Related papers: Pessimistic Cardinality Estimation
This article provides a critical review of the main methods used to produce conservative estimators of probabilities of rare events, or critical failures, for reliability and certification studies in the broadest sense. These probabilities…
This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
In many applications, accurate class probability estimates are required, but many types of models produce poor quality probability estimates despite achieving acceptable classification accuracy. Even though probability calibration has been…
Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…
We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
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…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Models such as finite state automata are widely used to abstract the behavior of software systems by capturing the sequences of events observable during their execution. Nevertheless, models rarely exist in practice and, when they do, get…
In a sequential regression setting, a decision-maker may be primarily concerned with whether the future observation will increase or decrease compared to the current one, rather than the actual value of the future observation. In this…
We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to canonical correlation analysis. The challenge is to adjust for the selection…
Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…
The standard mathematical approach to fourth-down decision making in American football is to make the decision that maximizes estimated win probability. Win probability estimates arise from machine learning models fit from historical data.…
Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is…
Large language models (LLMs) are stochastic, and not all models give deterministic answers, even when setting temperature to zero with a fixed random seed. However, few benchmark studies attempt to quantify uncertainty, partly due to the…
In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…
Calibration is a popular framework to evaluate whether a classifier knows when it does not know - i.e., its predictive probabilities are a good indication of how likely a prediction is to be correct. Correctness is commonly estimated…
Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…