Postgraduate Diploma in Computer Science: Artificial Intelligence and Machine Learning

This course introduces basic probability theory , statistical methods and computational algorithms to perform mathematically rigorous data analysis. The course starts with basic foundational concepts of random variables, histograms, and various plots (PMF, PDF and CDF). Students learn various popular discrete and continuous distributions like Bernoulli, Binomial, Poisson, Gaussian, Exponential, Pareto, log-normal etc., both mathematically and from an applicative perspective. Students learn various measures like mean, median, percentiles, quantiles, variance and interquartile-range. Students learn the pros and cons of each metric and understand when and how to use them in practice. Students will learn conditional probability and Bayes theorem in the applied context of real-world problems in medicine and healthcare. The module teaches the foundations of non-parametric statistics and applies them to solve problems using computational tools. Students learn various methods to determine correlations rigorously in data. This is followed by applied and mathematical understanding of the statistics underlying control- treatment (A/B) experiments and hypothesis testing. The module engages computation tools in modern statics like Bootstrapping, Monte-Carlo methods, RANSAC etc.

Mathematics and computer science are closely related fields. Problems in computer science are often formalized and solved with mathematical methods. It is likely that many important problems currently facing computer scientists will be solved by researchers skilled in algebra, analysis, combinatorics, logic, and/or probability theory, as well as computer science. This course covers discrete mathematics for computer science and engineering. Topics may include asymptotic notation and growth of functions; permutations and combinations; counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. Students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in computer science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems. The focus of the course is real-world problems and applications often found in business and industry.

This course helps students translate advanced mathematical/statistical/scientific concepts into code. This is a module for writing code to solve real-world problems. It introduces programming concepts (such as control structures, recursion, classes and objects) assuming no prior programming knowledge, to make this course accessible to advanced professionals from scientific fields like Biology, Physics, Medicine, Chemistry, Civil & Mechanical Engineering etc. After building a strong foundation for converting scientific knowledge into programming concepts, the course advances to dive deeply into Object-Oriented Programming and its methodologies. It also covers when and how to use inbuilt-data structures like 1-Dimensional and 2-Dimensional Arrays before introducing the concepts of computational complexity to help students write optimized code using appropriate data structures and algorithmic design methods. The module can be taught to allow students to learn these concepts using a modern programming language such as Java or Python. The course offers students the ability to identify and solve computer programming problems in scientific fields

at a graduate level.

This course focuses on modelling sequences (text, music, time-series, genes) using deep-learning models. We start with a simple Recurrent Neural Network and its limitations with long-sequences. Students learn LSTMs and GRUs which can handle significantly longer sequences to model sequence data like text, music, gene-sequences and time-series data. We study variations of LSTM like bi-directional LSTMs and encoder-decoder architectures. This is followed by a detailed study of attention mechanism and Transformer based models which are currently the state-of-the-art for NLP and sequence modelling. The module teaches encoder-decoder Transformers, BERT, BERT-variations, GPT-1,2 &3 models from both the architectural and mathematical viewpoints and also a practical viewpoint. Studnets learn to implement many of these complex models from scratch (using TensorFlow 2 and Keras) to gain a deeper understanding of how they work internally. Students will study popular applications of deep-learning in NLP like parts-of-speech tagging, question-answering systems, conversational engines (chatbots), Semantic search with low-latency etc. For each of these problems, Students will study cutting edge deep-learning models along with code implementations.

This course aims to build the core competency of building real world end-to-end ML systems and deploy them into production for a variety of problems and scenarios. Students would learn a variety of ML systems ranging from high throughput and low latency internet scale systems to low compute power and energy constrained IoT devices like smart watches. Students will study the ML lifecycle and various components in detail. We also use real world ML platforms like Google’s KubeFlow, TensorFlow Lite, and Amazon’s SageMaker to implement real world systems and understand the engineering trade-offs and challenges. Students also learn relevant technologies and tools like Containerization (Docker) and Container Orchestration (Kubernetes) and Git which are often used extensively in real world scalable ML systems. This course is a hands-on course where we solve

multiple real world cases and discuss solutions built by various companies and

organizations to provide the students a comprehensive understanding of varied

systems and design choices.

This course provides a comprehensive overview of Computer vision problems and how they can be tackled using various Convolutional Neural networks (CNNs). Students start with classical image processing operations like edge detection, convolution, shape detectors and colour space conversions. This is followed by a foundational understanding of Deep-Convolutional Neural networks and how their training and evaluation works. We introduce various CNN specific layers like pooling-layers and upsampling layers. We also introduce various Data Augmentation techniques that are very helpful for image-related problems. This is followed by a dive deep into the internals of popular CNN architectures like: AlexNet, VGGNet, ResNet etc. Students also learn how to use these methods practically for transfer learning. Students will study how various computer-vision related tasks like image segmentation, image-generation, object detection and localization, contrastive learning etc., can be performed using state of the art algorithms for each of these tasks. Most of these techniques would be studied directly from the original research papers and open-source code provided by the authors. Students would also implement some of these algorithms from scratch in this course.

