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Contraction coefficients give a quantitative strengthening of the data processing inequality. As such, they have many natural applications whenever closer analysis of information processing is required. However, it is often challenging to…
How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information…
Quantifying uncertainty in automatically generated text is important for letting humans check potential hallucinations and making systems more reliable. Conformal prediction is an attractive framework to provide predictions imbued with…
This paper discusses the design of an extremum seeking controller that relies on a monitoring function for a class of SISO uncertain nonlinear systems characterized by arbitrary and uncertain relative degree. Our demonstration illustrates…
We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
This paper discusses the importance of uncovering uncertainty in end-to-end dialog tasks, and presents our experimental results on uncertainty classification on the Ubuntu Dialog Corpus. We show that, instead of retraining models for this…
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
In Euclidean space there is a trivial upper bound on the maximum length of a compound "walk" built up of variable-length jumps, and a considerably less trivial lower bound on its minimum length. The existence of this non-trivial lower bound…
A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…
In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer…
Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
While optimal control theory offers effective strategies for minimizing energetic costs in noisy microscopic systems over finite durations, a significant opportunity lies in exploiting the temporal structure of non-equilibrium forces. We…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
In this paper, for a geometrically integral projective scheme, we will give an upper bound of the product of the norms of its non-geometrically integral reductions over an arbitrary number field. For this aim, we take the adelic viewpoint…
This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…
In order to certify performance and safety, feedback control requires precise characterization of sensor errors. In this paper, we provide guarantees on such feedback systems when sensors are characterized by solving a supervised learning…
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…
It is well known that if a submartingale $X$ is bounded then the increasing predictable process $Y$ and the martingale $M$ from the Doob decomposition $% X=Y+M$ can be unbounded. In this paper for some classes of increasing convex functions…