Madhurima Panja

Tanujit Chakraborty, Ujjwal Reddy K S, Shraddha M. Naik et al.

Since their inception in 2014, Generative Adversarial Networks (GANs) have rapidly emerged as powerful tools for generating realistic and diverse data across various domains, including computer vision and other applied areas. Consisting of a discriminative network and a generative network engaged in a Minimax game, GANs have revolutionized the field of generative modeling. In February 2018, GAN secured the leading spot on the ``Top Ten Global Breakthrough Technologies List'' issued by the Massachusetts Science and Technology Review. Over the years, numerous advancements have been proposed, leading to a rich array of GAN variants, such as conditional GAN, Wasserstein GAN, CycleGAN, and StyleGAN, among many others. This survey aims to provide a general overview of GANs, summarizing the latent architecture, validation metrics, and application areas of the most widely recognized variants. We also delve into recent theoretical developments, exploring the profound connection between the adversarial principle underlying GAN and Jensen-Shannon divergence, while discussing the optimality characteristics of the GAN framework. The efficiency of GAN variants and their model architectures will be evaluated along with training obstacles as well as training solutions. In addition, a detailed discussion will be provided, examining the integration of GANs with newly developed deep learning frameworks such as Transformers, Physics-Informed Neural Networks, Large Language models, and Diffusion models. Finally, we reveal several issues as well as future research outlines in this field.

Madhurima Panja, Tanujit Chakraborty, Uttam Kumar et al.

Forecasting time series data is a critical area of research with applications spanning from stock prices to early epidemic prediction. While numerous statistical and machine learning methods have been proposed, real-life prediction problems often require hybrid solutions that bridge classical forecasting approaches and modern neural network models. In this study, we introduce the Probabilistic AutoRegressive Neural Networks (PARNN), capable of handling complex time series data exhibiting non-stationarity, nonlinearity, non-seasonality, long-range dependence, and chaotic patterns. PARNN is constructed by improving autoregressive neural networks (ARNN) using autoregressive integrated moving average (ARIMA) feedback error, combining the explainability, scalability, and "white-box-like" prediction behavior of both models. Notably, the PARNN model provides uncertainty quantification through prediction intervals, setting it apart from advanced deep learning tools. Through comprehensive computational experiments, we evaluate the performance of PARNN against standard statistical, machine learning, and deep learning models, including Transformers, NBeats, and DeepAR. Diverse real-world datasets from macroeconomics, tourism, epidemiology, and other domains are employed for short-term, medium-term, and long-term forecasting evaluations. Our results demonstrate the superiority of PARNN across various forecast horizons, surpassing the state-of-the-art forecasters. The proposed PARNN model offers a valuable hybrid solution for accurate long-range forecasting. By effectively capturing the complexities present in time series data, it outperforms existing methods in terms of accuracy and reliability. The ability to quantify uncertainty through prediction intervals further enhances the model's usefulness in decision-making processes.

Madhurima Panja, Tanujit Chakraborty, Sk Shahid Nadim et al.

Dengue fever is a virulent disease spreading over 100 tropical and subtropical countries in Africa, the Americas, and Asia. This arboviral disease affects around 400 million people globally, severely distressing the healthcare systems. The unavailability of a specific drug and ready-to-use vaccine makes the situation worse. Hence, policymakers must rely on early warning systems to control intervention-related decisions. Forecasts routinely provide critical information for dangerous epidemic events. However, the available forecasting models (e.g., weather-driven mechanistic, statistical time series, and machine learning models) lack a clear understanding of different components to improve prediction accuracy and often provide unstable and unreliable forecasts. This study proposes an ensemble wavelet neural network with exogenous factor(s) (XEWNet) model that can produce reliable estimates for dengue outbreak prediction for three geographical regions, namely San Juan, Iquitos, and Ahmedabad. The proposed XEWNet model is flexible and can easily incorporate exogenous climate variable(s) confirmed by statistical causality tests in its scalable framework. The proposed model is an integrated approach that uses wavelet transformation into an ensemble neural network framework that helps in generating more reliable long-term forecasts. The proposed XEWNet allows complex non-linear relationships between the dengue incidence cases and rainfall; however, mathematically interpretable, fast in execution, and easily comprehensible. The proposal's competitiveness is measured using computational experiments based on various statistical metrics and several statistical comparison tests. In comparison with statistical, machine learning, and deep learning methods, our proposed XEWNet performs better in 75% of the cases for short-term and long-term forecasting of dengue incidence.

Madhurima Panja, Tanujit Chakraborty, Uttam Kumar et al.

