Related papers: Tempered Christoffel-Weighted Polynomial Chaos Exp…
In this work we study propagation of chaos for solutions of the Liouville equation for the classical discrete Cucker-Smale system. Assuming that the communication kernel satisfies the heavy tail condition -- known to be necessary to induce…
Gradient compression has surfaced as a key technique to address the challenge of communication efficiency in distributed learning. In distributed deep learning, however, it is observed that gradient distributions are heavy-tailed, with…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…
This letter proposes a novel and highly efficient distribution system state estimation (DSSE) algorithm with nonlinear measurements from supervisory control and data acquisition (SCADA) systems. Conventional DSSE, i.e., a weighted least…
To facilitate effective decision-making, precipitation datasets should include uncertainty estimates. Quantile regression with machine learning has been proposed for issuing such estimates. Distributional regression offers distinct…
In this study, we investigated the stability of dynamic mode decomposition (DMD) algorithms to noisy data. To achieve a stable DMD algorithm, we applied the truncated total least squares (T-TLS) regression and optimal truncation level…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
Assessing small-signal stability of power systems composed of thousands of interacting generators is a computationally challenging task. To reduce the computational burden, this paper introduces a novel condition to assess and certify…
We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy-tailed response variable. In this distribution-free regression setting, we show that boundedness of the conditional second…
Conformal Predictive Systems (CPS) offer a versatile framework for constructing predictive distributions, allowing for calibrated inference and informative decision-making. However, their applicability has been limited to scenarios adhering…
The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…
We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame- work. Our method is motivated by generalized Polynomial…
We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive…
To ensure that real-world infrastructure is safe and durable, systems are designed to not fail for any but the most rarely occurring parameter values. By only happening deep in the tails of the parameter distribution, failure probabilities…
Microgrids (MGs) are regarded as effective solutions to provide ramping support to the main grid during heavy-load periods. Nevertheless, the uncertain renewable energy sources (RES) and electric vehicles (EVs) integrated into an MG may…
Weighting methods are essential tools for estimating causal effects in observational studies, with the goal of balancing pre-treatment covariates across treatment groups. Traditional approaches pursue this objective indirectly, for example,…
This paper addresses the challenge of forecasting corporate distress, a problem marked by three key statistical hurdles: (i) right censoring, (ii) high-dimensional predictors, and (iii) mixed-frequency data. To overcome these complexities,…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional…
Increasing frequency and intensity of extreme weather events motivates the assessment of power system resilience. The random nature of power system failures during these events mandates probabilistic resilience assessment, but…