Theses
Permanent URI for this collectionhttps://dspace.isical.ac.in/handle/10263/2744
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Item Exploring Resource-Efficient Deep Learning for Medical Image Segmentation(2026-05-19) Dutta, PallabiAutomated medical image segmentation improves diagnostic accuracy by au tomating the precise delineation of target anatomical structures in the input images. Artificial Intelligence (AI), and specifically, Deep Learning (DL), has emerged as a state-of-the-art approach for this task. However, the significant computational demands of DL approaches often hinders their deployment. Ad vanced models, including Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs), require substantial processing power and a large memory footprint, limiting their use in resource-constrained settings. This thesis aims to address this challenge by developing a series of novel, resource-efficient DL models that achieve high segmentation accuracy with reduced computational costs. The research follows a logical progression of architectural novelty. First, global context-aware attention frameworks, FuDSA-Net and VoCANet, are in troduced by leveraging multi-scalar features and global-context aware attention for efficient 2D/3D segmentation. The spatial and spectral domains are then integrated using a novel hybrid CNN-ViT framework WaveCoformer for learn ing robust representation of the target structure. The developed model achieves high segmentation accuracy with a lower parameter count. Subsequently, the research investigates a computationally efficient alternative to ViTs for segmen tation, called Vision-xLSTM, by developing the U-VixLSTM model. This is extended to the Rot-UViL architecture, capable of modeling cross-dimensional dependencies in volumetric inputs with its novel rotational attention. Finally, the thesis presents a prompt-driven pruning framework for ViT-based segmenta tion models, called PrATo, which dynamically prunes irrelevant ViT tokens with a parameter-free prompt-driven scoring mechanism. The framework achieves ∼ 35−55% reduction of processed tokens. The frameworks developed in this thesis are validated across multiple publicly available datasets; demonstrating their high segmentation accuracy along with computational efficiency.Item On the Jordan-Chevalley-Dunford Decomposition of Certain Classes of Operators and Convergence of Their Normalized Power Sequences(Indian Statistical Institute, 2026-02-25) Shekhawat, RenuThe classical Jordan–Chevalley decomposition expresses a matrix A ∈ Mn(C) as a unique commuting sum A = D + N, where D is diagonalizable and N is nilpotent. Although this decomposition is algebraic in origin, it encodes significant spectral information and, as shown by Nayak, has an important analytic consequence: the convergence of the normalized power sequence {|A^n|^ 1/n }n∈N ; |A| := (A∗A)^1/2 . In this thesis we study Jordan-Chevalley–type decompositions in infinite-dimensional settings and their connection with the convergence behaviour of normalized power sequences. In particular, we discuss this phenomenon for Dunford’s spectral operators and compact operators on a complex Hilbert space, and further extend the theory to operators affiliated with finite type I von Neumann algebras.Item Essays on Monetary-Fiscal Interactions in Emerging Market and Developing Economies(Indian Statistical Institute, 2025-07-17) Bahl, OjasvitaThis thesis contains three chapters on monetary-fiscal interactions in Emerging Market and Developing Economies. Governments in emerging markets and developing economies (EMDEs) frequently intervene in agricultural markets to stabilize food prices following adverse shocks. These interventions often take the form of large-scale food procurement and redistribution, which we define as a redistributive policy shock. This chapter examines the effects of such shocks on inflation and the distribution of consumption between rich and poor households. We develop a tractable two-sector, two-agent New Keynesian DSGE model and estimate its parameters for the Indian economy using Bayesian methods. Our findings reveal that under an inflation-targeting regime, consumer heterogeneity plays a crucial role in determining whether monetary policy responses to various shocks enhance or reduce aggregate welfare. The second chapter evaluates the welfare implications of redistributive policy shocks under alternative monetary policy regimes. Building on Chapter 1, which finds that redistributive policy shocks are inflationary and expansionary in terms of aggregate output, we assess how different monetary responses alter welfare outcomes. Following Schmitt-Grohe Uribe (2007), we compute consumptionequivalent welfare gains to compare the welfare cost of these shocks under the optimised simple monetary rule and the planner’s solution (Ramsey Optimal Monetary Policy). The optimal rule features no interest rate smoothing, a strong response to inflation, and a limited reaction to output. Our findings demonstrate the critical role of monetary policy in shaping the welfare impact of redistributive shocks. We further compare these welfare effects to those of an agricultural productivity shock and show that the