Infectious diseases remain among the top contributors to human illness and death worldwide, among which many diseases produce epidemic waves of infection. The unavailability of specific drugs and ready-to-use vaccines to prevent most of these epidemics makes the situation worse. These force public health officials and policymakers to rely on early warning systems generated by reliable and accurate forecasts of epidemics. Accurate forecasts of epidemics can assist stakeholders in tailoring countermeasures, such as vaccination campaigns, staff scheduling, and resource allocation, to the situation at hand, which could translate to reductions in the impact of a disease. Unfortunately, most of these past epidemics exhibit nonlinear and non-stationary characteristics due to their spreading fluctuations based on seasonal-dependent variability and the nature of these epidemics. We analyse a wide variety of epidemic time series datasets using a maximal overlap discrete wavelet transform (MODWT) based autoregressive neural network and call it EWNet model. MODWT techniques effectively characterize non-stationary behavior and seasonal dependencies in the epidemic time series and improve the nonlinear forecasting scheme of the autoregressive neural network in the proposed ensemble wavelet network framework. From a nonlinear time series viewpoint, we explore the asymptotic stationarity of the proposed EWNet model to show the asymptotic behavior of the associated Markov Chain. We also theoretically investigate the effect of learning stability and the choice of hidden neurons in the proposal. From a practical perspective, we compare our proposed EWNet framework with several statistical, machine learning, and deep learning models. Experimental results show that the proposed EWNet is highly competitive compared to the state-of-the-art epidemic forecasting methods.

Madhurima Panja, Danny D'Agostino, Huitao Li et al.

The increasing adoption of data-driven decision-making in public health has established epidemic forecasting as a critical area of research. Recent advances in multivariate forecasting models better capture complex temporal dependencies than conventional univariate approaches, which model individual series independently. Despite this potential, the development of robust epidemic forecasting methods is constrained by the lack of high-quality benchmarks comprising diverse multivariate datasets across infectious diseases and geographical regions. To address this gap, we present EpiCastBench, a large-scale benchmarking framework featuring 40 curated (correlated) multivariate epidemic datasets. These publicly available datasets span a wide range of infectious diseases and exhibit diverse characteristics in terms of temporal granularity, series length, and sparsity. We analyze these datasets to identify their global features and structural patterns. To ensure reproducibility and fair comparison, we establish standardized evaluation settings, including a unified forecasting horizon, consistent preprocessing pipelines, diverse performance metrics, and statistical significance testing. By leveraging this framework, we conduct a comprehensive evaluation of 15 multivariate forecasting models spanning statistical baselines to state-of-the-art deep learning and foundation models. All datasets and code are publicly available on Kaggle (https://www.kaggle.com/datasets/aimltsf/epicastbench) and GitHub (https://github.com/aimltsf/EpiCastBench).

Yash Jakhmola, Madhurima Panja, Nitish Kumar Mishra et al.

Spatiotemporal forecasting of traffic flow data represents a typical problem in the field of machine learning, impacting urban traffic management systems. In general, spatiotemporal forecasting problems involve complex interactions, nonlinearities, and long-range dependencies due to the interwoven nature of the temporal and spatial dimensions. Due to this, traditional statistical and machine learning methods cannot adequately handle the temporal and spatial dependencies in these complex traffic flow datasets. A prevalent approach in the field combines graph convolutional networks and multi-head attention mechanisms for spatiotemporal processing. This paper proposes a wavelet-based temporal attention model, namely a wavelet-based dynamic spatiotemporal aware graph neural network (W-DSTAGNN), for tackling the traffic forecasting problem. Wavelet decomposition can help by decomposing the signal into components that can be analyzed independently, reducing the impact of non-stationarity and handling long-range dependencies of traffic flow datasets. Benchmark experiments using three popularly used statistical metrics confirm that our proposal efficiently captures spatiotemporal correlations and outperforms ten state-of-the-art models (including both temporal and spatiotemporal benchmarks) on three publicly available traffic datasets. Our proposed ensemble method can better handle dynamic temporal and spatial dependencies and make reliable long-term forecasts. In addition to point forecasts, our proposed model can generate interval forecasts that significantly enhance probabilistic forecasting for traffic datasets.

Rajdeep Pathak, Rahul Goswami, Madhurima Panja et al.

