Related papers: A Flexible, Scalable and Efficient Algorithmic Fra…
In recent years, there is a growing interest in combining techniques attributed to the areas of Statistics and Machine Learning in order to obtain the benefits of both approaches. In this article, the statistical technique lasso for…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
Time-series datasets are central in machine learning with applications in numerous fields of science and engineering, such as biomedicine, Earth observation, and network analysis. Extensive research exists on state-space models (SSMs),…
We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
In this paper, we study the problem of minimizing a sum of convex objective functions, which are locally available to agents in a network. Distributed optimization algorithms make it possible for the agents to cooperatively solve the…
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems.…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
The advent of parameter-efficient fine-tuning methods has significantly reduced the computational burden of adapting large-scale pretrained models to diverse downstream tasks. However, existing approaches often struggle to achieve robust…
We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…
We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D…
Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…