Related papers: Composite Lp-quantile regression, near quantile re…
The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…
Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is…
Modern datasets arising from social media, genomics, and biomedical informatics are often heterogeneous and (ultra) high-dimensional, creating substantial challenges for conventional modeling techniques. Quantile regression (QR) not only…
To make inferences about the shape of a population distribution, the widely popular mean regression model, for example, is inadequate if the distribution is not approximately Gaussian (or symmetric). Compared to conventional mean regression…
We are interested in renewable estimations and algorithms for nonparametric models with streaming data. In our method, the nonparametric function of interest is expressed through a functional depending on a weight function and a conditional…
Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…
Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…
In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold…
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and…
In this paper we propose the adaptive lasso for predictive quantile regression (ALQR). Reflecting empirical findings, we allow predictors to have various degrees of persistence and exhibit different signal strengths. The number of…
Post-training quantization of Large Language Models (LLMs) is challenging. In this work, we introduce Low-rank Quantization Error Reduction (LQER), which combines quantization and low-rank approximation to recover the model capability. LQER…
Low-rank multivariate regression (LRMR) is an important statistical learning model that combines highly correlated tasks as a multiresponse regression problem with low-rank priori on the coefficient matrix. In this paper, we study quantized…
Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple…
Recent advances in large language model (LLM) pretraining have led to high-quality LLMs with impressive abilities. By compressing such LLMs via quantization to 3-4 bits per parameter, they can fit into memory-limited devices such as laptops…
Ordinal classification has been widely applied in many high-stakes applications, e.g., medical imaging and diagnosis, where reliable uncertainty quantification (UQ) is essential for decision making. Conformal prediction (CP) is a general UQ…
The quantification of uncertainty in prediction models is crucial for reliable decision-making, yet remains a significant challenge. Interval time series forecasting offers a principled solution to this problem by providing prediction…
Quantile regression is fundamental to distributional modeling, yet independent estimation of multiple quantiles frequently produces crossing -- where estimated quantile functions violate monotonicity, implying impossible negative…
A collection of quantile curves provides a complete picture of conditional distributions. Properly centered and scaled versions of estimated curves at various quantile levels give rise to the so-called quantile regression process (QRP). In…
This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The…
In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…