Related papers: On the Treatment of Optimization Problems with L1 …
Sparsity-inducing penalties are useful tools for variable selection and they are also effective for regression settings where the data are functions. We consider the problem of selecting not only variables but also decision boundaries in…
In text classification, the problem of overfitting arises due to the high dimensionality, making regularization essential. Although classic regularizers provide sparsity, they fail to return highly accurate models. On the contrary,…
In this paper we consider high-dimensional multiclass classification by sparse multinomial logistic regression. We propose first a feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size…
Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effective under strong regularity assumptions, but…
There are different problems for resolution of complex LC-MS or GC-MS data, such as the existence of embedded chromatographic peaks, continuum background and overlapping in mass channels for different components. These problems cause…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual…
Deep learning models form one of the most powerful machine learning models for the extraction of important features. Most of the designs of deep neural models, i.e., the initialization of parameters, are still manually tuned. Hence,…
We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in machine learning, statistics and signal processing. It is well known that a…
Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…
This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context,…
We consider the l1-regularized Markowitz model, where a l1-penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution. The l1-penalty term can…
The optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…
Scaling the capacity of language models has consistently proven to be a reliable approach for improving performance and unlocking new capabilities. Capacity can be primarily defined by two dimensions: the number of model parameters and the…
Compressed sensing of sparse sources can be improved by incorporating prior knowledge of the source. In this paper we demonstrate a method for optimal selection of weights in weighted $L_1$ norm minimization for a noiseless reconstruction…
Stochastic computer simulations enable users to gain new insights into complex physical systems. Optimization is a common problem in this context: users seek to find model inputs that maximize the expected value of an objective function.…
We study two factors in neural network training: data parallelism and sparsity; here, data parallelism means processing training data in parallel using distributed systems (or equivalently increasing batch size), so that training can be…
Regularization has long been utilized to learn sparsity in deep neural network pruning. However, its role is mainly explored in the small penalty strength regime. In this work, we extend its application to a new scenario where the…