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We investigate two asymmetric loss functions, namely LINEX loss and power divergence loss for optimal spatial prediction with area-level data. With our motivation arising from the real estate industry, namely in real estate valuation, we…
Building an accurate load forecasting model with minimal underpredictions is vital to prevent any undesired power outages due to underproduction of electricity. However, the power consumption patterns of the residential sector contain…
Divergence measures have a long association with statistical inference, machine learning and information theory. The density power divergence and related measures have produced many useful (and popular) statistical procedures, which provide…
Accurately forecasting the probability distribution of phenomena of interest is a classic and ever more widespread goal in statistics and decision theory. In comparison to point forecasts, probabilistic forecasts aim to provide a more…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
This letter establishes the asymptotic optimality of equal power allocation for measurements of a continuous wide-sense stationary (WSS) random process with a square-integrable autocorrelation function when linear estimation is used on…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…
This paper provides a systematic investigation into the various nonlinear objective functions which can be used to explore the feasible space associated with the optimal power flow problem. A total of 40 nonlinear objective functions are…
This paper extends the mathematical theory of axisymmetrization and vorticity depletion within the two-dimensional (2D) Euler equations, with an emphasis on the dynamics of radially symmetric, monotonic vorticity profiles. By analyzing…
This paper proposes a novel asymmetric continuous probabilistic score (ACPS) for evaluating and comparing density forecasts. It extends the proposed score and defines a weighted version, which emphasizes regions of interest, such as the…
We analyze and contrast two ways to train machine learning models for solving AC optimal power flow (OPF) problems, distinguished with the loss functions used. The first trains a mapping from the loads to the optimal dispatch decisions,…
We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize only this information to numerically approximate the…
The objective of this paper is to improve the accuracy and robustness of optimal power flow (OPF) formulations for distribution systems modeled down to the low-voltage point of connection of individual buildings. An approach for addressing…
Azimuthal asymmetries play an important role in scattering processes with polarized particles. This paper introduces a new procedure using event weighting to extract these asymmetries. It is shown that the resulting estimator has several…
We introduce novel variants of momentum by incorporating the variance of the stochastic loss function. The variance characterizes the confidence or uncertainty of the local features of the averaged loss surface across the i.i.d. subsets of…
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
In most machine learning training paradigms a fixed, often handcrafted, loss function is assumed to be a good proxy for an underlying evaluation metric. In this work we assess this assumption by meta-learning an adaptive loss function to…
The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they…