steady-state level of redistribution significantly affects the relative costs of redistribution-driven fluctuations. We find that non-optimised rules lead to significantly higher welfare costs than optimised simple rules. In the third chapter, we study the interactions between informality, underdeveloped financial markets and fiscal consolidation by developing a two-sector, twoagent medium-scale NK-DSGE model that allows public expenditure and private consumption to be either substitutes or complements. While there is a large literature that tries to understand the effects of fiscal consolidation in AEs, there is a relatively small literature on fiscal consolidation in EMDEs. We find that greater informality dampens the reduction in public debt from a contractionary fiscal policy shock. We find tax-based shocks to exhibit greater decline in debt at the cost of a greater contraction in output than spending-based shocks. Our analysis suggests that a fiscal consolidation shock can be expansionary when private consumption and public spending exhibit moderately-high substitutability consistent with the literature on expansionary fiscal consolidations.Item Flexible Modeling of non-Gaussian Longitudinal Data: Some Approaches using Copula(Indian Statistical Institute, Kolkata, 2026-03-16) Chattopadhyay, SubhajitLongitudinal data are common in medical and biological sciences, where measurements are gathered from subjects over time to explore relationships with explanatory variables (covariates) and to uncover the underlying mechanisms of dependence among these measurements. The responses observed at each instance can be either discrete or continuous. One of the primary challenges in longitudinal data analysis lies in the non-Gaussian nature of the response variables. As a result, there are relatively few multivariate models in the literature that effectively address the specific characteristics observed in such datasets. In this dissertation, we address four problems concerning longitudinal data analysis by developing new statistical models. These models specifically address the time-related relationships found in various types of non-Gaussian longitudinal data by employing suitable classes of parametric copulas. In the third chapter of this dissertation, we examine a motivating dataset from a recent HIV-AIDS study conducted in Livingstone district, Zambia. The histogram plots of the repeated measurements at each time point reveal asymmetry in the marginal distributions, and pairwise scatter plots uncover nonelliptical dependence patterns. Traditional linear mixed models, typically used for longitudinal data, struggle to capture these complexities effectively. We introduced skew-elliptical copula based mixed models to analyze this continuous data, where we use generalized linear mixed models (GLMM) for the marginals (e.g., Gamma mixed model), and address the temporal dependence of repeated measurements by utilizing copulas associated with skew-elliptical distributions (such as skew-normal/skew-t). The proposed class of copula-based mixed models addresses asymmetry, between-subject variability, and non-standard temporal dependence simultaneously, thereby extending beyond the limitations of standard linear mixed models based on multivariate normality. We estimate the model parameters using the IFM (inference function of margins) method, and outline the procedure for obtaining standard errors of the parameter estimates. To evaluate the performance of this approach under finite sample conditions, rigorous simulation studies are conducted, encompassing skewed and symmetric marginal distributions along with various copula selections. Finally, we apply these models to the HIV dataset and present the insight gained from the analysis. In the fourth chapter of this dissertation, we introduce factor copula models tailored for unbalanced non-Gaussian longitudinal data. Modeling the joint distribution of such data, where subjects may have varying numbers of repeated measurements and responses can be continuous or discrete, poses practical challenges, especially with numerous measurements per subject. Factor copula models, which are canonical vine copulas, leverage latent variables to elucidate the underlying dependence structure of multivariate data. This approach aids in interpretation and implementation for unbalanced longitudinal datasets, enhancing our ability to model complex dependencies effectively. We develop regression models for continuous, binary and ordinal longitudinal data, incorporating covariates, using factor copula constructions with subject-specific latent variables. With consideration for homogeneous within-subject dependence, the proposed models enable feasible parametric inference in moderate to high dimensional scenarios, employing a two-stage (IFM) estimation method. We also present a method for evaluating the residuals of factor copula models to visually assess the goodness of fit. The performance of the proposed models in finite samples is assessed through extensive simulation studies. In empirical analyses, we apply these models to analyze various longitudinal responses from two real-world datasets. Furthermore, we compare the performance of these models with widely used random effects models using standard selection techniques, revealing significant improvements. Our findings suggest that factor copula models can serve as viable alternatives to random effect models, offering deeper insights into the temporal dependence of longitudinal data across diverse contexts. In the fifth chapter of this dissertation, we address the issue of modeling complex and hidden temporal dependence of count longitudinal data. