, stylized example illustrates that inferences may be degraded, rather than improved, by incorporating supplementary data via a joint likelihood. In the example, the likelihood is assumed to be correctly specified, as is the prior…
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not…
Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…
The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…
A new measure of information leakage for quantum encoding of classical data is defined. An adversary can access a single copy of the state of a quantum system that encodes some classical data and is interested in correctly guessing a…
The inability to correctly resolve rumours circulating online can have harmful real-world consequences. We present a method for incorporating model and data uncertainty estimates into natural language processing models for automatic rumour…
By probabilistic means, the concept of contextuality is extended so that it can be used in non-ideal situations. An inequality is presented, which at least in principle enables a test to discard non-contextual hidden-variable models at low…
Large language models (LLMs) have recently been applied to forecasting tasks, with some works claiming these systems match or exceed human performance. In this paper, we argue that, as a community, we should be careful about such…
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
Physical implementations of cryptographic algorithms leak information, which makes them vulnerable to so-called side-channel attacks. The problem of secure computation in the presence of leakage is generally known as leakage resilience. In…
Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…
We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly, for defining the misspecification risk of a…
We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a…