Related papers: An Unconstrained Optimization Approach to Moment F…
In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
Hierarchical models allow for heterogeneous behaviours in a population while simultaneously borrowing estimation strength across all subpopulations. Unfortunately, existing likelihood-based methods for fitting hierarchical models have high…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
In this paper, we consider statistical estimation of time-inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi-state life insurance to model the biometric states of an…
We study the fully generalized Grover's algorithm to find the optimal phase changes for each step of the iteration to maximize gain in probability of observation of the target, and when phase matching is required. We find that classical…
Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution $\pi$ defined on a space $(\Theta,\mathcal{T})$ consist of the simulation of realisations of Markov chains $\{\theta_{n},n\geq1\}$ of invariant distribution…
The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
This paper is concerned with a recently developed paradigm for population-based optimization, termed particle filter optimization (PFO). This paradigm is attractive in terms of coherence in theory and easiness in mathematical analysis and…
We study a class of two-stage stochastic programs, namely, those with fixed recourse matrix and fixed costs, and linear second stage. We show that, under mild assumptions, the problem can be solved with just one scenario, which we call an…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation. This fixed approach is inefficient because of a dynamic trade-off between cost and speed -- larger batches are more…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…
Achieving valid conditional coverage in conformal prediction is challenging due to the theoretical difficulty of satisfying pointwise constraints in finite samples. Building upon the characterization of conditional coverage through marginal…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
Current instance segmentation models achieve high performance on average predictions, but lack principled uncertainty quantification: their outputs are not calibrated, and there is no guarantee that a predicted mask is close to the ground…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…