Related papers: On Some Problems of Confidence Region Construction
Recent advances in statistics introduced versions of the central limit theorem for high-dimensional vectors, allowing for the construction of confidence regions for high-dimensional parameters. In this note, $s$-sparsely convex…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Given the black box nature of machine learning models, a plethora of explainability methods have been developed to decipher the factors behind individual decisions. In this paper, we introduce a novel problem of black box (probabilistic)…
Assuming that one-step transition kernel of a discrete time, time-homogenous Markov chain model is parameterized by a parameter $\theta\in \boldsymbol \Theta$, we derive a recursive (in time) construction of confidence regions for the…
Classically, confidence intervals are required to have consistent coverage across all values of the parameter. However, this will inevitably break down if the underlying estimation procedure is biased. For this reason, many efforts have…
The compound broadcast channel with confidential messages (BCC) generalizes the BCC by modeling the uncertainty of the channel. For the compound BCC, it is only known that the actual channel realization belongs to a pre-specified…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
Embodied AI systems, comprising AI models and physical plants, are increasingly prevalent across various applications. Due to the rarity of system failures, ensuring their safety in complex operating environments remains a major challenge,…
We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables. Our approach builds on conformal prediction, a powerful framework to…
Certified defenses promise provable robustness guarantees. We study the malicious exploitation of probabilistic certification frameworks to better understand the limits of guarantee provisions. Now, the objective is to not only mislead a…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
The asymptotic results pertaining to the distribution of the log likelihood ratio allow for the creation of a confidence region, which is a general extension of the confidence interval. Two and three dimensional regions can be displayed…
The goal of this paper is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of the…
Trust-region algorithms can be applied to very abstract optimization problems because they do not require a specific direction of descent or gradient. This has lead to recent interest in them, in particular in the area of integer optimal…
Nearly all spatial reasoning problems involve uncertainty of one sort or another. Uncertainty arises due to the inaccuracies of sensors used in measuring distances and angles. We refer to this as directional uncertainty. Uncertainty also…
Conformal prediction offers a distribution-free framework for constructing prediction sets with coverage guarantees. In practice, multiple valid conformal prediction sets may be available, arising from different models or methodologies.…
The P versus NP problem is addressed in a context of provability and limitations on the possibility of finding sound axioms for formal theories. It is shown that if the term "constructible theory" is defined in a way which satisfies certain…
Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…
In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…
In human-AI interactions, explanation is widely seen as necessary for enabling trust in AI systems. We argue that trust, however, may be a pre-requisite because explanation is sometimes impossible. We derive this result from a formalization…