2024 SEMINARS

T-helper cells play a key role in the regulation of the immune response. Disregulations of their differentiation can lead to various pathological conditions, including leukemia, persistance of other kinds of tumors, and autoimmune diseases.  

The development and differentiation of T-helper cells is controlled by a complex molecular network involving dozens of signalling pathways, transcriptional factors and epigenetic regulatory mechanims. Mathematical modelling of such complex networks can be used to integrate and verify the consistency of the available information, and to predict network behaviour in novel situation, e.g. following (epi)genetic perturbations or therapeutical interventions.

Over the last decade, we have developped a series of discrete, logical models accounting for the development of T-helper cells and for their differentiation in various effector or regulatory subtypes [1-7]. In order to cope with increasing model sizes and ensure the reproducibility of our model analyses, we developed and combined generic computational methods and tools, which are available from the Consortium for Logical Models and Tools website (https://github.com/colomoto) [8].

This talk will provide an overview of this work with a special focus on reproducibility issues and discuss current trends and challenges

References 

[1] Naldi et al., PLoS Computational Biology 6: e1000912 (2010).

[2] Abou-Jaoudé et al., Frontiers in Bioengineering and Biotechnology 2: 86 (2015). 

[3] Cacace et al., Current Topics in Developmental Biology 139: 205-38 (2020).

[4] Rodríguez-Jorge et al., Science Signaling 12: eaar3641 (2019).

[5] Sánchez-Villanueva et al., PLoS One 14: e0226388 (2019).

[6] Grandclaudon et al., Cell 179: 432-47. (2019).

[7] Corral-Jara et al., Molecular Biomedicine 2:9 (2021).

[8] Naldi et al. Frontiers in Physiology 9: 680 (2018).

Gene expression is regulated by proteins called transcription factors (TFs) which bind DNA and recruit or inhibit the transcriptional machinery. Individual TFs recognize and bind to short patterns or "motifs" in DNA, typically 8-15 basepairs long, and identifying these motifs, both de novo and from databases of known motifs, is a longstanding problem. These are traditionally represented as position weight matrices, that is, independent position-specific probability distributions of nucleotides, and visualized using sequence logos.

In 2010 (PLOS One 2010) we proposed going beyond the position weight matrix model to incorporate dinucleotide correlations. Not only are correlations significant within binding sites, but we found that incorporating flanking sequence improved predictive performance.

In 2018 we presented an algorithm, THiCweed (NAR 2018), for analysing ChIP-seq data by clustering similar peaks. We found that clustering ChIP-seq sequence based on sequence similarity uncovers known motifs, but also many variants of known motifs, extraneous motifs, and sequence signatures extending well beyond the core motif. An update is in progress.

Recently we have developed CoNNsequence  (in preparation), which uses a multilayer convolutional neural network to distinguish binding from non-binding sequence. CoNNsequence accurately distinguishes binding from non-binding sequence even when the core motif is removed from the sequence, suggesting that there are other strong sequence signatures for TF-binding DNA.  It also provides a framework for analysing and visualising the significance of mutations, individually and in combination, revealing sequence signatures over hundreds of basepairs surrounding the core motif.  Extension of this work to identifying other functional sequence, such as TAD boundaries, is in progress, and a future goal is to generate synthetic sequence that can perform such functions in vivo.

The picture that emerges is that the typical picture of regulatory DNA sequence, as essentially random sequence with a few short binding sites embedded in it, is far from reality, and understanding the full 

Fluorescence microscopy faces limitations due to the microscope’s optics, fluorophore chemistry, and photon exposure limits. This necessitates trade-offs in imaging speed, resolution, and depth. In my talk, I will discuss the two deep-learning-based computational multiplexing techniques I developed during my PhD that enhanced the imaging of multiple cellular structures within a single fluorescent channel, allowing faster imaging and reduced photon exposure. Given a superimposed image (say containing Nucleus and Tubulin), my PhD research is to predict its constituent images separately. Our approach can sample diverse predictions from a trained posterior. In other words, we provide multiple plausible solutions for a given input image, and the diversity of these solutions scales with the uncertainty in each input. At last, I will end my talk with a brief mention of our ongoing collaboration with researchers from Google towards a related problem of bleed-through removal using InDI, a diffusion-like iterative model.

