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A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit…
Nonlinear Model Predictive Control (NMPC) is a powerful and widely used technique for nonlinear dynamic process control under constraints. In NMPC, the state and control weights of the corresponding state and control costs are commonly…
Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…
In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which…
Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy data sets with applications in data mining, text recognition, dimension reduction, face…
Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
We consider a class of doubly weighted rank-based estimating methods for the transformation (or accelerated failure time) model with missing data as arise, for example, in case-cohort studies. The weights considered may not be predictable…
We develop a constructive approach for $\ell_0$-penalized estimation in the sparse accelerated failure time (AFT) model with high-dimensional covariates. Our proposed method is based on Stute's weighted least squares criterion combined with…
We propose a novel approach to input design for identification of nonlinear state space models. The optimal input sequence is obtained by maximizing a scalar cost function of the Fisher information matrix. Since the Fisher information…
We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a…
Variable selection for recovering sparsity in nonadditive nonparametric models has been challenging. This problem becomes even more difficult due to complications in modeling unknown interaction terms among high dimensional variables. There…
In this paper, we develop a nonparametric system identification method for the nonlinear gradient-flow dynamics. In these systems, the vector field is the gradient field of a potential energy function. This fundamental fact about the…
For many profilometry techniques, phase unwrapping is one of the most challenging process. In order to sidestep the phase unwrapping process, Perciante et. al [Appl Opt 2015; 54(10):3018-23] proposed a wrapping-free method based on the…
The identification of multivariable state space models in innovation form is solved in a subspace identification framework using convex nuclear norm optimization. The convex optimization approach allows to include constraints on the unknown…
A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is…
We present an SMT-based active learning algorithm for nondeterministic weighted automata (WFAs) as a practical and robust alternative to Hankel/L*-style methods. Our algorithm is parametric in a given semiring and, if it terminates,…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…