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We propose a novel framework for analyzing convergence rates of stochastic optimization algorithms with adaptive step sizes. This framework is based on analyzing properties of an underlying generic stochastic process, in particular by…
A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a…
Conformal risk control (CRC) is a recently proposed technique that applies post-hoc to a conventional point predictor to provide calibration guarantees. Generalizing conformal prediction (CP), with CRC, calibration is ensured for a set…
This note examines the question of randomness in a sequence based on the continued fraction (CF) representation of its corresponding representation as a number, or as D sequence. We propose a randomness measure that is directly equal to the…
Support vector machine (SVM) is a well known binary linear classification model in supervised learning. This paper proposes a globalized distributionally robust chance-constrained (GDRC) SVM model based on core sets to address uncertainties…
As an equilibrium refinement of the Nash equilibrium, evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory and has attracted growing interest. An ESS can be either a pure strategy or a mixed strategy. Even…
As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the uncertainty of the…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
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…
This paper presents a stochastic model predictive control (SMPC) algorithm for linear systems subject to additive Gaussian mixture disturbances, with the goal of satisfying chance constraints. We focus on a special case where each Gaussian…
Motivated by a broad range of potential applications, we address the quantile prediction problem of real-valued time series. We present a sequential quantile forecasting model based on the combination of a set of elementary nearest…
This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates. The first step is learning the dynamics of the system via Gaussian process…
The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in $[0,1]$. This distance plays a fundamental role in machine learning and signal…
This paper studies a formulation of 1-bit Compressed Sensing (CS) problem based on the maximum likelihood estimation framework. In order to solve the problem we apply the recently proposed Gradient Support Pursuit algorithm, with a minor…
The following working document summarizes our work on the clustering of financial time series. It was written for a workshop on information geometry and its application for image and signal processing. This workshop brought several experts…
Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…
Randomized experiments have become the standard method for companies to evaluate the performance of new products or services. In addition to augmenting managers' decision-making, experimentation mitigates risk by limiting the proportion of…
We consider universal inference in variance components models, focusing on settings where the parameter is near or at the boundary of the parameter set. Two cases, which are not handled by existing state-of-the-art methods, are of…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using…