Quantile-Quantile (Q-Q) plots are widely used for assessing the distributional similarity between two univariate datasets. Q-Q plots in multivariate settings, however, fail to capture complex dependencies present in the data. In this work, we propose a novel approach for constructing multivariate Q-Q plots, which extend the traditional Q-Q plot methodology to handle high-dimensional data. Our approach utilizes optimal transport (OT) and entropy-regularized optimal transport (EOT) to align the empirical quantiles of the two datasets. Additionally, we introduce another technique based on OT and EOT potentials which can effectively compare two multivariate datasets. Through extensive simulations and real data examples, we demonstrate the effectiveness of our proposed approach in capturing multivariate dependencies and identifying distributional differences such as tail behaviour. We also propose two test statistics based on the Q-Q and potential plots to compare two distributions rigorously. This talk is based on a joint work with Sibsankar Singha and Marie Kratz. 

There are a number of interesting questions regarding the inference of dynamical systems from observations of the state variable.After reviewing several of these questions, I will introduce the concept of a Luenberger observer, which is a widely used method in controltheory to estimate the state of a dynamical system given some observations (usually a time-series). Despite its relative simplicity, and notable robustness, the convergence properties of the Luenberger observer are not well understood. In this talk, I will introduce some recent work that establishes a path to proving convergence for a class of finite-dynamical systems. 

Large neural models are often compressed before deployment. Model compression is necessary for many practical reasons, such as inference latency, memory footprint, and energy consumption. In this talk, we will discuss two key questions related to model compression.

First, are compressed models really the miniature versions of large models? For various model characteristics, compressed models significantly differ from the original large model. Even among compressed models, they differ from each other on various model characteristics. Apart from the expected loss in model performance, there are major side effects of using compressed models to replace large neural models.

Second, can we customize the model compression process to target a particular task? Existing model compression methods do not utilize the information about the target application. As a result, the compressed models are application agnostic. Our method, Application Specific Compression (ASC), identifies and prunes components of the large Deep Learning model that are redundant specifically for the given target application. We observe that customized compressed models created using our ASC method perform better than existing model compression methods and off-the-shelf compressed models

The work aims at an inquiry of the optimal policy path for major macroeconomic variables most important of which are maintaining a high income level and a low level of inflation. We develop a policy model in a dynamic framework that can be used to choose optimal policy path for attaining certain macroeconomic goals in a finite time. The theoretical model is applied in the context of two economies,  India and UK. India is a lower middle income country while UK is a developed mature capitalist economy. The choice of the economies are based on our attempt to show general applicability of our model.

It is shown that all targets, whether to achieve a GDP level from a regime of low income caused by external shock, such as a pandemic or a recession and or a high inflation, may not be achievable in a finite time. However, a reasonable target can be achieved with appropriate choice of fiscal-monetary policies.

Such models can be used for finding policies for various issues including that of  sustainable development goals.

Problems of interest in many disciplines of science and engineering can be formulated mathematically as partial differential equations (PDEs). Scientific computing is a powerful approach to solving PDEs when the analytic solution is not available, as often is the case. My goal is to design accurate numerical methods to solve PDEs, in particular hyperbolic PDEs. In the interest of large-scale applications, these methods must also be suitable for constructing efficient computational algorithms to be deployed on modern high-performance computing (HPC) machines. In this talk, I will discuss the motivations behind designing the HPC suitable computational methods for problems in fluid dynamics, plasma physics, structural mechanics, etc. I will present their role in addressing outstanding real-life problems, including the design of fusion reactors. I will make some remarks on the role of data science techniques in the development of computational workflows and the possibilities of connections of my work across disciplines.

