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In applied research, Lee (2009) bounds are widely applied to bound the average treatment effect in the presence of selection bias. This paper extends the methodology of Lee bounds to accommodate outcomes in a general metric space, such as…
Rigorous guarantees about the performance of predictive algorithms are necessary in order to ensure their responsible use. Previous work has largely focused on bounding the expected loss of a predictor, but this is not sufficient in many…
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic…
We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each…
In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…
We propose data-dependent uniform generalization bounds by approaching the problem from a PAC-Bayesian perspective. We first apply the PAC-Bayesian framework on "random sets" in a rigorous way, where the training algorithm is assumed to…
A general approach is established for deriving one-shot performance bounds for information-theoretic problems on general alphabets beyond countable alphabets. It is mainly based on the quantization idea and a novel form of "likelihood…
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
We derive a Cram\'er-Rao lower bound for the variance of Floquet multiplier estimates that have been constructed from stable limit cycles perturbed by noise. To do so, we consider perturbed periodic orbits in the plane. We use a periodic…
We present a general approach, based on exponential inequalities, to derive bounds on the generalization error of randomized learning algorithms. Using this approach, we provide bounds on the average generalization error as well as bounds…
We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be…
Deep Probabilistic Programming (DPP) allows powerful models based on recursive computation to be learned using efficient deep-learning optimization techniques. Additionally, DPP offers a unified perspective, where inference and learning…
New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities…
With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
Effective bounds on the union probability are well known to be beneficial in the analysis of stochastic problems in many areas, including probability theory, information theory, statistical communications, computing and operations research.…
The evaluation of the probability of union of a large number of independent events requires several combinations involving the factorial and the use of high performance computers with several hours of processing. Bounds and simplifications…
PAC-Bayes is a popular and efficient framework for obtaining generalization guarantees in situations involving uncountable hypothesis spaces. Unfortunately, in its classical formulation, it only provides guarantees on the expected risk of a…
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…