Snehashish Chakraverty

Sandeep Kumar Samota, Snehashish Chakraverty, Narayan Sethi

Poverty is a complex dynamic challenge that cannot be adequately captured using predefined differential equations. Nowadays, artificial machine learning (ML) methods have demonstrated significant potential in modelling real-world dynamical systems. Among these, Neural Ordinary Differential Equations (Neural ODEs) have emerged as a powerful, data-driven approach for learning continuous-time dynamics directly from observations. This chapter applies the Neural ODE framework to analyze poverty dynamics in the Indian state of Odisha. Specifically, we utilize time-series data from 2007 to 2020 on the key indicators of economic development and poverty reduction. Within the Neural ODE architecture, the temporal gradient of the system is represented by a multi-layer perceptron (MLP). The obtained neural dynamical system is integrated using a numerical ODE solver to obtain the trajectory of over time. In backpropagation, the adjoint sensitivity method is utilized for gradient computation during training to facilitate effective backpropagation through the ODE solver. The trained Neural ODE model reproduces the observed data with high accuracy. This demonstrates the capability of Neural ODE to capture the dynamics of the poverty indicator of concrete-structured households. The obtained results show that ML methods, such as Neural ODEs, can serve as effective tools for modeling socioeconomic transitions. It can provide policymakers with reliable projections, supporting more informed and effective decision-making for poverty alleviation.

Sandeep Kumar Samota, Reema Gupta, Snehashish Chakraverty

This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends and variations together in this type of data. To tackle this, a Variational Neural Stochastic Differential Equation (V-NSDE) model is designed that combines the expressive dynamics of Neural SDEs with the generative capabilities of Variational Autoencoders (VAEs). This model uses an encoder and a decoder. The encoder takes the initial observations and district embeddings and translates them into a Gaussian distribution, which determines the mean and log-variance of the first latent state. Then the obtained latent state initiates the Neural SDE, which utilize neural networks to determine the drift and diffusion functions that govern continuous-time latent dynamics. These governing functions depend on the time index, latent state, and district embedding, which help the model learn the unique characteristics specific to each district. After that, using a probabilistic decoder, the observations are reconstructed from the latent trajectory. The decoder outputs a mean and log-variance for each time step, which follows the Gaussian likelihood. The Evidence Lower Bound (ELBO) training loss improves by adding a KL-divergence regularization term to the negative log-likelihood (nll). The obtained results demonstrate the effective learning of V-NSDE in recognizing complex patterns over time, yielding realistic outcomes that include clear trends and random fluctuations across different areas.

Pramod Kumar Parida, Tshilidzi Marwala, Snehashish Chakraverty

A major problem of causal inference is the arrangement of dependent nodes in a directed acyclic graph (DAG) with path coefficients and observed confounders. Path coefficients do not provide the units to measure the strength of information flowing from one node to the other. Here we proposed the method of causal structure learning using collider v-structures (CVS) with Negative Percentage Mapping (NPM) to get selective thresholds of information strength, to direct the edges and subjective confounders in a DAG. The NPM is used to scale the strength of information passed through nodes in units of percentage from interval from 0 to 1. The causal structures are constructed by bottom up approach using path coefficients, causal directions and confounders, derived implementing collider v-structure and NPM. The method is self-sufficient to observe all the latent confounders present in the causal model and capable of detecting every responsible causal direction. The results are tested for simulated datasets of non-Gaussian distributions and compared with DirectLiNGAM and ICA-LiNGAM to check efficiency of the proposed method.

Sukanta Nayak, Snehashish Chakraverty

Here a novel idea to handle imprecise or vague set viz. Pseudo fuzzy set has been proposed. Pseudo fuzzy set is a triplet of element and its two membership functions. Both the membership functions may or may not be dependent. The hypothesis is that every positive sense has some negative sense. So, one membership function has been considered as positive and another as negative. Considering this concept, here the development of Pseudo fuzzy set and its property along with Pseudo fuzzy numbers has been discussed.

Sukanta Nayak, Snehashish Chakraverty

In this paper an alternative approach to solve uncertain Stochastic Differential Equation (SDE) is proposed. This uncertainty occurs due to the involved parameters in system and these are considered as Triangular Fuzzy Numbers (TFN). Here the proposed fuzzy arithmetic in [2] is used as a tool to handle Fuzzy Stochastic Differential Equation (FSDE). In particular, a system of Ito stochastic differential equations is analysed with fuzzy parameters. Further exact and Euler Maruyama approximation methods with fuzzy values are demonstrated and solved some standard SDE.