185 research outputs found
Outlier detection using distributionally robust optimization under the Wasserstein metric
We present a Distributionally Robust Optimization (DRO) approach to outlier detection in a linear regression setting, where the closeness of probability distributions is measured using the Wasserstein metric. Training samples contaminated with outliers skew the regression plane computed by least squares and thus impede outlier detection. Classical approaches, such as robust regression, remedy this problem by downweighting the contribution of atypical data points. In contrast, our Wasserstein DRO approach hedges against a family of distributions that are close to the empirical distribution. We show that the resulting formulation encompasses a class of models, which include the regularized Least Absolute Deviation (LAD) as a special case. We provide new insights into the regularization term and give guidance on the selection of the regularization coefficient from the standpoint of a confidence region. We establish two types of performance guarantees for the solution to our formulation under mild conditions. One is related to its out-of-sample behavior, and the other concerns the discrepancy between the estimated and true regression planes. Extensive numerical results demonstrate the superiority of our approach to both robust regression and the regularized LAD in terms of estimation accuracy and outlier detection rates
Polyhedral Predictive Regions For Power System Applications
Despite substantial improvement in the development of forecasting approaches,
conditional and dynamic uncertainty estimates ought to be accommodated in
decision-making in power system operation and market, in order to yield either
cost-optimal decisions in expectation, or decision with probabilistic
guarantees. The representation of uncertainty serves as an interface between
forecasting and decision-making problems, with different approaches handling
various objects and their parameterization as input. Following substantial
developments based on scenario-based stochastic methods, robust and
chance-constrained optimization approaches have gained increasing attention.
These often rely on polyhedra as a representation of the convex envelope of
uncertainty. In the work, we aim to bridge the gap between the probabilistic
forecasting literature and such optimization approaches by generating forecasts
in the form of polyhedra with probabilistic guarantees. For that, we see
polyhedra as parameterized objects under alternative definitions (under
and norms), the parameters of which may be modelled and predicted.
We additionally discuss assessing the predictive skill of such multivariate
probabilistic forecasts. An application and related empirical investigation
results allow us to verify probabilistic calibration and predictive skills of
our polyhedra.Comment: 8 page
Rank-based Decomposable Losses in Machine Learning: A Survey
Recent works have revealed an essential paradigm in designing loss functions
that differentiate individual losses vs. aggregate losses. The individual loss
measures the quality of the model on a sample, while the aggregate loss
combines individual losses/scores over each training sample. Both have a common
procedure that aggregates a set of individual values to a single numerical
value. The ranking order reflects the most fundamental relation among
individual values in designing losses. In addition, decomposability, in which a
loss can be decomposed into an ensemble of individual terms, becomes a
significant property of organizing losses/scores. This survey provides a
systematic and comprehensive review of rank-based decomposable losses in
machine learning. Specifically, we provide a new taxonomy of loss functions
that follows the perspectives of aggregate loss and individual loss. We
identify the aggregator to form such losses, which are examples of set
functions. We organize the rank-based decomposable losses into eight
categories. Following these categories, we review the literature on rank-based
aggregate losses and rank-based individual losses. We describe general formulas
for these losses and connect them with existing research topics. We also
suggest future research directions spanning unexplored, remaining, and emerging
issues in rank-based decomposable losses.Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine
Intelligence (TPAMI
Data Consistency for Data-Driven Smart Energy Assessment
In the smart grid era, the number of data available for different applications has increased considerably. However, data could not perfectly represent the phenomenon or process under analysis, so their usability requires a preliminary validation carried out by experts of the specific domain. The process of data gathering and transmission over the communication channels has to be verified to ensure that data are provided in a useful format, and that no external effect has impacted on the correct data to be received.
Consistency of the data coming from different sources (in terms of timings and data resolution) has to be ensured and managed appropriately. Suitable procedures are needed for transforming data into knowledge in an effective way. This contribution addresses the previous aspects by highlighting a number of potential issues and the solutions in place in different power and energy system, including the generation, grid
and user sides. Recent references, as well as selected historical references, are listed to support the illustration of the conceptual aspects
Reweighted Mixup for Subpopulation Shift
Subpopulation shift exists widely in many real-world applications, which
refers to the training and test distributions that contain the same
subpopulation groups but with different subpopulation proportions. Ignoring
subpopulation shifts may lead to significant performance degradation and
fairness concerns. Importance reweighting is a classical and effective way to
handle the subpopulation shift. However, recent studies have recognized that
most of these approaches fail to improve the performance especially when
applied to over-parameterized neural networks which are capable of fitting any
training samples. In this work, we propose a simple yet practical framework,
called reweighted mixup (RMIX), to mitigate the overfitting issue in
over-parameterized models by conducting importance weighting on the ''mixed''
samples. Benefiting from leveraging reweighting in mixup, RMIX allows the model
to explore the vicinal space of minority samples more, thereby obtaining more
robust model against subpopulation shift. When the subpopulation memberships
are unknown, the training-trajectories-based uncertainty estimation is equipped
in the proposed RMIX to flexibly characterize the subpopulation distribution.
We also provide insightful theoretical analysis to verify that RMIX achieves
better generalization bounds over prior works. Further, we conduct extensive
empirical studies across a wide range of tasks to validate the effectiveness of
the proposed method.Comment: Journal version of arXiv:2209.0892
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