Navjot Singh

Ritesh Chandra, Kumar Abhishek, Sonali Agarwal et al.

The forests are significant assets for every country. When it gets destroyed, it may negatively impact the environment, and forest fire is one of the primary causes. Fire weather indices are widely used to measure fire danger and are used to issue bushfire warnings. It can also be used to predict the demand for emergency management resources. Sensor networks have grown in popularity in data collection and processing capabilities for a variety of applications in industries such as medical, environmental monitoring, home automation etc. Semantic sensor networks can collect various climatic circumstances like wind speed, temperature, and relative humidity. However, estimating fire weather indices is challenging due to the various issues involved in processing the data streams generated by the sensors. Hence, the importance of forest fire detection has increased day by day. The underlying Semantic Sensor Network (SSN) ontologies are built to allow developers to create rules for calculating fire weather indices and also the convert dataset into Resource Description Framework (RDF). This research describes the various steps involved in developing rules for calculating fire weather indices. Besides, this work presents a Web-based mapping interface to help users visualize the changes in fire weather indices over time. With the help of the inference rule, it designed a decision support system using the SSN ontology and query on it through SPARQL. The proposed fire management system acts according to the situation, supports reasoning and the general semantics of the open-world followed by all the ontologies

Navjot Singh, Edgar Solomonik

CP decomposition (CPD) is prevalent in chemometrics, signal processing, data mining and many more fields. While many algorithms have been proposed to compute the CPD, alternating least squares (ALS) remains one of the most widely used algorithm for computing the decomposition. Recent works have introduced the notion of eigenvalues and singular values of a tensor and explored applications of eigenvectors and singular vectors in areas like signal processing, data analytics and in various other fields. We introduce a new formulation for deriving singular values and vectors of a tensor by considering the critical points of a function different from what is used in the previous work. Computing these critical points in an alternating manner motivates an alternating optimization algorithm which corresponds to alternating least squares algorithm in the matrix case. However, for tensors with order greater than equal to $3$, it minimizes an objective function which is different from the commonly used least squares loss. Alternating optimization of this new objective leads to simple updates to the factor matrices with the same asymptotic computational cost as ALS. We show that a subsweep of this algorithm can achieve a superlinear convergence rate for exact CPD with known rank and verify it experimentally. We then view the algorithm as optimizing a Mahalanobis distance with respect to each factor with ground metric dependent on the other factors. This perspective allows us to generalize our approach to interpolate between updates corresponding to the ALS and the new algorithm to manage the tradeoff between stability and fitness of the decomposition. Our experimental results show that for approximating synthetic and real-world tensors, this algorithm and its variants converge to a better conditioned decomposition with comparable and sometimes better fitness as compared to the ALS algorithm.

Ritesh Chandra, Sadhana Tiwari, Sonali Agarwal et al.

Vector-borne diseases (VBDs) are a kind of infection caused through the transmission of vectors generated by the bites of infected parasites, bacteria, and viruses, such as ticks, mosquitoes, triatomine bugs, blackflies, and sandflies. If these diseases are not properly treated within a reasonable time frame, the mortality rate may rise. In this work, we propose a set of ontologies that will help in the diagnosis and treatment of vector-borne diseases. For developing VBD's ontology, electronic health records taken from the Indian Health Records website, text data generated from Indian government medical mobile applications, and doctors' prescribed handwritten notes of patients are used as input. This data is then converted into correct text using Optical Character Recognition (OCR) and a spelling checker after pre-processing. Natural Language Processing (NLP) is applied for entity extraction from text data for making Resource Description Framework (RDF) medical data with the help of the Patient Clinical Data (PCD) ontology. Afterwards, Basic Formal Ontology (BFO), National Vector Borne Disease Control Program (NVBDCP) guidelines, and RDF medical data are used to develop ontologies for VBDs, and Semantic Web Rule Language (SWRL) rules are applied for diagnosis and treatment. The developed ontology helps in the construction of decision support systems (DSS) for the NVBDCP to control these diseases.

Amritansh Maurya, Navjot Singh, Mohammed Javed et al.

Large Language Models (LLMs) have shown promising results on NLP tasks, however, their performance on tabular data still needs research attention, because Table Question-Answering (TQA) requires precise cell retrieval and multi-step structured reasoning. Existing work improves TQA either by fine-tuning or training LLMs on task-specific tabular data, but often lacks verifiable control over how the model navigates tables and derives answers. In this work, we propose a training-free TQA approach with two structured prompting frameworks: TableGrid Navigation (TGN), which iteratively navigates rows and columns via a three-module loop to locate evidence and refine answers, and Progressive Inference Prompting (PIP), which enforces columns identification for explicit progressive row selection constraint according to the query. We evaluate 17 LLMs against 6 baselines on TableBench and FeTaQa dataset. On TableBench, TGN improves over the strongest baseline by 3.8 points, and on FeTaQa, PIP achieves SOTA performance over ReAct and Chain-of-Thought. Beyond inference-time gains, PIP and TGN can also serve as supervision templates to fine-tune small models, narrowing the performance gap to much larger architectures in resource-constrained settings, offering versatile and cost-efficient solution for TQA.

Navjot Singh, Kipton Barros, Xiaoye Sherry Li

Objectives involving bilinear forms $u^\top f(A(θ))v$ for Hermitian $A$ arise widely in scientific computing and probabilistic machine learning. For large matrices, Lanczos efficiently approximates these quantities, but differentiating them with respect to $θ$ is challenging. Existing approaches either backpropagate through the Lanczos recurrence, requiring reorthogonalization for stability, or apply Arnoldi to an augmented block matrix of twice the original size. Both introduce extra computation and orthogonalization costs that can limit performance on modern hardware. We propose a forward-only gradient approximation that reuses the Lanczos pass and adds very minimal overhead in most cases. We prove that its error is proportional to the Lanczos residual norm, the same quantity controlling the forward approximation. Whereas a traditional adjoint-based calculation would be unstable without reorthogonalization, the new method appears unconditionally stable in our tests. It is also faster than existing state-of-the-art approaches.

