Projects and Interests

Projects

Carathéodory's Theorem - Interactive Visualizer

Mar 2026 | Live Demo

Any point inside a convex hull in \(\mathbb{R}^2\) can be written as a convex combination of at most 3 of its vertices - this is Carathéodory's theorem. The interactive tool lets you click anywhere inside a convex polygon and instantly decomposes that point into its barycentric coordinates over the minimal triangle of hull vertices. Drag any vertex to reshape the polygon; the decomposition updates live. The page also includes an essay on the theorem, its proof, and why it keeps appearing in LP, SVMs, and sparse approximation.

Variance-Controlled SGD: Adaptive Batch Size via Gradient Noise

Mar 2026 | Project Link | Report

• Implemented a reproducible PyTorch research pipeline comparing fixed-batch SGD with an adaptive batching policy driven by online gradient variance estimates.
• Derived and deployed a control rule of the form \(b_t = \min(b_{\max}, \max(b_{\min}, C\,\sigma_t^2/(\|\bar g_t\|^2 + \epsilon)))\), with smoothing to reduce oscillatory batch-size updates.
• Logged iteration-level metrics including loss, gradient norm, gradient variance, signal-to-noise ratio, and effective batch size; exported all runs as CSV for analysis.
• Evaluated both naive per-sample and scalable micro-batch variance estimators, and generated comparison plots for convergence, variance decay, and SNR stabilization.
• Found that with calibrated control constant (C=100-200), adaptive batching matches fixed batch 512 performance on CIFAR-10 while demonstrating dynamic batch-size adaptation.

Player compatibility scoring using GNNs

Oct–Nov 2025 | Project Link

• Modeled player interactions as possession-level graphs and trained a Graph Neural Network to learn threat-aware player embeddings from pass events.
• Computed expected threat (xT) maps via Bellman iterations and derived enriched player feature vectors capturing position, pass style, and pressure behavior.
• Learned a neural compatibility scorer using player embeddings and co-occurrence patterns to predict synergy between player pairs.

NLP Analysis of the Israel-Syria War’s Impact on Gold, Oil, and Financial Markets

Oct–Nov 2024 | ECO318 - Money, Banking and Financial Markets | Project Link

• Explored how war narratives affect energy and finance sectors using LDA topic modeling on news data.
• Connected macroeconomic reactions to geopolitical sentiment and volatility trends.

Electricity Consumption Forecasting Using Time Series Analysis

Sept–Nov 2024 | DSE315 - Data Science in Practise | Project Link

• Used 15 years of UK electricity data to model seasonal patterns using SARIMA.
• Validated with ADF and Ljung-Box tests to confirm stationarity and independence.
• Compared forecast accuracy against ARIMA and exponential smoothing models.

Traffic Density Estimation and Vehicle Detection Using YOLOv8

Sept–Nov 2024 | DSE312 - Computer Vision| Project Link

• Trained YOLOv8 on a custom dataset; achieved mAP@50 of 0.973 for vehicle detection.
• Developed a scalable inference pipeline to count vehicles and estimate traffic density from CCTV frames.

From Scratch

I really like to implement things from scratch,I try out various algorithms, restricting myself only to using NumPy and similar basic standard libraries only.

Transformer

August 2025 | Project Link

I implemented a Transformer model completely from scratch using only NumPy, covering key components like multi-head self-attention, feedforward layers, and positional embeddings. The model stacks multiple Transformer blocks with residual connections and layer normalization. Finally, it projects outputs through a language modeling head, enabling sequence-to-sequence predictions. I am planning to implement more complex architectures from scratch in coming times.

ARIMA

August 2025 | Project Link

This implementation builds an ARIMA (AutoRegressive Integrated Moving Average) model entirely from scratch using only numpy. It avoids high-level libraries like statsmodels, making every step transparent: differencing for stationarity, manual AR and MA term calculations, and likelihood-based parameter estimation.

Paper Implementations

I find great joy in reading academic papers, and trying to implement them ground up.

Isolation Forest

July 2025 | Project Link

We've all learnt and implemented random forest; it's one of the first algorithms we encounter in ML. Most of the time, we strive to find patterns using such algorithms. Another paradigm is anomaly detection - and that's how I came across Isolation Forests. In this project, I wrote the full Isolation Forest algorithm from scratch using NumPy. The model builds binary trees by recursively splitting randomly sampled data to isolate outliers quickly. I used synthetic 2D data (normal + uniform noise), calculated anomaly scores based on average path lengths, and visualized the decision boundaries.

Gravitational Search Algorithm

June 2025 | Project Link

Implemented GSA on the Heterogeneous Truck Fleet Optimization problem. Inspired by evolutionary algorithms introduced in my AI course, I explored GSA - a nature-inspired metaheuristic. I implemented it on the same truck fleet problem to compare its effectiveness with genetic algorithms and MIP.

Heterogeneous Truck Fleet Optimization

DSE316 - Applied Optimization | Project Link

• Developed a truck fleet optimization model minimizing delivery cost under capacity and time constraints.
• Implemented a Mixed Integer Program using PuLP and benchmarked it against genetic algorithm solutions.
• Converted real-world logistics into mathematical constraints for optimal allocation.