The 'leader election' problem is one of the most fundamental problems in distributed computing. In this talk, we will explore how the time complexity and message complexity of this problem change with the diameter of the underlying network graph. We will discuss matching upper and lower bounds for networks of diameter two.

This talk will be based on the following article:
Soumyottam Chatterjee, Gopal Pandurangan, and Peter Robinson. The complexity of leader election in diameter-two networks. Distributed Computing, 33(2):189-205, 2020.

Medical image segmentation is a challenging task that poses a number of challenges. In medical imaging, many techniques produce poor contrast and inhomogeneous appearances, resulting in over- and under- segmentation. The dermoscopic images of skin lesions often show large variations in size and shape, making the construction of prior shape models challenging. A panoramic X-ray image is also challenged by many flaws, including the variation in tooth size between patients and the spacing between missing teeth. The human brain can be separated into different regions based on the type of matter it contains, including gray matter, white matter, and cerebrospinal fluid. An MRI segmentation involves dividing the image into well-defined regions, in which pixels have similar intensities and textures. It is difficult to segment brain tissues from MRI images due to their tissue intensities, and partial volume effects. To overcome these problems, we propose CNN architectures for segmenting medical images.

Understanding how neural networks learn features, or relevant patterns in data, for prediction is necessary for their reliable use in technological and scientific applications. In this work, we presented a unifying mathematical mechanism, known as average gradient outer product (AGOP), that characterized feature learning in neural networks. We provided empirical evidence that AGOP captured features learned by various neural network architectures, including transformer-based language models, convolutional networks, multilayer perceptrons, and recurrent neural networks. Moreover, we demonstrated that AGOP, which is backpropagation-free, enabled feature learning in machine learning models, such as kernel machines, that a priori could not identify task-specific features. Overall, we established a fundamental mechanism that captured feature learning in neural networks and enabled feature learning in general machine learning models.

Bio: Parthe Pandit is an Assistant Professor with the Center for Machine Intelligence and Data Science (C-MInDS) at IIT Bombay. He also holds the Thakur Family Chair at IIT Bombay. He was a Simons Postdoctoral Fellow at Halıcıoğlu Data Science Institute at UC San Diego, and obtained his Ph.D. from UCLA.

Understanding cellular activities in tissue homeostasis, inflammation, and disease states remains challenging. Cell types, characterized by specific gene expression patterns, play pivotal roles in these processes. However, interactions among cell types and communication among cellular states within the tissue niche are poorly understood. To address this gap, we present NiCo (Niche Covariation), which models the colocalization of cellular states from single-cell resolution spatial transcriptomics data to unravel niche cell type interactions. NiCo further infers spatial covariation of latent factors, capturing cell state variability in tissue niches and interpreting these factors by leveraging transcriptome-wide information from scRNAseq reference data. Applying NiCo to diverse biological contexts, including the developing mouse embryo, small intestine, and liver, we predict novel niche interactions contributing to cell state variation. NiCo predicts a feedback mechanism between Kupffer cells and neighboring stellate cells that limits stellate cell activation in the normal liver. NiCo presents a valuable tool for understanding omics data and opens avenues for further exploration into the intricate language of cellular communication, promising deeper insights into the dynamics of health and disease tissues.

Recent developments in diffusion models have demonstrated an exceptional capacity to generate high-quality, prompt-conditioned image edits. Nevertheless, previous approaches have primarily relied on textual prompts for image editing, which tend to be less effective when making precise edits to specific objects or fine-grained regions within a scene containing single/multiple objects. We introduce a novel framework for zero-shot localized multi-object editing through a multi-diffusion process to overcome this challenge. This framework empowers users to perform various operations on objects within an image, such as adding, replacing, or editing many objects in a complex scene in one pass. Our approach leverages foreground masks and corresponding simple text prompts that exert localized influences on the target regions, resulting in high-fidelity image editing. Further, we also observe that existing metrics fall short when it comes to the detection of object erasure. Traditional metrics fail to align with the intuitive definition of inpainting, which aims for (1) seamless object removal within masked regions and (2) preserving the background continuity. We introduce new metrics that not only correlate with state-of-the-art metrics but also align with human perception, providing a finer-grained evaluation of the generated outputs.