Reliable uncertainty quantification is critical in multivariate time series forecasting problems arising in domains such as energy systems and transportation networks, among many others. Although Transformer-based architectures have recently achieved strong performance for sequence modeling, most probabilistic forecasting approaches rely on restrictive parametric likelihoods or quantile-based objectives. They can struggle to capture complex joint predictive distributions across multiple correlated time series. This work proposes EnTransformer, a deep generative forecasting framework that integrates engression, a stochastic learning paradigm for modeling conditional distributions, with the expressive sequence modeling capabilities of Transformers. The proposed approach injects stochastic noise into the model representation and optimizes an energy-based scoring objective to directly learn the conditional predictive distribution without imposing parametric assumptions. This design enables EnTransformer to generate coherent multivariate forecast trajectories while preserving Transformers' capacity to effectively model long-range temporal dependencies and cross-series interactions. We evaluate our proposed EnTransformer on several widely used benchmarks for multivariate probabilistic forecasting, including Electricity, Traffic, Solar, Taxi, KDD-cup, and Wikipedia datasets. Experimental results demonstrate that EnTransformer produces well-calibrated probabilistic forecasts and consistently outperforms the benchmark models.

Nourin Jahan, Madhurima Panja, Muhammed Navas T et al.

Urban air quality forecasting is challenging because pollutant concentrations are nonlinear, nonstationary, spatiotemporally dependent, and often affected by anomalous observations caused by traffic congestion, industrial emissions, and seasonal meteorological variability. This study proposes a Graph Convolutional Support Vector Regression (GCSVR) framework for robust spatiotemporal forecasting of urban air pollution. The model combines graph convolutional learning to capture inter-station spatial dependence with support vector regression to model nonlinear temporal dynamics while reducing sensitivity to outlier observations. The proposed framework is evaluated using air quality records from 37 monitoring stations in Delhi and 18 stations in Mumbai, representing inland and coastal metropolitan environments in India. Forecasting performance is assessed across multiple horizons and compared with established temporal and spatiotemporal benchmarks. The results show that GCSVR consistently improves predictive accuracy and maintains stable performance across seasons and outlier-prone pollution episodes. Statistical test further confirms the reliability of the proposed approach across the two cities. Finally, conformal prediction is integrated with GCSVR to generate calibrated prediction intervals, enhancing its practical value for uncertainty-aware air quality monitoring and public health decision-making.

Madhab Barman, Madhurima Panja, Nachiketa Mishra et al.

Tuberculosis (TB) remains a formidable global health challenge, driven by complex spatiotemporal transmission dynamics and influenced by factors such as population mobility and behavioral changes. We propose an Epidemic-Guided Deep Learning (EGDL) approach that fuses mechanistic epidemiological principles with advanced deep learning techniques to enhance early warning systems and intervention strategies for TB outbreaks. Our framework is built upon a modified networked Susceptible-Infectious-Recovered (MN-SIR) model augmented with a saturated incidence rate and graph Laplacian diffusion, capturing both long-term transmission dynamics and region-specific population mobility patterns. Compartmental model parameters are rigorously estimated using Bayesian inference via the Markov Chain Monte Carlo approach. Theoretical analysis leveraging the comparison principle and Green's formula establishes global stability properties of the disease-free and endemic equilibria. Building on these epidemiological insights, we design two forecasting architectures, EGDL-Parallel and EGDL-Series, that integrate the mechanistic outputs of the MN-SIR model within deep neural networks. This integration mitigates the overfitting risks commonly encountered in data-driven methods and filters out noise inherent in surveillance data, resulting in reliable forecasts of real-world epidemic trends. Experiments conducted on TB incidence data from 47 prefectures in Japan and 31 provinces in mainland China demonstrate that our approach delivers robust and accurate predictions across multiple time horizons (short to medium-term forecasts), supporting its generalizability across regions with different population dynamics.

Tanujit Chakraborty, Donia Besher, Madhurima Panja et al.

Accurate forecasting of exchange rates remains a persistent challenge, particularly for emerging economies such as Brazil, Russia, India, and China (BRIC). These series exhibit long memory, nonlinearity, and non-stationarity properties that conventional time series models struggle to capture. Additionally, there exist several key drivers of exchange rate dynamics, including global economic policy uncertainty, US equity market volatility, US monetary policy uncertainty, oil price growth rates, and country-specific short-term interest rate differentials. These empirical complexities underscore the need for a flexible modeling framework that can jointly accommodate long memory, nonlinearity, and the influence of external drivers. To address these challenges, we propose a Neural AutoRegressive Fractionally Integrated Moving Average (NARFIMA) model that combines the long-memory representation of ARFIMA with the nonlinear learning capacity of neural networks, while flexibly incorporating exogenous causal variables. We establish theoretical properties of the model, including asymptotic stationarity of the NARFIMA process using Markov chains and nonlinear time series techniques. We quantify forecast uncertainty using conformal prediction intervals within the NARFIMA framework. Empirical results across six forecast horizons show that NARFIMA consistently outperforms various state-of-the-art statistical and machine learning models in forecasting BRIC exchange rates. These findings provide new insights for policymakers and market participants navigating volatile financial conditions. The \texttt{narfima} \textbf{R} package provides an implementation of our approach.

