arXiv subjects

Anubhab Biswas

Publications and source records attributed to Anubhab Biswas.

3 recordsLinked to original sources

arXiv2026

Nonlinear Probabilistic Forecast Reconciliation

Forecast reconciliation adjusts independently generated forecasts across multiple time series so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems involve nonlinear relationships among time series. In this paper, we address probabilistic forecast reconciliation with nonlinear constraints for the first time. We extend both reconciliation via projection and conditioning to the case of nonlinear constraints. The former approach reconciles forecast samples by mapping them onto the nonlinear coherent manifold. The latter approach conditions the joint forecast distribution on the constraints; the reconciled distribution is approximated with an algorithm based on the Unscented Kalman Filter (UKF). We evaluate both methods on synthetic and real datasets. Empirically, both reconciliation approaches generally improve forecast accuracy. The UKF-based approach achieves the best overall performance, is consistently retained in the Model Confidence Set -- either alone or alongside other reconciliation methods -- and is substantially faster than the projection-based approach.

stat.ME↗

arXiv2026

Nonlinear reconciliation: Error reduction theorems

Forecast reconciliation, an ex-post technique applied to forecasts that must satisfy constraints, has been a prominent topic in the forecasting literature over the past two decades. Recently, several efforts have sought to extend reconciliation methods to the probabilistic settings. Nevertheless, formal theorems demonstrating error reduction in nonlinear constraints, analogous to those presented in Panagiotelis et al.(2021), are still lacking. This paper addresses that gap by establishing such theorems for various classes of nonlinear hypersurfaces and vector-valued functions. Specifically, we derive an exact analog of Theorem 3.1 from Panagiotelis et al.(2021) for hypersurfaces with constant-sign curvature. Additionally, we provide an error reduction theorem for the broader case of hypersurfaces with non-constant-sign curvature and for general manifolds with codimension > 1. To support reproducibility and practical adoption, we release a JAX-based Python package, JNLR, implementing the presented theorems and reconciliation procedures.

cs.LG↗

arXiv2025

E-STGCN: Extreme Spatiotemporal Graph Convolutional Networks for Air Quality Forecasting

Modeling and forecasting air quality is crucial for effective air pollution management and protecting public health. Air quality data, characterized by nonlinearity, nonstationarity, and spatiotemporal correlations, often include extreme pollutant levels in severely polluted cities (e.g., Delhi, the capital of India). This is ignored by various geometric deep learning models, such as Spatiotemporal Graph Convolutional Networks (STGCN), which are otherwise effective for spatiotemporal forecasting. This study develops an extreme value theory (EVT) guided modified STGCN model (E-STGCN) for air pollution data to incorporate extreme behavior across pollutant concentrations. E-STGCN combines graph convolutional networks for spatial modeling and EVT-guided long short-term memory units for temporal sequence learning. Along with spatial and temporal components, it incorporates a generalized Pareto distribution to capture the extreme behavior of different air pollutants and embed this information into the learning process. The proposal is then applied to analyze air pollution data of 37 monitoring stations across Delhi, India. The forecasting performance for different test horizons is compared to benchmark forecasters (both temporal and spatiotemporal). It is found that E-STGCN has consistent performance across all seasons. The robustness of our results has also been evaluated empirically. Moreover, combined with conformal prediction, E-STGCN can produce probabilistic prediction intervals.

stat.AP↗