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The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
A lot is known about the H\"older regularity of stochastic processes, in particular in the case of Gaussian processes. Recently, a finer analysis of the local regularity of functions, termed 2-microlocal analysis, has been introduced in a…
Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…
Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…
Experimental comparisons of performance represent an important aspect of research on optimization algorithms. In this work we present a methodology for defining the required sample sizes for designing experiments with desired statistical…
Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
Many modern statistical applications involve a two-level sampling scheme that first samples subjects from a population and then samples observations on each subject. These schemes often are designed to learn both the population-level…
In many change point problems it is reasonable to assume that compared to a benchmark at a given time point $t_0$ the properties of the observed stochastic process change gradually over time for $t >t_0$. Often, these gradual changes are…
We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…
This work employs variational techniques to revisit and expand the construction and analysis of extreme value processes. These techniques permit a novel study of spatial statistics of the location of minimizing events. We develop integral…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted…
The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density $\pi$, when we are only able to estimate an unnormalized version of $\pi$…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…