相关论文: Exponentially Weighted l_2 Regularization Strategy…

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…

Trainable activation functions, whose parameters are optimized alongside network weights, offer increased expressivity compared to fixed activation functions. Specifically, trainable activation functions defined as ratios of polynomials…

We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our…

Recently, an interesting phenomenon called grokking has gained much attention, where generalization occurs long after the models have initially overfitted the training data. We try to understand this seemingly strange phenomenon through the…

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with…

We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…

We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…

Motivated by deep neural networks, the deep Gaussian process (DGP) generalizes the standard GP by stacking multiple layers of GPs. Despite the enhanced expressiveness, GP, as an $L_2$ regularization prior, tends to be over-smooth and…

We consider the estimation of smoothing parameters and variance components in models with a regular log likelihood subject to quadratic penalization of the model coefficients, via a generalization of the method of Fellner (1986) and Schall…

This paper employs a policy iteration reinforcement learning (RL) method to study continuous-time linear-quadratic mean-field control problems in infinite horizon. The drift and diffusion terms in the dynamics involve the states, the…

We consider an important problem in signal processing, which consists in finding the sparsest solution of a linear system $\Phi x=b$. This problem has applications in several areas, but is NP-hard in general. Usually an alternative convex…

We use the polynomial partitioning method of Guth to prove weighted Fourier restriction estimates in $\Bbb R^3$ with exponents $p$ that range between $3$ and $3.25$, depending on the weight. As a corollary to our main theorem, we obtain new…

Type-2 fuzzy set (T2 FS) were introduced by Zadeh in 1965, and the membership degrees of T2 FSs are type-1 fuzzy sets (T1 FSs). Owing to the fuzziness of membership degrees, T2 FSs can better model the uncertainty of real life, and thus,…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

Building on previous research of Chi and Chi (2022), the current paper revisits estimation in robust structured regression under the $\text{L}_2\text{E}$ criterion. We adopt the majorization-minimization (MM) principle to design a new…

It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of…

The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…

Mappings from biological sequences (DNA, RNA, protein) to quantitative measures of sequence functionality play an important role in contemporary biology. We are interested in the related tasks of (i) inferring predictive…

Fuzzy rough set theory is effective for processing datasets with complex attributes, supported by a solid mathematical foundation and closely linked to kernel methods in machine learning. Attribute reduction algorithms and classifiers based…

This paper introduces a novel data-driven approach to design a linear quadratic regulator (LQR) using a reinforcement learning (RL) algorithm that does not require a system model. The key contribution is to perform policy iteration (PI) by…