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of longitudinal data since they allow for different choices of the correlation structure. But these copulas lack in flexibility to model dependence and inference is only feasible under parametric restrictions. In this chapter, we propose the use of finite mixtures of elliptical copulas to enhance the modeling of temporal dependence in discrete longitudinal data. This approach enables the utilization of distinct correlation matrices within each component of the mixture copula. We theoretically explore the dependence properties of finite mixtures of copulas before employing them to construct regression models for count longitudinal data. Inference for this proposed class of models is based on a composite likelihood approach, and we evaluate the finite sample performance of parameter estimates through extensive simulation studies. To validate the fitting of the proposed models, we extend traditional techniques and introduce the t-plot method to accommodate finite mixtures of elliptical copulas. Finally we apply the proposed models to analyze the temporal dependence within two real-world count longitudinal datasets and demonstrate their superiority over standard elliptical copulas. In the final contributing chapter of this dissertation, we introduce a novel multivariate copula based on the multivariate geometric skew-normal (GSN) distribution. This asymmetric copula serves as an alternative to the skew-normal copula proposed by Azzalini. Unlike the standard skew-normal copula, the multivariate GSN copula retains closure properties under marginalization, which offers computational advantages for modeling multivariate discrete data. In this chapter, we outline the construction of the geometric skew-normal copula and its application in modeling the temporal dependence observed in non-Gaussian longitudinal data. We begin by exploring the theoretical properties of the proposed multivariate copula. Subsequently, we develop regression models tailored for both continuous and discrete longitudinal data using this innovative framework. Notably, the quantile function of this copula remains independent of the correlation matrix of its respective multivariate distribution, offering computational advantages in likelihood inference compared to copulas derived from skew-elliptical distributions proposed by Azzalini. Furthermore, composite likelihood inference becomes feasible for this multivariate copula, allowing for parameter estimation from ordered probit models with the same dependence structure as the geometric skew-normal distribution. We conduct extensive simulation studies to validate the geometric skew-normal copula based models and apply them to analyze the longitudinal dependence of two real-world data sets. Finally, We present our findings in terms of the improvements over regression models based on multivariate Gaussian copulas.Item Development of Some Scalable Pattern Recognition Algorithms for Real Life Data Analysis(2017-11-20) Garai, ParthaA huge amount of data is being generated continuously as a result of recent advancement and wide use of high-throughput technologies. With the rapid increase in size of data distributed worldwide, understanding the data has become critical. In this regard, dimensionality reduction and clustering have become the necessary preprocessing steps of multiple research areas and applications. One of the important problems of real life large data sets is uncertainty. Some of the sources of this uncertainty include imprecision in computation and vagueness in class denitions. The uncertainty may also be present in the denition of class membership function. In this background, the thesis addresses the problem of dimensionality reduction and clustering of real life data sets, in the presence of noise and uncertainty. The thesis rst presents the problem of feature selection using both type-1 and interval type-2 fuzzyrough sets, which are eective for dimensionality reduction of real life data sets when uncertainty is present in the data set. The properties of fuzzy-rough sets allow greater exibility in handling noisy and real valued data. While the concept of lower approximation and boundary region of rough sets deals with uncertainty, incompleteness, and vagueness in class denition, the use of either type-1 or interval type-2 fuzzy sets enables ecient handling of overlapping classes in uncertain environment. Moreover, a new concept of \simultaneous attribute selection and feature extraction" is introduced for dimensionality reduction, integrating judiciously the merits of both feature selection and extraction. A scalable rough-fuzzy clustering algorithm is introduced for large real life data sets, where the theory of rough