Related papers: An optimality property of the Bayes-Kelly algorith…
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…
Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having…
In this letter, we propose and experimentally test a quantumness criterion for single systems. The criterion is based on the violation of an already reported classical inequality. This inequality is expressed in terms of joint probabilities…
The vast majority of statistical theory on binary classification characterizes performance in terms of accuracy. However, accuracy is known in many cases to poorly reflect the practical consequences of classification error, most famously in…
This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the…
Although the Karush-Kuhn-Tucker conditions suggest a connection between a conic optimization problem and a complementarity problem, it is difficult to find an accessible explicit form of this relationship in the literature. This note will…
This paper presents a theory of error in cross-validation testing of algorithms for predicting real-valued attributes. The theory justifies the claim that predicting real-valued attributes requires balancing the conflicting demands of…
Naive Bayes classifiers have proven to be useful in many prediction problems with complete training data. Here we consider the situation where a naive Bayes classifier is trained with data where the response is right censored. Such…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
The k-satisfiability problem is a well-known task in computational complexity theory. In this paper approach for it's solving is introduced.
Field experiments are often difficult and expensive to make. To bypass these issues, industrial companies have developed computational codes. These codes intend to be representative of the physical system, but come with a certain amount of…
This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution $P$ over $\{0,1\}^n$, given sample access to $P$. We show that the sample complexity of the problem is…
Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al.…
We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found.…
A sender commits to an experiment to persuade a receiver. Accounting for the sender's experiment-choice incentives, and not presupposing a receiver tie-breaking rule when indifferent, we characterize when the sender's equilibrium payoff is…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
This paper introduces a conformal inference method to evaluate uncertainty in classification by generating prediction sets with valid coverage conditional on adaptively chosen features. These features are carefully selected to reflect…
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…
Herding and kernel herding are deterministic methods of choosing samples which summarise a probability distribution. A related task is choosing samples for estimating integrals using Bayesian quadrature. We show that the criterion minimised…
In nonstandard testing environments, researchers often derive ad hoc tests with correct (asymptotic) size, but their optimality properties are typically unknown a priori and difficult to assess. This paper develops a numerical framework for…