Related papers: Novel Computational Methods for High-Dimensional S…
In order to numerically solve high-dimensional nonlinear PDEs and alleviate the curse of dimensionality, a stochastic particle method (SPM) has been proposed to capture the relevant feature of the solution through the adaptive evolution of…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest these systems are analytically intractable, and one has to resort to computational methods to…
We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions. Our formulation is based on…
This paper develops a novel change point identification method for high-dimensional data using random projections. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for…
Sample average approximation--based stochastic dynamic programming (SDP) and model predictive control (MPC) are two different methods for approaching multistage stochastic optimization. In this paper we investigate the conditions under…
The presence of uncertainty in material properties and geometry of a structure is ubiquitous. The design of robust engineering structures, therefore, needs to incorporate uncertainty in the optimization process. Stochastic gradient descent…
Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…
Dynamic discrete choice models are widely employed to answer substantive and policy questions in settings where individuals' current choices have future implications. However, estimation of these models is often computationally intensive…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…
Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…
In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the…
At the scale of the individual cell, protein production is a stochastic process with multiple time scales, combining quick and slow random steps with discontinuous and smooth variation. Hybrid stochastic processes, in particular…
A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…
We introduce a new approach for deterministic sensitivity analysis of Markov reward processes, commonly used in cost-effectiveness analyses, via reformulation into a polynomial system. Our approach leverages cylindrical algebraic…
Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…
Safety in stochastic control systems, which are subject to random noise with a known probability distribution, aims to compute policies that satisfy predefined operational constraints with high confidence throughout the uncertain evolution…