hypercuboid approach, interval type-2 fuzzy sets, and c-means algorithm are integrated judiciously to handle the uncertainty present in a data set. While the concept of rough hypercuboid approach deals with uncertainty, incompleteness, and vagueness in cluster denition, the use of fuzzy membership of interval type-2 fuzzy sets in the boundary region of a cluster enables ecient handling of overlapping partitions in uncertain environment. Finally, the application of both clustering and feature selection algorithms is demonstrated by grouping functionally similar microRNAs from microarray data. The proposed approach can automatically select the optimum set of features while clustering the microRNAs, making the complexity of the algorithm lower.Item A Study of the SHA-2 Cryptographic Hash Family(Indian Statistical Institute, Kolkata, 2009-02-01) Sanadhya Somitra KumarItem Projective corepresentations and cohomology of compact quantum groups(Indian Statistical Institute, Kolkata, 2026-01-22) Maity, KiranIn this thesis, we briefly review various types of projective corepresentations of compact quantum groups and prove the existence of suitable envelopes for them. We also study the associated invariant (dual) 2-cohomology and calculate it in a few concrete examples.Item Generalization under Sub-population Shift: Equitable Models for Imbalanced, Long-tailed, and Fair Representation Learning(Indian Statistical Institute, Kolkata, 2026-02-09) Ansari, FaizanuddinMachine learning systems often experience performance degradation in real-world scenarios due to subpopulation shift defined as mismatches in the distribution of classes or attributes within datasets. This thesis investigates generalization failures arising from class imbalance, long-tailed distributions, and attribute-level biases (specifically, attribute-level biases that originate from demographic imbalances in sensitive domains, such as medical imaging). It proposes principled strategies to mitigate these effects in both classical and deep learning frameworks. Class imbalance and long-tailed distributions pose significant challenges, especially in real-world applications where minority classes are underrepresented yet critically important. To address these challenges, this work develops novel algorithms and frameworks that enhance model generalization on imbalanced and long-tailed datasets. The contributions encompass data-level, model-level, and loss-level innovations, each designed to mitigate bias and improve performance in minority classes while maintaining accuracy in majority classes. First, we propose a data-level solution for classical class imbalance in tabular data through a novel oversampling technique that estimates minority class statistics using neighborhood-based distributional calibration. Unlike existing methods that rely on synthetic interpolation without accounting for class-specific geometry, the proposed approach preserves the fidelity of minority class distributions, leading to significant gains in both binary and multi-label imbalanced settings. Next, we introduce STTP-Net, a two-pronged framework for long-tailed learning in vision tasks. It integrates hybrid augmentation and sampling strategies with a newly proposed Effective Balanced Softmax (EBS) loss to correct label distribution shifts, enabling robust feature learning and improved accuracy across head, medium, and tail classes. Extensive evaluations on benchmark datasets such as CIFAR-LT, ImageNet-LT, and NIH-CXR-LT confirm its superiority over state-of-the-art methods. We address decision boundary distortion under class imbalance by introducing the Goldilocks principle to achieve ``just-right'' boundary fidelity. Our approach leverages this concept to design a training pipeline that produces smoother, more adaptive decision boundaries for tail classes. Specifically, we propose a Dual-Branch Sampler-Guided Mixup (DBSGM) strategy combined with an Adaptive Class-Aware Feature Regularization (ACFR) mechanism. These components jointly enhance intra-class compactness and inter-class separability, improving generalization, especially under extreme imbalance. By dynamically adjusting boundaries and applying adaptive regularization, our method achieves optimal fidelity for minority classes without compromising the performance of majority classes. Extensive experiments validate its effectiveness across a range of imbalance ratios. Furthermore, we extend these ideas to medical imaging, addressing both class imbalance and demographic fairness. This includes the Mixture of Two Experts (Mo2E) framework and fairness-aware lesion classification strategies that ensure equitable performance across subgroups. Mo2E combines asymmetric sampling with adaptive mixup to improve the detection of rare disease classes and is validated across tasks such as Gastrointestinal (GI) Tract Classification of Endoscopic Images and Diabetic Retinopathy (DR) grading. Additionally, we introduce a bias-aware training method to mitigate both \emph{class imbalance and skin tone bias}, achieving fair performance across demographic subgroups, as demonstrated on the ASAN and ISIC-2018 datasets. These results lay the groundwork for demographically fair model