Related papers: A new approach to data assimilation initialization…

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…

In the context of distributed estimation, we consider the problem of sensor collaboration, which refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. While incorporating the cost of…

Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in…

The most effective dimensionality reduction procedures produce interpretable features from the raw input space while also providing good performance for downstream supervised learning tasks. For many methods, this requires optimizing one or…

Predicting missing segments in partially observed functions is challenging due to infinite-dimensionality, complex dependence within and across observations, and irregular noise. These challenges are further exacerbated by the existence of…

State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…

Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…

This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…

In the big data era, integrating diverse data modalities poses significant challenges, particularly in complex fields like healthcare. This paper introduces a new process model for multimodal Data Fusion for Data Mining, integrating…

The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is…

We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the…

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…

Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…

With the growing prevalence of diabetes and the associated public health burden, it is crucial to identify modifiable factors that could improve patients' glycemic control. In this work, we seek to examine associations between medication…

This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…

In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…

This paper considers the ill-posed data assimilation problem associated with hyperbolic/parabolic systems describing 2D coupled sound and heat flow. Given hypothetical data at time T > 0, that may not correspond to an actual solution of the…

Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…

In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…

Using piezoelectric impedance/admittance sensing for structural health monitoring is promising, owing to the simplicity in circuitry design as well as the high-frequency interrogation capability. The actual identification of fault location…