This course provides a strong mathematical and applicative introduction to Deep Learning. The module starts with the perceptron model as an over simplified approximation to a biological neuron. We motivate the need for a network of neurons and how they can be connected to form a Multi Layered Perceptron (MLPs). This is followed by a rigorous understanding of back-propagation algorithms and its limitations from the 1980s. Students study how modern deep learning took off with improved computational tools and data sets. We teach more modern activation units (like ReLU and SeLU) and how they overcome problems with the more classical Sigmoid and Tanh units. Students learn weight initialization methods, regularization by dropouts, batch normalization etc., to ensure that deep MLPs can be successfully trained. The module teaches variants of Gradient Descent that have been specifically designed to work well for deep learning systems like ADAM, AdaGrad, RMSProp etc. Students also learn AutoEncoders, VAEs and Word2Vec as unsupervised, encoding deep-learning architectures. We apply all of the foundational theory learned to various real world problems using TensorFlow 2 and Keras. Students also understand how TensorFlow 2 works internally with specific focus on computational graph processing

This course introduces more advanced ML techniques like ensembles: bagging, boosting, cascading and stacking classifiers and regressors. It covers both the theoretical foundations and applicative details of these techniques along with popular implementations of boosting like LightGBM, CatBoost and XGBoost. Students also delve into kernel methods with specific focus on SVMs for classification and regression. Students will study state of the art model agnostic feature importance and model-interpretability techniques like LIME and SHAP. Students also study classical NLP based text encoding methods like Bag-of-words, TF-IDF etc. The module teaches various classical methods in time series analysis and forecasting like ARMA, ARIMA etc. Students also learn how to pose time series forecasting problems as regression and classification problems to leverage well studied ML techniques. This is followed by various domain and problem specific Feature engineering techniques that are often helpful in real world problem solving. Students will study methods like error analysis, ablative analysis etc., to debug and understand why and where a model is performing well and where it is not performing well. This will further help us in designing appropriate features. Students study model calibration techniques like Platt Scaling, Isotonic Regression etc. Later in this course, we cover how to build recommender systems using content-based and collaborative filtering methods. The module also teaches the detailed solution of the Netflix prize (2009) and various recent advances in RecSys

This course is aimed to help learners understand various techniques and algorithms to visualize, analyse and understand high dimensional data which is very common in Data Science and ML. The module starts with linear algebraic methods like Principal Component Analysis (PCA) and SVD (Singular Value Decomposition) for obtaining linear projection of high dimensional data. This is followed by more advanced nonlinear and state of the art techniques like t-SNE and UMAP for visualizing high dimensional data. Each of these techniques would be covered in full mathematical detail from first principles along with applying them to real world datasets in NLP, Genomics and internet-datasets. Students will also study how PCA and SVD are related to general Matrix Factorization techniques. To analyse and understand high dimensional un-labelled data, students learn clustering techniques like K-Means, Gaussian Mixture models, Hierarchical Clustering and DBSCAN. The modules show how some of the techniques are mathematically related to Matrix Factorization. Students study various outlier detection techniques based on density, proximity, factorization and cluster analysis.

This course focuses on building basic classification and regression models and understanding these models rigorously both with a mathematical and an applicative focus. The module starts with a basic introduction to high dimensional geometry of points, distance-metrics, hyperplanes and hyperspheres. We build on top this to introduce the mathematical formulation of logistic regression to find a separating hyperplane. Students learn to solve the optimization problem using vector calculus and gradient descent (GD) based algorithms. The module introduces computational variations of GD like mini-batch and stochastic gradient descent. Students also learn other popular classification and regression methods like k-Nearest Neighbours, NaiveI Bayes, Decision Trees, Linear Regression etc. Students also learn how each of these techniques under various real world situations like the presence of outliers, imbalanced data, multi class classification etc. Students learn bias and variance trade-off and various techniques to avoid overfitting and underfitting. Students also study these algorithms from a Bayesian viewpoint along with geometric intuition. This module is hands-on and students apply all these classical techniques to real world problems.

This is a project-based course, with the aim of building the required skills for creating web-based software systems. The course covers the entire lifecycle of building software projects, from requirement gathering and scope definition from a product document, to designing the architecture of the system, and all the way to delivery and maintenance of the software system. The course covers both frontend, which is, building browser-based interfaces for users, using frontend web frameworks, and also building the backend, which is the server running an API to serve the information to the frontend, and running on an

SQL or similar database management system for storage.

All aspects of delivering a software project, including security, user authentication and authorisation, monitoring and analytics, and maintaining the project are covered. The course also covers the aspects of project maintenance, like using a version control system, setting up continuous integration and deployment pipelines

and bug trackers. The Applied Computer Science Project will focus on the outcome of how computer science and its associated tools as a field of study can be beneficial to other fields of study or how such tools can be applied to modify existing processes for better outcomes.