Madhurima Panja, Grace Younes, Tanujit Chakraborty

Chaotic time series are notoriously difficult to forecast. Small uncertainties in initial conditions amplify rapidly, while strong nonlinearities and regime dependent variability constrain predictability. Although modern deep learning often delivers strong short horizon accuracy, its black box nature limits scientific insight and practical trust in settings where understanding the underlying dynamics matters. To address this gap, we propose two complementary symbolic forecasters that learn explicit, interpretable algebraic equations from chaotic time series data. Symbolic Neural Forecaster (SyNF) adapts a neural network based equation learning architecture to the forecasting setting, enabling fully differentiable discovery of compact and interpretable algebraic relations. The Symbolic Tree Forecaster (SyTF) builds on evolutionary symbolic regression to search directly over equation structures under a principled accuracy complexity trade off. We evaluate both approaches in a rolling window nowcasting setting with one step ahead forecasting using several accuracy metrics and compare against a broad suite of baselines spanning classical statistical models, tree ensembles, and modern deep learning architectures. Numerical experiments cover a benchmark of 132 low dimensional chaotic attractors and two real world chaotic time series, namely weekly dengue incidence in San Juan and the Nino 3.4 sea surface temperature index. Across datasets, symbolic forecasters achieve competitive one step ahead accuracy while providing transparent equations that reveal salient aspects of the underlying dynamics.

Madhurima Panja, Dhiman Das, Tanujit Chakraborty et al.

Understanding and forecasting precipitation events in the Arctic maritime environments, such as Bear Island and Ny-Ålesund, is crucial for assessing climate risk and developing early warning systems in vulnerable marine regions. This study proposes a probabilistic machine learning framework for modeling and predicting the dynamics and severity of precipitation. We begin by analyzing the scale-dependent relationships between precipitation and key atmospheric drivers (e.g., temperature, relative humidity, cloud cover, and air pressure) using wavelet coherence, which captures localized dependencies across time and frequency domains. To assess joint causal influences, we employ Synergistic-Unique-Redundant Decomposition, which quantifies the impact of interaction effects among each variable on future precipitation dynamics. These insights inform the development of data-driven forecasting models that incorporate both historical precipitation and causal climate drivers. To account for uncertainty, we employ the conformal prediction method, which enables the generation of calibrated non-parametric prediction intervals. Our results underscore the importance of utilizing a comprehensive framework that combines causal analysis with probabilistic forecasting to enhance the reliability and interpretability of precipitation predictions in Arctic marine environments.

Shraddha M. Naik, Tanujit Chakraborty, Madhurima Panja et al.

Real-world datasets often exhibit imbalanced data distribution, where certain class levels are severely underrepresented. In such cases, traditional pattern classifiers have shown a bias towards the majority class, impeding accurate predictions for the minority class. This paper introduces an imbalanced data-oriented classifier using probabilistic neural networks (PNN) with a skew-normal kernel function to address this major challenge. PNN is known for providing probabilistic outputs, enabling quantification of prediction confidence, interpretability, and the ability to handle limited data. By leveraging the skew-normal distribution, which offers increased flexibility, particularly for imbalanced and non-symmetric data, our proposed Skew-Probabilistic Neural Networks (SkewPNN) can better represent underlying class densities. Hyperparameter fine-tuning is imperative to optimize the performance of the proposed approach on imbalanced datasets. To this end, we employ a population-based heuristic algorithm, the Bat optimization algorithm, to explore the hyperparameter space effectively. We also prove the statistical consistency of the density estimates, suggesting that the true distribution will be approached smoothly as the sample size increases. Theoretical analysis of the computational complexity of the proposed SkewPNN and BA-SkewPNN is also provided. Numerical simulations have been conducted on different synthetic datasets, comparing various benchmark-imbalanced learners. Real-data analysis on several datasets shows that SkewPNN and BA-SkewPNN substantially outperform most state-of-the-art machine-learning methods for both balanced and imbalanced datasets (binary and multi-class categories) in most experimental settings.