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Found 33 papers, 3 papers with code
l1-Norm Minimization with Regula Falsi Type Root Finding Methods
Sparse level-set formulations allow practitioners to find the minimum 1-norm solution subject to likelihood constraints.
Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning
Indeed, emerging methods in machine learning may be thought of as data-driven optimization techniques that are ideal for high-dimensional, non-convex, and constrained, multi-objective optimization problems, and that improve with increasing volumes of data.
A Proof of Principle: Multi-Modality Radiotherapy Optimization
In this paper, we propose a mathematical framework to optimize full radiation dose distributions and fractionation schedules of multiple radiation modalities, aiming to maximize the damage to the tumor while limiting the damage to the normal tissue to the corresponding tolerance level.
Optimization and Control Medical Physics
Trimmed Constrained Mixed Effects Models: Formulations and Algorithms
We consider ME models where the random effects component is linear.
A unified sparse optimization framework to learn parsimonious physics-informed models from data
This flexible approach can be tailored to the unique challenges associated with a wide range of applications and data sets, providing a powerful ML-based framework for learning governing models for physical systems from data.
A Unified Framework for Sparse Relaxed Regularized Regression: SR3
We demonstrate the advantages of SR3 (computational efficiency, higher accuracy, faster convergence rates, greater flexibility) across a range of regularized regression problems with synthetic and real data, including applications in compressed sensing, LASSO, matrix completion, TV regularization, and group sparsity.
Computer Assisted Localization of a Heart Arrhythmia
We consider the problem of locating a point-source heart arrhythmia using data from a standard diagnostic procedure, where a reference catheter is placed in the heart, and arrival times from a second diagnostic catheter are recorded as the diagnostic catheter moves around within the heart.
Learning Nonlinear Brain Dynamics: van der Pol Meets LSTM
Many real-world data sets, especially in biology, are produced by complex nonlinear dynamical systems.
Sparse Principal Component Analysis via Variable Projection
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales.
Mean Reverting Portfolios via Penalized OU-Likelihood Estimation
We study an optimization-based approach to con- struct a mean-reverting portfolio of assets.
Fast Robust Methods for Singular State-Space Models
We therefore suggest that the proposed approach be the {\it default choice} for estimating state space models outside of the Gaussian context, regardless of whether the error covariances are singular or not.
Learning Robust Representations for Computer Vision
Unsupervised learning techniques in computer vision often require learning latent representations, such as low-dimensional linear and non-linear subspaces.
Time Series Using Exponential Smoothing Cells
We propose a flexible model for time series analysis, using exponential smoothing cells for overlapping time windows.
Estimating Shape Parameters of Piecewise Linear-Quadratic Problems
The normalization constant inherent in this requirement helps to inform the optimization over shape parameters, giving a joint optimization problem over these as well as primary parameters of interest.
Boosting as a kernel-based method
We show that boosting with this learner is equivalent to estimation with a special {\it boosting kernel} that depends on $K$, as well as on the regression matrix, noise variance, and hyperparameters.
Beating level-set methods for 3D seismic data interpolation: a primal-dual alternating approach
Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to `fill in' data volumes from critically subsampled data acquired in the field.
Dynamic matrix factorization with social influence
Matrix factorization is a key component of collaborative filtering-based recommendation systems because it allows us to complete sparse user-by-item ratings matrices under a low-rank assumption that encodes the belief that similar users give similar ratings and that similar items garner similar ratings.
Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition
We focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants.
Automatic Inference of the Quantile Parameter
However, loss functions such as quantile and quantile Huber generalize the symmetric $\ell_1$ and Huber losses to the asymmetric setting, for a fixed quantile parameter.
Adaptive As-Natural-As-Possible Image Stitching
Computing the warp is fully automated and uses a combination of local homography and global similarity transformations, both of which are estimated with respect to the target.
Robust EM kernel-based methods for linear system identification
In this paper, we introduce a novel method to robustify kernel-based system identification methods.
Beyond L2-Loss Functions for Learning Sparse Models
We propose an algorithm to learn dictionaries and obtain sparse codes when the data reconstruction fidelity is measured using any smooth PLQ cost function.
Sparse Quantile Huber Regression for Efficient and Robust Estimation
We consider new formulations and methods for sparse quantile regression in the high-dimensional setting.
Outlier robust system identification: a Bayesian kernel-based approach
In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification.
Generalized system identification with stable spline kernels
This paper extends linear system identification to a wide class of nonsmooth stable spline estimators, where regularization functionals and data misfits can be selected from a rich set of piecewise linear-quadratic (PLQ) penalties.
Improvements to deep convolutional neural networks for LVCSR
We find that with these improvements, particularly with fMLLR and dropout, we are able to achieve an additional 2-3% relative improvement in WER on a 50-hour Broadcast News task over our previous best CNN baseline.
Accelerating Hessian-free optimization for deep neural networks by implicit preconditioning and sampling
This study aims at speeding up Hessian-free training, both by means of decreasing the amount of data used for training, as well as through reduction of the number of Krylov subspace solver iterations used for implicit estimation of the Hessian.
Semistochastic Quadratic Bound Methods
Batch methods based on the quadratic bound were recently proposed for this class of problems, and performed favorably in comparison to state-of-the-art techniques.
Fast Dual Variational Inference for Non-Conjugate LGMs
Latent Gaussian models (LGMs) are widely used in statistics and machine learning.
Fast methods for denoising matrix completion formulations, with applications to robust seismic data interpolation
In this paper, we consider matrix completion formulations designed to hit a target data-fitting error level provided by the user, and propose an algorithm called LR-BPDN that is able to exploit factorized formulations to solve the corresponding optimization problem.
The connection between Bayesian estimation of a Gaussian random field and RKHS
Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS).
Sparse/Robust Estimation and Kalman Smoothing with Nonsmooth Log-Concave Densities: Modeling, Computation, and Theory
We introduce a class of quadratic support (QS) functions, many of which play a crucial role in a variety of applications, including machine learning, robust statistical inference, sparsity promotion, and Kalman smoothing.
Smoothing Dynamic Systems with State-Dependent Covariance Matrices
One of the basic assumptions required to apply the Kalman smoothing framework is that error covariance matrices are known and given.
