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Given a probability measure $\mu$ supported on a convex subset $\Omega$ of Euclidean space $(\mathbb{R}^d,g_0)$, we are interested in obtaining Poincar\'e and log-Sobolev type inequalities on $(\Omega,g_0,\mu)$. To this end, we change the…
We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…
Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
Large language models can be aligned with human preferences through offline reinforcement learning (RL) on small labeled datasets. While single-objective alignment is well-studied, many real-world applications demand the simultaneous…
Optimal Experiment Design for parameter estimation in water networks has been traditionally formulated to maximize either hydraulic model accuracy or spatial coverage. Because a unique sensor configuration that optimizes both objectives may…
This work presents PESMOC, Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based strategy for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
Efficient assessment of convolved hidden Markov models is discussed. The bottom-layer is defined as an unobservable categorical first-order Markov chain, while the middle-layer is assumed to be a Gaussian spatial variable conditional on the…
Parameter reconstructions are indispensable in metrology. Here, the objective is to to explain $K$ experimental measurements by fitting to them a parameterized model of the measurement process. The model parameters are regularly determined…
Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and…
The Expected Improvement (EI) method, proposed by Jones et al. (1998), is a widely-used Bayesian optimization method, which makes use of a fitted Gaussian process model for efficient black-box optimization. However, one key drawback of EI…
Accurate monocular metric depth estimation (MMDE) is crucial to solving downstream tasks in 3D perception and modeling. However, the remarkable accuracy of recent MMDE methods is confined to their training domains. These methods fail to…
$E$-optimal experimental designs for a second-order response surface model with $k\geq1$ predictors are investigated. If the design space is the $k$-dimensional unit cube, Galil and Kiefer [J. Statist. Plann. Inference 1 (1977a) 121-132]…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…
We consider a meromorphic family of endomorphisms of degree at least 2 of a complex projective space that is parameterized by the unit disk.We prove that the measure of maximal entropy of these endomorphisms converges to the equilibrium…
The main objective of this paper is to apply linear and pretest shrinkage estimation techniques to estimating the parameters of two 2-parameter Burr-XII distributions. Further more, predictions for future observations are made using both…
Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate…
We consider the problem of constrained multi-objective blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number…