Mini lecture series:
Prof. Arindam Chatterjee (Stat Math Unit, ISI Delhi)
Title: Network models in Statistics
Abstract: Various network models and related estimation techniques will be presented. If time permits, we will also discuss aspects of network sampling and some extensions of networks for modelling multiway interactions.
Prof. Anil Ghosh (Stat Math Unit, ISI Kolkata)
Title: Statistical Machine Learning
Abstract: The following topics will be covered from the statistical perspective.
Basic introduction to statistical machine learning.
Brief idea about supervised, unsupervised and semi-supervised classification
Bayes classifier
LDA, QDA
Kernel Discriminant Analysis (if time permits)
Nearest neighbour classification
Logistic regression
Classification tree
Neural network
Support Vector Machines (if time permits)
Prof. Sandeep Juneja (School of Technology and Computer Science Tata Institute of Fundamental Research, Mumbai )
Title: Sequential learning under uncertainty through multi armed bandit framework
Abstract: Multi armed bandits provide an elegant framework to study the simplest and the foundational problems in sequential learning theory. Multiple arms correspond to multiple independent probability distributions that are unknown but can be sampled from. The aim typically is to address fundamental problems underlying many complex practical settings including identifying the arm with the highest mean, or another statistical performance measure, with a desirable confidence and at the fastest possible rate. Or to sample from arms optimally to maximize the expected sum of outputs or rewards.
In this short course we study the underlying probabilistic ideas for a few simple and foundational problems in the field. We see how tools from basic probability, martingale theory, large deviations, concentration inequalities, Bayesian methods and optimization come together to arrive at lower bounds on sample complexity, or regret, of all good algorithms, and to arrive at algorithms that closely match the lower bounds.
The underlying theory and algorithms are not only beautiful, they are also widely used in practice including in clinical trials, online advertising, recommendation systems and in many other settings.
Invited Talks:
Prof. Samiran Ghosh (University of Texas School of Public Health)
Title: An Introduction to Clinical Trials: History, Current State, and Opportunities
Abstract: - Randomized controlled trials are considered the gold standard for Intervention development as they deliver the highest level of evidence, due to their potential to limit many sources of bias. Albeit the development of RCT has a long history and the design (and analysis) of RCT is not always uniform across all circumstances. In this talk, I will give a brief history of RCT development and then venture onto various Statistical Challenges that an RCT can phase. I will also give some open research areas/problems where more work is needed.
Prof. Sourish Das (Chennai Mathematical Institute)
To be announced...
Prof. Snigdhanshu Chatterjee (University of Minnesota)
To be announced...
Prof. Priyam Das (Virginia Commonwealth University)
Title : NExUS: Bayesian simultaneous network estimation across unequal sample sizes
Abstract : Network-based analyses of high-throughput genomics data provide a holistic, systems-level understanding of various biological mechanisms for a common population. However, when estimating multiple networks across heterogeneous sub-populations, varying sample sizes pose a challenge in the estimation and inference, as network differences may be driven by differences in power. We are particularly interested in addressing this challenge in the context of proteomic networks for related cancers, as the number of subjects available for rare cancer (sub-)types is often limited. We develop NExUS (Network Estimation across Unequal Sample sizes), a Bayesian method that enables joint learning of multiple networks while avoiding artefactual relationship between sample size and network sparsity. We demonstrate through simulations that NExUS outperforms existing network estimation methods in this context, and apply it to learn network similarity and shared pathway activity for groups of cancers with related origins represented in The Cancer Genome Atlas (TCGA) proteomic data.
Prof. Soham Sarkar (ISI Delhi)
Title: Covariance Networks for Functional Data on Multidimensional Domains
Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations
over multidimensional domains introduces computational and statistical challenges, rendering the
standard methods effectively inapplicable. We introduce Covariance Networks (CovNet) as a modeling
and estimation tool to address this problem. The CovNet model is universal; it can be used to approximate
any covariance up to desired precision. Moreover, the model can be fitted efficiently and its neural
network architecture allows us to employ modern computational tools in the implementation. The CovNet
model also admits a closed-form eigendecomposition, which can be computed efficiently, without
constructing the covariance itself. This facilitates easy storage and subsequent manipulation of the
estimator. Moreover, the proposed estimator comes with theoretical guarantees in the form of consistency
and rate of convergence. We demonstrate the usefulness of the proposed method on resting-state fMRI
data.
Based on joint works with Victor M. Panaretos.
Prof. Sanjeev Sabnis (IIT Bombay)
Title: Preservation of Log-concavity under Multi-state Series and Multi-state Parallel Systems
Abstract: Log-concavity of multivariate distributions is an important concept in general and has a very special place in the field of Reliability Theory. The preservation of univariate unimodality under binary coherent systems of n independent binary components has been studied by Sabnis and Nair [11] as an extension of Alam’s [1] result for k −out−of −n systems. Here an attempt has been made to study the preservation of continuous version of multivariate log-concavity under multi-state series and multi-state parallel systems made up of n independent components and states of both, systems and components, taking values in set S = {0, 1, 2, . . . , M } and under the assumption that random variables representing times spent by these systems are available in specific forms. Similar preservation results for discrete version of multivariate log-concavity for multi-state series and multi-state parallel systems consisting of n independent components have been established for a subset {0, 1, 2} of S. These results for continuous and discrete versions of log-concavity have also been extended to systems that are formed using both multi-state series and multi-state parallel systems. The log-concavity and these preservation results have, in turn, enabled obtaining bounds on relevant joint probabilities for the systems under consideration.
Prof. Suresh Kumar (IIT Bombay)
Title : A multi parameter nonlinear eigenvalue problem and a non zero sum
stochastic differential game.
Abstract: in this talk, we discuss a class of nonlinear eigenvalue problem and use it to study
a non zero sum stochastic differential game with risk-sensitive type cost structure.
Prof. Siuli Mukhopaddhayay (IIT Bombay)
Title: A disease modelling initiative and a brief overview of models for zero inflated disease data
Abstract: In this talk we will discuss a new pan India disease modelling initiative for tracking the spread of infectious diseases. Also, we will discuss a statistical modelling approach to handle zero inflated disease data in form of counts. Zero inflation is a common nuisance while monitoring disease progression over time. We will discuss a new observation driven model for zero inflated and over-dispersed count time series. The proposed model will be illustrated using dengue and syphilis data sets.