 An evolving system state can be modelled as (Si, ERi, ti), such that the system state Si and the evolution representor ERi is representing system at the ith time point ti, where ‘i’ varies from 1 to N. An evolving system is expressed as a state series, SS = {S1, S2… SN}, such that each state is pre-processed to make an evolution representor ER = {ER1, ER2… ERN} for example evolving networks EN = {EN1, EN2… ENN}. We introduce a System Evolution Analytics(SysEvoAnalytics) with the following contributory approaches. First, we apply two types of pattern mining to retrieve: the Stable Network Evolution Rule and the Network Evolution Subgraph. Second, we formulate two metrics: the Stability metric and the Changeability metric. Third, we also formulate another two metrics: the System State Complexities (SSCs), and the Evolving System Complexity (ESC). Fourth, we apply Graph Evolution and Change Learning (GECL) with the help of deep evolution learning, which constructs System Neural Network to accomplish the System Evolution Recommender (SysEvoRecomd). Sixth, we discuss the change mining and evolution mining of an evolving web service system on two cloud services: the AWS, and the Eucalyptus. Fifth, we briefly discuss the Big scholarly data analytics. We discuss experimentations done using the prototypes of these techniques as different tools to perform SysEvo-Analytics. Experimentsreport information of system evolution analytics on six different domains: Software, Natural-language analytics, Retailmarket, Movie-name, Cloud-service, and Scholarly-data.

Factor analysis and principal component analysis (PCA) are popular statistical methods for summarizing and explaining the variability in multivariate datasets. By default, FA and PCA assume the number of components or factors to be known \emph{apriori}. However, in practice, the users first estimate numbers of factors or components and then perform FA and PCA analyses using the point estimate. Therefore, in practice, the users ignore any uncertainty in the point estimate of the number of factors or components. For datasets where the uncertainty in the point estimate is not ignorable, it is prudent to estimate the confidence sets for the number of factors or components. We address this problem by proposing a data intensive approach to estimate confidence sets. We also study the coverage accuracy of the confidence sets and provide theoretical guarantees. Finally, we demonstrate the usefulness of our approach through numerical simulations and real data analysis

My talk will introduce some natural language processing (NLP) problems involving customer reviews, product search and other text data. I will then briefly discuss how the language modeling landscape has evolved to the recent emergence of large language models (LLMs). LLMs, despite their popularity, have not yet been as widely adopted for real-world use-cases. I will discuss some challenges in leveraging large models in production environments for large systems with some of our recent contributions in this context. I will conclude with a brief discussion of how it is impacting various applications like search and retrieval, content generation, etc., and some interesting directions for research including technical (like evaluation, fairness, etc) and regulatory (going beyond LLMs to general artificial intelligence applications).

Measuring scientific processes results in a set of real-valued functions (scalar fields) which may be related temporally, be part of an ensemble, or unrelated. Understanding and visualizing such processes require the study of both individual fields and the development of methods to compare them meaningfully. We focus on designing meaningful measures to compare scalar fields by comparing their abstract representations called topological structures, with emphasis on intuitive and practical measures.

We present global and local comparison measures to compare topological structures called merge trees, a global comparison measure to compare extremum graphs. We follow that with faster comparison methods for merge trees using Locality Sensitive Hashing. We also provide some applications such as symmetry detection, temporal summarization, and feature tracking in time-varying fields. 

Finally, we introduce topological structures for metric measure spaces and conclude with ongoing work involving Mapper graphs and their applications in Topological Data Analysis.

