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The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…
We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation { transforming the original…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
A convex optimization model predicts an output from an input by solving a convex optimization problem. The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
FOCal Underdetermined System Solver (FOCUSS) is a powerful tool for sparse representation and underdetermined inverse problems, which is extremely easy to implement. In this paper, we give a comprehensive convergence analysis on the FOCUSS…
Biased regularization and fine-tuning are two recent meta-learning approaches. They have been shown to be effective to tackle distributions of tasks, in which the tasks' target vectors are all close to a common meta-parameter vector.…
We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized…
Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization…
Inverse optimization (IO) aims to determine optimization model parameters from observed decisions. However, IO is not part of a data scientist's toolkit in practice, especially as many general-purpose machine learning packages are widely…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…
This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a…
We consider online fractional covering problems with a convex objective, where the covering constraints arrive over time. Formally, we want to solve $\min\,\{f(x) \mid Ax\ge \mathbf{1},\, x\ge 0\},$ where the objective function…
A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
This paper presents a Fuzzy Cognitive Map model to quantify implicit bias in structured datasets where features can be numeric or discrete. In our proposal, problem features are mapped to neural concepts that are initially activated by…
We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We present an abstract analysis for two…