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Quantum neural networks (QNNs) have shown remarkable potential due to their capability of representing complex functions within exponentially large Hilbert spaces. However, their application to multivariate regression tasks has been…
Quantum Machine Learning (QML) presents as a revolutionary approach to weather forecasting by using quantum computing to improve predictive modeling capabilities. In this study, we apply QML models, including Quantum Gated Recurrent Units…
Regression models that go beyond the mean, alongside coherent risk measures, have been important tools in modern data analysis. This paper introduces the innovative concept of Average Quantile Regression (AQR), which is smooth at the…
A two-stage approach is proposed to overcome the problem in quantile regression, where separately fitted curves for several quantiles may cross. The standard Bayesian quantile regression model is applied in the first stage, followed by a…
In this paper, we address the challenge of multivariate time-series forecasting using quantum machine learning techniques. We introduce adaptation strategies that extend variational quantum circuit models, traditionally limited to…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
Here, we propose a general method for probabilistic time series forecasting. We combine an autoregressive recurrent neural network to model temporal dynamics with Implicit Quantile Networks to learn a large class of distributions over a…
While neural networks are achieving high predictive accuracy in multi-horizon probabilistic forecasting, understanding the underlying mechanisms that lead to feature-conditioned outputs remains a significant challenge for forecasters. In…
This paper studies the inference problem in quantile regression (QR) for a large sample size $n$ but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A natural method is the na\"ive…
Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which…
Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (QRCM), is to model quantile regression coefficients as…
This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for…
Uncertainty analysis in the form of probabilistic forecasting can provide significant improvements in decision-making processes in the smart power grid for better integrating renewable energies such as wind. Whereas point forecasting…
We develop an online method that guarantees calibration of quantile forecasts at multiple quantile levels simultaneously. In this work, a sequence of quantile forecasts is said to be calibrated provided that its $\alpha$-level predictions…
We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial…
In this paper, we propose an invariant quantile regression (IQR) framework specifically designed for multi-environment datasets, which captures the invariance across different environments. This framework is closely related to transfer…
In this paper, we consider Bayesian methods for non-parametric quantile regressions with multiple continuous predictors ranging values in the unit interval. In the first method, the quantile function is assumed to be smooth over the…