Related papers: Gradient flows and randomised thresholding: sparse…
State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. By enforcing such representation to be sparse, sparse subspace clustering is…
Modern large scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as…
We explore an explicit link between stochastic gradient descent using common batching strategies and splitting methods for ordinary differential equations. From this perspective, we introduce a new minibatching strategy (called Symmetric…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
This paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the function value at the considered point by the averaged function value over a ball (in $l_1$-norm or…
We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
Recent investigations have established the physical relevance of spatially-localized instability mechanisms in fluid dynamics and their potential for technological innovations in flow control. In this letter, we show that the mathematical…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…