Related papers: Generalized L$_p$-norm joint inversion of gravity …

$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…

We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood…

This paper presents an in-depth analysis of the generalized isotonic recursive partitioning (GIRP) algorithm for fitting isotonic models under separable convex losses, proposed by Luss and Rosset [J. Comput. Graph. Statist., 23 (2014), pp.…

Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…

This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a…

Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…

State-space models (SSMs) are a common tool for modeling multi-variate discrete-time signals. The linear-Gaussian (LG) SSM is widely applied as it allows for a closed-form solution at inference, if the model parameters are known. However,…

Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

Regularized optimization has been a classical approach to solving imaging inverse problems, where the regularization term enforces desirable properties of the unknown image. Recently, the integration of flow matching generative models into…

In groundwater hydrology, geophysical imaging holds considerable promise for improving parameter estimation, due to the generally high resolution and spatial coverage of geophysical data. However, inversion of geophysical data alone cannot…

This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global…

In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…

Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited…

In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the…

The generalization capacity of various machine learning models exhibits different phenomena in the under- and over-parameterized regimes. In this paper, we focus on regression models such as feature regression and kernel regression and…

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

Stochastic gradient descent (SGD) has been widely studied in the literature from different angles, and is commonly employed for solving many big data machine learning problems. However, the averaging technique, which combines all iterative…

To fully uncover the great potential of deep neural networks (DNNs), various learning algorithms have been developed to improve the model's generalization ability. Recently, sharpness-aware minimization (SAM) establishes a generic scheme…

We investigate the use of Tikhonov regularization with the minimum support stabilizer for underdetermined 2-D inversion of gravity data. This stabilizer produces models with non-smooth properties which is useful for identifying geologic…