Despite significant past efforts, solving the elastoplastic response of the material can be challenging due to the highly non-linear nature of underlying partial differential equations which are costly to simulate numerically.  To tackle this, physics-informed neural networks (PINNs) have emerged as a promising alternative that embedded physics into machine learning. To this end, we build an accurate, robust, and highly physics-augmented deep learning framework for surrogate modeling for von Mises and non-associative Drucker-Prager elastoplastic constitutive models. We formulate and implement an improved multi-objective loss function that can efficiently incorporate physical information corresponding to the elastoplastic laws into the neural network. Further improvement of the predictive power of our model has been achieved by considering various degrees of data-driven estimate and implementing a transfer learning approach for better accuracy, faster training, and improved generalization.

Single-cell and spatial transcriptomics has enabled profiling cell types, states from complex tissues, facilitating better understanding of human health and diseases. I will present interdisciplinary experimental and computational efforts to investigating transcriptional regulation, gene regulatory networks and cell-fate paradigms. Firstly, using big-data single-cell atlases, we infer gene regulatory networks and causal drivers, acting across multiple cell types. I will highlight use cases in diseases, where regulatory activity better predicts perturbation and disease states. Secondly, by single-cell profiling of developing respiratory epithelium, we identify a novel multipotent progenitors and chart its differentiation and lineage transitions into mature cell types (secretory, ciliated and basal cell types). Thirdly, I will present ongoing work on stem cell (iPS) models incl. iPS-derived microglia and adversarial deep learning frameworks for cell type prediction. Our work provides an avenue to further extract regulatory crosstalk from single-cell expression data and uncover cell fate paradigms in development.

As we delve into future directions and challenges, it becomes evident that the integration of deep learning in ultrasound image processing holds immense promise for advancing healthcare practices and enhancing the quality of medical care worldwide. In my talk, I will explore the transformative potential of efficient, mobile-friendly, and deployable deep learning-based models for ultrasound image processing for heart and lung. By utilizing the power of deep learning algorithms, these models promise to revolutionize the interpretation of ultrasound images by offering faster processing times, enhanced image processing accuracy, and automation of tasks. By optimizing these models for efficiency, we can ensure real-time analysis while minimizing computational resources. Moreover, their compatibility with mobile devices enables point-of-care diagnostics, allowing easy access to healthcare professionals across diverse clinical settings. I will illustrate the practical applications of these models, demonstrating their ability to support medical decision-making and improve patient outcomes. 

With the success of Deep Learning (DL), AI has immensely impacted our lives through different applications from several prominent AI fields. (including computer vision, natural language processing, and bioinformatics. The proliferation of AI-based methods has brought to light critical issues about bias (or unfairness) in classification and weak privacy guarantees of the training data. It is crucial to prioritize addressing these issues to prevent the potentially significant negative impact on users. With proliferation of Internet, distributed way of learning is becoming popular, Thus, there is need to build future AI systems that make fair decisions, protect privacy of individuals and additionally robust to manipulation by different agents, that is ensure strategyproofness. In this talk, we give an overview of all three essential aspects of AI systems, and in particular, we talk about fair and privately distributed AI.

In the dynamic domains of machine learning, robotics, and software engineering, the necessity to enhance the intelligence and awareness of artificial agents becomes increasingly critical. This presentation investigates innovative methodologies for cultivating multi-modal self-awareness and collective awareness within networks of intelligent agents, focusing particularly on anomaly detection.

The talk commences with the introduction of a pioneering approach to endow dynamic agents with self-awareness. Through leveraging multi-sensory data and meticulous feature selection, this method facilitates the prediction of future instances and the identification of abnormalities. Subsequently, various strategies for fostering collective awareness in agent networks are discussed, utilizing machine learning-equipped Internet of Things nodes to estimate states and detect anomalies during collaborative tasks. Furthermore, the examination extends to the impact of networking protocols and communications on state estimation and anomaly detection, underscoring the importance of model interpretability for precise inference in future scenarios based on anomaly data. Additionally, the presentation demonstrates the utilization of advanced graph-matching techniques to augment the clarity and interpretability of these models, promising valuable insights for the advancement of the field.

