Related papers: Risk Bounds for Quantile Trend Filtering
We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved…
Linear regression models have been extensively considered in the literature. However, in some practical applications they may not be appropriate all over the range of the covariate. In this paper, a more flexible model is introduced by…
We investigate different methods for regularizing quantile regression when predicting either a subset of quantiles or the full inverse CDF. We show that minimizing an expected pinball loss over a continuous distribution of quantiles is a…
This paper considers estimation and model selection of quantile vector autoregression (QVAR). Conventional quantile regression often yields undesirable crossing quantile curves, violating the monotonicity of quantiles. To address this…
We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…
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…
There is currently a huge effort to understand the potential and limitations of variational quantum machine learning (QML) based on the optimization of parameterized quantum circuits. Recent proposals toward dequantizing variational QML…
In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor.…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
When data are collected subject to a detection limit, observations below the detection limit may be considered censored. In addition, the domain of such observations may be restricted; for example, values may be required to be non-negative.…
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems…
We develop new semiparametric methods for estimating treatment effects. We focus on settings where the outcome distributions may be thick tailed, where treatment effects may be small, where sample sizes are large and where assignment is…
In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…
Finding the hedge ratios for a portfolio and risk compression is the same mathematical problem. Traditionally, regression is used for this purpose. However, regression has its own limitations. For example, in a regression model, we can't…
Quantile regression and partial frontier are two distinct approaches to nonparametric quantile frontier estimation. In this article, we demonstrate that partial frontiers are not quantiles. Both convex and nonconvex technologies are…
Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…
This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…
This paper develops a semi-parametric procedure for estimation of unconditional quantile partial effects using quantile regression coefficients. The estimator is based on an identification result showing that, for continuous covariates,…