experience

A description of my research internships and other projects

research

Counting k-Matchings of Bipartite Graphs

We studied the use of message passing algorithms to compute the matching number, and to lower bound the number of matchings of a given size in bipartite graphs. The bounds are achieved asymptotically for a sequence of 2-lifts of the original graph. These graphical models can also be used to approximate the permanets and subpermanent sums of positive matrices. We also conducted basic experiments to check efficiency of MPA to approximate permanents of various ensembles of sparse matrices. This was one of the two projects I did during MSc thesis while interning at IISc, Bangalore.

Capacity Achieving Distribution of Amplitude-Constrained AWGN Channel

We survey the nature of the capacity achieving input distribution of the AWGN channel, its behavior as the amplitude constraint is relaxed, and certain bounds on its support. Lastly we made an attempt at generalizing the bounds in a discrete setting. This was one of the two projects I did during MSc thesis while interning at IISc, Bangalore.

Approximating Permanents of Positive Matrices Using Probabilistic Graphical Models

The primary approach is to create a Markov Random Field whose partition function is the permanent of a square matrix. Then use Belief Propagation to compute Bethe Free Energy which approximates the permanent. We then try to generalize the algorithm to compute permanent of rectangular matrices. This internship at CMI was a part of my bachelor’s thesis.

Polynomial GCD

Computing GCD of sparse multivariate polynomials, primarily using probabilistic sparse interpolation algorithms. The project started when I was a summer intern at IIT-Gn during 2017. I continued this internship throughout the third year of my undergrad, during which we studied a number of research papers and textbooks (mainly _Modern Computer Algebra_ by _Gathen & Gerhard_ ).

other

Insider Threat Detection

Conducted experiments for the chapter _Insider Threat Detection: Machine Learning Way_ in _Versatile Cybersecurity_, Springer, Cham, 2018.

Outlier Detection on FPGA

The project involves designing, implementation and analysis of anomaly detection algorithms. The desired goal is to build a hardware for an online (real-time) algorithm designed to detect anomalies when the input is real-time data. A regression model is maintained in online fashion and Cook's Distance is used as a metric to find outlier. Results are compared with a Mahalanobis Distance based similar approach. The Cook's Distance gives accurate results even when the fraction of outliers is large. The final code was dumped on an FPGA.