Finally, the talk will conclude with a brief discussion of recent research projects that the researcher has been involved in, including the development of real-time Covid-19 transmission models utilizing Bayesian frameworks like MCMC and SMC algorithms. Additionally, there will be a discussion on the development of Machine Learning/Deep Learning models tailored for hardware platforms to enhance system state estimation and design.

While machine learning (ML)-based artificial intelligence (AI) systems are increasingly deployed in safety-critical settings, they continue to remain unreliable under adverse conditions that violate underlying statistical assumptions, leading to critical failures. These conditions can arise in both the training and test phases of ML pipelines. In this talk, I focus on attacks in the training phase, known as poisoning. 

I will first introduce federated learning, a recent paradigm in distributed learning where agents collaborate with a server to jointly learn models. Then, I show how strong poisoning attacks are possible via a small number of compromised agents modifying model parameters via optimized updates to ensure desired data is misclassified by the global model. Experimentally, the proposed model poisoning attack is highly effective while bypassing standard detection methods. Defending against model poisoning continues to be an active area of research and I will conclude by discussing some recent approaches. 

In a world increasingly reliant on Cyber-Physical Systems (CPS), there are critical challenges associated with the integration of complex software and hardware. The enormous and diverse nature of data, alongside pressing security and privacy concerns, demands innovative solutions. My work aims to enhance the intelligence of CPS through AI, aiming for systems that are not only self-aware but also capable of adapting in real-time to changing environments. To that end, my work has spanned the automotive, energy, and hardware sectors, delivering practical solutions engineered alongside industry partners. I have made significant strides in enhancing security in automotive systems and have pioneered tools for deciphering the decision-making processes of machine learning models. In the realm of hardware design, I am exploring the potentials of Large Language Models (LLMs) to automate and optimize the process, reducing human error and increasing efficiency. In the future, I want to expand upon the challenges and scope of applying generative AI in CPS for developing time-efficient, scalable, safe and transparent real-world applications.

In a world increasingly reliant on Cyber-Physical Systems (CPS), there are critical challenges associated with the integration of complex software and hardware. The enormous and diverse nature of data, alongside pressing security and privacy concerns, demands innovative solutions. My work aims to enhance the intelligence of CPS through AI, aiming for systems that are not only self-aware but also capable of adapting in real-time to changing environments. To that end, my work has spanned the automotive, energy, and hardware sectors, delivering practical solutions engineered alongside industry partners. I have made significant strides in enhancing security in automotive systems and have pioneered tools for deciphering the decision-making processes of machine learning models. In the realm of hardware design, I am exploring the potentials of Large Language Models (LLMs) to automate and optimize the process, reducing human error and increasing efficiency. In the future, I want to expand upon the challenges and scope of applying generative AI in CPS for developing time-efficient, scalable, safe and transparent real-world applications.

Likelihood-based inferences have been remarkably successful in wide-spanning application areas. However, even after due diligence in selecting a good model for the data at hand, there is inevitably some amount of model misspecification: outliers, data contamination, or inappropriate parametric assumptions such as Gaussianity mean that most models are at best rough approximations of reality. A significant practical concern is that under large sample sizes, even small amounts of model misspecification may have a substantial impact on our inferences. In this talk, we discuss how one can robustly estimate likelihood-based models by re-weighting terms in the likelihood. We term this as "optimistic re-weighting" because the weights are chosen to make the re-weighted data look like that arising from our model. We describe a theoretically motivated alternating optimization procedure called Optimistically Weighted Likelihood (OWL) to obtain these weights. We describe two applications of OWL: first to estimate the average treatment effect in a micro credit study in the presence of outliers, and second to robustly fit a Gaussian mixture model to single cell RNA-Seq data.

