Short Bio
As a Data Scientist I build and deploy machine learning based solutions to interesting problems. Currently I am working on the problem of detection of anomalies in large data centers. Previosuly, my work has centered around problems in online-advertising, marketing and operational forecasting for the most part. As part of solution, I employ Machine learning, Deep learning (RNNs, CNNs), and statistical techniques along with cloud frameworks for scalable deployment. Some of the problems I have worked on are ad-impression predictions, attribution, anomaly detection, causal inference and personalization in digital marketing. The engineering side of my work involves writiing code to deploy models to production, working with various cloud frameworks and building ML platforms.
Previously, I obtained a PhD in Mathematics. Specifically, I worked in Index theory (out of Atiyah-Singer Index theorem) which, briefly speaking, explores the interplay between analysis and topology. An excellent example of this relationship is Gauss-Bonnet theorem. In addition, I have also worked in Riemannian geometry and smooth dynamical systems. Both of the areas involve solving (class of)partial differential equations over a space with non-trivial geometry.
In general, I maintain a strong interest in problems involving rich geometry. In machine learning, its fascinating to see applications of geometric techniques in areas of Topological data analysis, Geometric deep learning (Graph Convolution Networks, manifold learning) and and Knowledge graphs.
Contact
Publications & Research interests
- Stochastic approach to anomaly detection in large networks with edge attributes, Working.
- Adiabatic limit of Calderon projector on manifold with cylindrical end
- Bounding topological entropy of geodesic flows of \(C^{(1, \alpha)}\) Riemannian metric
Research Interests
Machine learning/Deep learning on graphs (GNN,GCN etc) and its applications to Knowledge graphs, Anomaly detection and Spectral techniques.
Feel free to reach out to me if these topics interest you and would like to explore a problem together.
Expository writings
- Graph Convolutional Network My attempt to put together some details around the definition of convolution on graphs in the context of Graph Convolution networks.
- Spark:An overview A short summary of of Spark’s working based on my reading and professional experience with it. (I took the liberty of borrowing pictures)
- Topological analysis & Robotics This is a short note on interesting topological results, and outline of ideas in Robotics:The ideas on Robotics grew out my interest in studying the topology of configuration spaces of “mechanical” or “factory” robots. Working jointly with Paul Loya we found new examples of configuration spaces with rich topology. However, this project wasn’t taken much further due to my developing interest in machine learning. Nevertheless, robotics continues to benefit greatly by borrowing ideas from Topology.
Graph Neural Network papers
There are several approaches to GNNs but I focus here on spectral approaches, especially in GCNs.
- Graph Neural Network model A relatively early paper on GNN applying fixed point theorems.
- Good overview
- Spectral approach by Bruna et al This extends CNN to graph data by defining convolutions on spectrum of Laplacian.
- GCN w/ Chebyshev polynomial approach
- Graph Wavelet network which replaces the Fourier transform with Wavelet transform to extend spectral GCNs.