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Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…
We study the problem of estimating the parameters of a regression model from a set of observations, each consisting of a response and a predictor. The response is assumed to be related to the predictor via a regression model of unknown…
Regularization methods, specifically those which directly alter weights like $L_1$ and $L_2$, are an integral part of many learning algorithms. Both the regularizers mentioned above are formulated by assuming certain priors in the parameter…
We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning…
Random graph models are widely used to understand network properties and graph algorithms. Key to such analyses are the different parameters of each model, which affect various network features, such as its size, clustering, or degree…
Recently, a novel family of biologically plausible online algorithms for reducing the dimensionality of streaming data has been derived from the similarity matching principle. In these algorithms, the number of output dimensions can be…
The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify…
High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to…
Streaming analysis is widely used in cloud as well as edge infrastructures. In these contexts, fine-grained application performance can be based on accurate modeling of streaming operators. This is especially beneficial for computationally…
Artistic style transfer is the problem of synthesizing an image with content similar to a given image and style similar to another. Although recent feed-forward neural networks can generate stylized images in real-time, these models produce…
This paper discusses the incorporation of local sparsity information, e.g. in each pixel of an image, via minimization of the $\ell^{1,\infty}$-norm. We discuss the basic properties of this norm when used as a regularization functional and…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
Understanding and tuning the performance of extreme-scale parallel computing systems demands a streaming approach due to the computational cost of applying offline algorithms to vast amounts of performance log data. Analyzing large…