Spectrahedral Regression
Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data, i.e. a function that is the maximum eigenvalue of an affine matrix expression of the input. This method represents a significant generalization of polyhedral (also called max-affine) regression, in which a polyhedral function (a maximum of a fixed number of affine functions) is fit to the data. We prove bounds on how well spectrahedral functions can approximate arbitrary convex functions via statistical risk analysis. We also analyze an alternating minimization algorithm for the non-convex optimization problem of fitting the best spectrahedral function to a given data set. We show that this algorithm converges geometrically with high probability to a small ball around the optimal parameter given a good initialization. Finally, we demonstrate the utility of our approach with experiments on synthetic data sets as well as real data arising in applications such as economics and engineering design.
Code (0)
등록된 구현이 없습니다.
Tasks
regressionSimilar Papers 제목 키워드 기반
Sparse Spectrahedral Shadows for State Estimation and Reachability Analysis: Set Operations, Validations and Order Reductions
Set representations are the foundation of various set-based approaches in state estimation, reachability analysis and fault diagnosis. In this paper, we investigate spectrahedral shadows, a class of nonlinear geometric o…
Fault DiagnosisState EstimationDictionary Learning under Symmetries via Group Representations
The dictionary learning problem can be viewed as a data-driven process to learn a suitable transformation so that data is sparsely represented directly from example data. In this paper, we examine the problem of learning…
Dictionary LearningDimensionality ReductionMulti-Object TrackingObject Tracking+1Convex Relaxations of SE(2) and SE(3) for Visual Pose Estimation
This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of $SE(2)$ and $SE(3)$. The approach can use dense point cloud data from stereo vision …
Pose EstimationCertified Safety Radii in Forecast-Error Space for Wasserstein Distributionally Robust Small Signal Stability-Constrained AC Optimal Power Flow via Lifted Spectrahedral Containment
Directly robustifying small-signal stability in AC optimal power flow is challenging since the stability boundary in the original uncertainty space is implicit, highly nonconvex, and changes with the operating decision. …
Evaluating Hospital Case Cost Prediction Models Using Azure Machine Learning Studio
Ability for accurate hospital case cost modelling and prediction is critical for efficient health care financial management and budgetary planning. A variety of regression machine learning algorithms are known to be effe…
BIG-bench Machine LearningGaussian ProcessesManagementregression