3,186 research outputs found
Doubly Robust Smoothing of Dynamical Processes via Outlier Sparsity Constraints
Coping with outliers contaminating dynamical processes is of major importance
in various applications because mismatches from nominal models are not uncommon
in practice. In this context, the present paper develops novel fixed-lag and
fixed-interval smoothing algorithms that are robust to outliers simultaneously
present in the measurements {\it and} in the state dynamics. Outliers are
handled through auxiliary unknown variables that are jointly estimated along
with the state based on the least-squares criterion that is regularized with
the -norm of the outliers in order to effect sparsity control. The
resultant iterative estimators rely on coordinate descent and the alternating
direction method of multipliers, are expressed in closed form per iteration,
and are provably convergent. Additional attractive features of the novel doubly
robust smoother include: i) ability to handle both types of outliers; ii)
universality to unknown nominal noise and outlier distributions; iii)
flexibility to encompass maximum a posteriori optimal estimators with reliable
performance under nominal conditions; and iv) improved performance relative to
competing alternatives at comparable complexity, as corroborated via simulated
tests.Comment: Submitted to IEEE Trans. on Signal Processin
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Sparse projections onto the simplex
Most learning methods with rank or sparsity constraints use convex
relaxations, which lead to optimization with the nuclear norm or the
-norm. However, several important learning applications cannot benefit
from this approach as they feature these convex norms as constraints in
addition to the non-convex rank and sparsity constraints. In this setting, we
derive efficient sparse projections onto the simplex and its extension, and
illustrate how to use them to solve high-dimensional learning problems in
quantum tomography, sparse density estimation and portfolio selection with
non-convex constraints.Comment: 9 Page
- …