design in high-stakes medical applications. Collectively, these contributions advance the field of imbalanced learning by offering scalable, practical solutions grounded in theoretical insight and empirical validation. This thesis provides a comprehensive toolkit for researchers and practitioners confronting the challenges of subpopulation shift, integrating principled data synthesis, loss rebalancing, and fairness constraints. It pushes the frontiers of robust, fair, and generalizable deep learning, particularly in domains where class rarity and demographic underrepresentation have tangible real-world consequences.Item On Robust Estimation of Multivariate Location and Scale with Applications(Indian Statistical Institute, Kolkata, 2026-02-04) Chakraborty, SoumyaThe principal objective of this thesis is, in a nutshell, to provide robust estimators of multivariate location and scale which have reasonable to high model efficiency but avoid high computational complexity so as to be practically useful in real problems. We utilize the minimum density power divergence (DPD) and the related philosophy to invoke robustness. There are some computational issues while minimizing the DPD in different multivariate set-ups. We will work on this problem rigorously and come up with three types of estimation procedures which are explicitly or implicitly related to the minimum DPD methodology, keeping the computational issue in mind each time. In particular, we develop a robust clustering algorithm based on mixture normal models in the first work where the component mean vectors and covariance matrices are estimated by minimizing the DPD with a suitable iteratively reweighted least squares (IRLS) algorithm. The second work proposes a sequential approach to minimize the DPD for location-scale estimation in case of elliptically symmetric probability models. The third work studies the one-step minimization of the DPD with various highly robust initializations and iterative procedures. We derive the theoretical properties (asymptotic and robustness features) of these methods, empirically validate them with extensive simulation studies in various set-ups and apply them in different problems in the domains of pattern recognition and machine learning.Item Statistical Guarantees of Deep Generative Models Involving Diverse Spaces: Generation Consistency and Robustness(Indian Statistical Institute, Kolkata, 2026-02-04) Chakrabarty, AnishGenerative modeling focuses on the task of producing new data samples that closely resemble those drawn from an original, unknown distribution. Despite being well-known in statistical estimation theory, the approach has gained substantial traction in recent years, driven by groundbreaking results in areas such as image synthesis, natural language generation, and network modeling. The complexity of modern-era data domains and the ensuing adaptations that suitable models must undergo have presented new challenges. These advances raise several fundamental questions, the first of which is: When do generative models accurately approximate the true data distribution? One may also ask: How well do these models perform under contaminated data? This work explores these questions through the lens of generative modeling frameworks that, by design, involve distinct data spaces. We focus on two major classes of such models that blend optimal transport and representation learning in their objectives: Wasserstein autoencoders (WAE) and Cycle-consistent cross-domain translators. WAE, on its way to regeneration, learns a latent code, which in turn aids the simulation of newer pseudo-random replicates. By providing statistical characterizations of the latent distribution and the transforms inducing a dimensionality reduction in the process, we present a detailed error analysis underlying WAEs. From a non-parametric density estimation perspective, we establish deterministic bounds on the latent and reconstruction errors that adapt to the intrinsic dimensions of input data. We also study the extent of distortion that WAE-generated samples suffer when learned using contaminated data. Key takeaways for practitioners from our analysis include specific architectural suggestions that foster near-perfect sampling. The framework developed thus far fittingly extends to unpaired cycle-consistent cross-domain models. We show that the sufficient conditions for successful data translation under Sobolev and H¨older-smooth distributions resemble those in the case of WAEs. Our analysis also suggests error upper bounds due to ill-posed transformations and validates the choice of divergences used in objectives. Finally, in search of a consolidated solution to the robustification problem, we present parallel formulations based on the Gromov-Wasserstein (GW) distance. Due to the equivalence of Gromov-Monge samplers (GW), following GW, and cross-domain translation models, including WAE and GWAE, this answers the second question. We study the robust recovery guarantees, concentration, and tractable computational properties of the newly introduced distance measures under diverse contamination scenarios. We substantiate all our findings based on real-world data in varying generative tasks.