Given observations, Linear Regression aims to learn a linear relationship between an outcome variable and a set of predictor variables. The usual least squares estimator (and its associated confidence interval) is derived under the assumption that the errors are Gaussian with zero mean and constant variances. In this talk, we discuss diagnostic measures to detectwhen some of the assumptions underlying linear regression are violated in a way that may adversely affect our inferences. This includes the case when the errors are non-Gaussian, have non-constant variances, or there are outliers and high-leverage data points that unduly influence our model fit. We discuss some strategies to correct for these problems based on transforming data and using robust regression methods

Take a chess game. How does the brain enable the complex cognition required? Large-scale brain functional networks are known to be key, and disruptions to these networks likely underlie brain disorders. Hence, several Data Science methods have been developed to characterise brain networks from human Neuroscience data. However, these methods use general statistical models whose parameters lack a neurophysiological interpretation. This hampers understanding brain networks in neurophysiological terms. In contrast, Brain Computational Models use differential equations to express neurophysiological understanding on the generation of brain networks. In this talk, I will speak about my recent work on developing Data Science methods to inform Brain Computational Models with human Neuroscience data, thereby advancing neurophysiological understanding on the generation of empirically observed brain networks. I will complete my talk by outlining how I will advance this line of work to answer our original question on how the brain works.

Take a chess game. How does the brain enable the complex cognition required? Large-scale brain functional networks are known to be key, and disruptions to these networks likely underlie brain disorders. Hence, several Data Science methods have been developed to characterise brain networks from human Neuroscience data. However, these methods use general statistical models whose parameters lack a neurophysiological interpretation. This hampers understanding brain networks in neurophysiological terms. In contrast, Brain Computational Models use differential equations to express neurophysiological understanding on the generation of brain networks. In this talk, I will speak about my recent work on developing Data Science methods to inform Brain Computational Models with human Neuroscience data, thereby advancing neurophysiological understanding on the generation of empirically observed brain networks. I will complete my talk by outlining how I will advance this line of work to answer our original question on how the brain works.

This talk will present results on applying linear transfer operator theory involving Perron-Frobenius and Koopman operators for data-driven control problems. The control problem with safety constraints for a system involving nonlinear dynamics can be written as a non-convex optimization problem. The main contribution of this work is to show that optimal control problems with safety constraints can be formulated as convex optimization problems using methods and techniques from linear operator theory. Furthermore, finite-dimensional approximation of the linear operators and their spectrum can be used to design data-driven controllers without explicit knowledge of system dynamics. We will also discuss the application of these results for analyzing power systems dynamics and safe control design for vehicle autonomy

Real-world applications involve making decisions sequentially through dynamic interactions with the environment. Tech giants like Google and Meta use sequential learning algorithms to generate billions in revenue via online advertising. While the potential applications of these algorithms in high-stakes fields such as medicine, defense, and autonomous vehicles are vast, their adoption to safety-critical domains is low due to a limited understanding of their behavior in diverse practical environments.

We will look at designing robust algorithms safe for real-world applications. In the first part, we will consider the regret minimisation problem in the multi-armed bandit setting with minimal distributional assumptions. We will discuss an optimal algorithm for this problem and the ideas involved in its design and analysis. A crucial component will be a novel mean estimator for heavy-tailed distributions, which may be of independent interest to researchers and practitioners. In the second part, we will briefly explore a scenario where the algorithm may observe data that is occasionally corrupted and ideas for robustness in such settings.

When thousands or millions of entities of interest are parallelly or sequentially tested, false discovery rate control emerges as a powerful concept instead of the stringent goal of making no mistakes. The seminal works of Benjamini and Hochberg (BH) in 1995 and Sun and Cai (SC) in 2007 apply to the simplest possible scenario. The introduction to the idea of false discovery rate control and the BH and SC procedures will be the introductory part of the talk. Inevitably, several complex data structures in contemporary datasets may arise: the entities or hypotheses may have a natural hierarchical structure, further auxiliary information may be available, differentiation of small and large effect sizes may become relevant, and there may also be an asymmetry in directional errors. Using weights provides an effective strategy to incorporate prior domain knowledge in large-scale inference. In the second part of the talk, I will discuss one concrete statistical methodology we developed to solve the weighted multiple testing in a decision-theoretic framework.