The Schedule

Keynote Talk 1 (Prof. Subhashis Ghoshal)

Title: Optimal Bayesian Inference for High-dimensional Linear Regression Based on Sparse Projection-posterior

Abstract: We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors may even be nearly exponentially large relative to the sample size. Instead of the traditional method of putting a spike-and-slab prior or a similar alternative on the regression coefficients, we put a conjugate normal prior initially disregarding sparsity. However, to make an inference, instead of the original multivariate normal posterior, we use the posterior distribution induced by a map transforming the vector of regression coefficients to a sparse vector of the same dimension obtained by minimizing the sum of squares of deviations plus a suitably scaled $\ell_1$-penalty on the vector. We show that the resulting induced posterior distribution of this sparse projection, to be called the sparse projection-posterior distribution, concentrates around the true value of the parameter at the optimal rate adapted to the sparsity of the vector. We obtain a key sign-consistency result that shows that the true sparsity structure gets a large sparse projection-posterior probability, and hence the method consistently selects the active predictors. We further show that an appropriately re-centered sparse projection-posterior credible ball gives the correct asymptotic frequentist coverage. Finally, we describe how the computational burden of sampling from the sparse projection-posterior distribution can be distributed to a large number of machines each dealing with only a small fraction of the whole dataset. This, apart from increasing the computing speed by an order of magnitude, allows handling very big datasets without the need of storing those in a single machine. We conduct a comprehensive simulation study under a variety of settings and found that the proposed method performs well for finite sample sizes.  

This is a joint work with my doctoral student Samhita Pal. 

Keynote Talk 2 (Prof. Sujit Ghosh)

Title: ProGO: An Automated Global Optimization Approach 

Abstract: In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to initial conditions, often lead to suboptimal solutions or failed convergence. This is true even for Metaheuristic algorithms designed to amalgamate different optimization techniques to improve their efficiency and robustness. To address these challenges, we develop a sequence of multidimensional integration-based methods that we show to converge to the global optima under some mild regularity conditions. Our probabilistic approach does not require the use of gradients and is underpinned by a mathematically rigorous convergence framework anchored in the nuanced properties of nascent optima distribution. In order to alleviate the problem of multidimensional integration, we develop a latent slice sampler that enjoys a geometric rate of convergence in generating samples from the nascent optima distribution, which is used to approximate the global optima. The proposed Probabilistic Global Optimizer (ProGO) provides a scalable unified framework to approximate the global optima of any continuous function defined on a domain of arbitrary dimension. Empirical illustrations of ProGO across a variety of popular non-convex test functions (having finite global optima) reveal that the proposed algorithm outperforms, by order of magnitude, many existing state-of-the-art methods, including gradient-based, zeroth-order gradient-free, and some Bayesian Optimization methods, in term regret value and speed of convergence. It is, however, to be noted that our approach may not be suitable for functions that are expensive to compute. 

Invited Talk 1 (Prof. Ajit Rajwade)

Title: Signal Reconstruction from Samples at Unknown Locations with Application to 2D Unknown View Tomography 

Abstract: It is well known that a band-limited signal can be reconstructed from its uniformly spaced samples if the sampling rate is sufficiently high. More recently, it has been proved that one can reconstruct a 1D band-limited signal even if the exact sample locations are unknown, but given a uniform distribution of the sample locations and their ordering in 1D. In this work, we extend the analytical error bounds in such scenarios for quasi-bandlimited (QBL) signals, and for the case of arbitrary but known sampling distributions. We also prove that such reconstruction methods are resilient to a certain proportion of errors in the specification of the sample location ordering. We then express the problem of tomographic reconstruction of 2D images from 1D Radon projections under unknown angles (2D UVT) with known angle distribution, as a special case for reconstruction of QBL signals from samples at unknown locations with known distribution. Building upon our theoretical background, we present asymptotic bounds for 2D QBL image reconstruction from 1D Radon projections in the unknown angles setting, and present an extensive set of simulations to verify these bounds in varied parameter regimes. To the best of our knowledge, this is the first piece of work to perform such an analysis for 2D UVT and explicitly relate it to advances in sampling theory, even though the associated reconstruction algorithms have been known for a long time. 

Panel Discussion with Speakers

(Host: Mr. Shuvayan Banerjee and Miss. Unnati Nigam)

An open panel discussion on high dimensional data challenges with speakers is scheduled. Participants can ask their query with speakers and opportunity in their domain of expertise. Participants can also provide their questions to the host of panel discussion during registration.

Keynote Talk 3 (Prof. Haavard Rue)

Title: Scalable approximate inference for latent Gaussian models

Abstract: In this talk, I will discuss our on-going work to achieve accurate approximate inference for the class of latent Gaussian models with the INLA-approach (see {www.r-inla.org}), while maintaining reasonable scalability of the computational cost with respect to both model size and number of observations. A main ingredient, is to use the Variational Bayes formulation to automatically create a low-rank correction for the mean, variance and skewness. The    correction for the marginal skewness is much more involved but can still be achived while maintaining scalability.

Invited Talk 2 (Prof. Subhajit Dutta)

Title: On Pairwise Feature Screening in Binary Classification

Abstract: We first discuss a new model-free feature screening method based on energy distances for ultrahigh-dimensional binary classification problems. Using energy distances, we then propose a paired screening method to identify pairs of variables that are marginally undetectable, but have differences in their joint distributions using the idea of a non-bipartite matching problem in a graph. We further modify this algorithm to identify pairs that may contain a marginal feature as well as a noise. Finally, we build a classifier that maintains coherence between the proposed feature selection criteria and discrimination method. A numerical study shows convincing advantages of our classifier over existing state-of-the-art methods. 

Invited Talk 3 (Prof. Buddhnanda Banerjee)

Title: Data-driven dimension reduction in functional principal component analysis identifying the change-point in functional data

Abstract: Functional principal component analysis (FPCA) is the most commonly used technique to analyze infinite-dimensional functional data in finite lower-dimensional space for the ease of computational intensity. However, the power of a test detecting the existence of a change-point falls with the inclusion of more principal dimensions explaining a larger proportion of variability. We propose a new methodology for dynamically selecting the dimensions in FPCA that are used further for the testing of the existence of any change-point in the given data. This data-driven and efficient approach leads to a more powerful test than those available in the literature. We illustrate this method on the monthly global average anomaly of temperatures. 

Invited Talk 4 (Prof. Radhendushka Srivastava)

Title:  Two sample test in high dimension 

Abstract: Testing the equality of mean of two population is an important statistical problem and has wide application in bio-informatics. Assuming that populations are Gaussian with equal covariance structure, the classical Hotelling's T-square test is the likelihood ratio test. However, this test tends to have low power or becomes undefined due to singularity of the sample covariance matrix in high dimensional regime. In this talk, we will explore the recent advances in the area of two sample test in high dimension. We will also discuss projection based test, especially RAPTT (RAndom Projection T-Test) which is an exact test for equality of means of two normal populations. RAPTT does not require any constraints on the dimension of the data or the sample size. Some desirable statistical properties of RAPTT will also be illustrated.