Navjot Singh, Edgar Solomonik, Xiaoye Sherry Li et al.

This paper presents low-complexity tensor completion algorithms and their efficient implementation to reconstruct highly oscillatory operators discretized as $n\times n$ matrices. The underlying tensor decomposition is based on the reshaping of the input matrix and its butterfly decomposition into an order $O (\log n)$ tensor. The reshaping of the input matrix into a tensor allows for representation of the butterfly decomposition as a tensor decomposition with dense tensors. This leads to efficient utilization of the existing software infrastructure for dense and sparse tensor computations. We propose two tensor completion algorithms in the butterfly format, using alternating least squares and gradient-based optimization, as well as a novel strategy that uses low-rank matrix completion to efficiently generate an initial guess for the proposed algorithms. To demonstrate the efficiency and applicability of our proposed algorithms, we perform three numerical experiments using simulated oscillatory operators in seismic applications. In these experiments, we use $O (n \log n)$ observed entries in the input matrix and demonstrate an $O(n\log^3 n)$ computational cost of the proposed algorithms, leading to a speedup of orders of magnitudes per iteration for large matrices compared to the low-rank matrix and quantized tensor-train completion. Moreover, the proposed butterfly completion algorithms, equipped with the novel initial guess generation strategy, achieve reconstruction errors that are smaller by an order of magnitude, enabling accurate recovery of the underlying structure compared to the state-of-the-art completion algorithms.

Ritesh Chandra, Sonali Agarwal, Navjot Singh

Timely detection of critical health conditions remains a major challenge in public health analytics, especially in Big Data environments characterized by high volume, rapid velocity, and diverse variety of clinical data. This study presents an ontology-enabled real-time analytics framework that integrates Complex Event Processing (CEP) and Large Language Models (LLMs) to enable intelligent health event detection and semantic reasoning over heterogeneous, high-velocity health data streams. The architecture leverages the Basic Formal Ontology (BFO) and Semantic Web Rule Language (SWRL) to model diagnostic rules and domain knowledge. Patient data is ingested and processed using Apache Kafka and Spark Streaming, where CEP engines detect clinically significant event patterns. LLMs support adaptive reasoning, event interpretation, and ontology refinement. Clinical information is semantically structured as Resource Description Framework (RDF) triples in Graph DB, enabling SPARQL-based querying and knowledge-driven decision support. The framework is evaluated using a dataset of 1,000 Tuberculosis (TB) patients as a use case, demonstrating low-latency event detection, scalable reasoning, and high model performance (in terms of precision, recall, and F1-score). These results validate the system's potential for generalizable, real-time health analytics in complex Big Data scenarios.

Navjot Singh, Suhas Diggavi

In this paper, we consider the problem of learning a linear regression model on a data domain of interest (target) given few samples. To aid learning, we are provided with a set of pre-trained regression models that are trained on potentially different data domains (sources). Assuming a representation structure for the data generating linear models at the sources and the target domains, we propose a representation transfer based learning method for constructing the target model. The proposed scheme is comprised of two phases: (i) utilizing the different source representations to construct a representation that is adapted to the target data, and (ii) using the obtained model as an initialization to a fine-tuning procedure that re-trains the entire (over-parameterized) regression model on the target data. For each phase of the training method, we provide excess risk bounds for the learned model compared to the true data generating target model. The derived bounds show a gain in sample complexity for our proposed method compared to the baseline method of not leveraging source representations when achieving the same excess risk, therefore, theoretically demonstrating the effectiveness of transfer learning for linear regression.

Navjot Singh, Xuanyu Cao, Suhas Diggavi et al.

We consider a multi-agent network where each node has a stochastic (local) cost function that depends on the decision variable of that node and a random variable, and further the decision variables of neighboring nodes are pairwise constrained. There is an aggregate objective function for the network, composed additively of the expected values of the local cost functions at the nodes, and the overall goal of the network is to obtain the minimizing solution to this aggregate objective function subject to all the pairwise constraints. This is to be achieved at the node level using decentralized information and local computation, with exchanges of only compressed information allowed by neighboring nodes. The paper develops algorithms and obtains performance bounds for two different models of local information availability at the nodes: (i) sample feedback, where each node has direct access to samples of the local random variable to evaluate its local cost, and (ii) bandit feedback, where samples of the random variables are not available, but only the values of the local cost functions at two random points close to the decision are available to each node. For both models, with compressed communication between neighbors, we have developed decentralized saddle-point algorithms that deliver performances no different (in order sense) from those without communication compression; specifically, we show that deviation from the global minimum value and violations of the constraints are upper-bounded by $\mathcal{O}(T^{-\frac{1}{2}})$ and $\mathcal{O}(T^{-\frac{1}{4}})$, respectively, where $T$ is the number of iterations. Numerical examples provided in the paper corroborate these bounds and demonstrate the communication efficiency of the proposed method.

Kaan Ozkara, Navjot Singh, Deepesh Data et al.

Traditionally, federated learning (FL) aims to train a single global model while collaboratively using multiple clients and a server. Two natural challenges that FL algorithms face are heterogeneity in data across clients and collaboration of clients with {\em diverse resources}. In this work, we introduce a \textit{quantized} and \textit{personalized} FL algorithm QuPeD that facilitates collective (personalized model compression) training via \textit{knowledge distillation} (KD) among clients who have access to heterogeneous data and resources. For personalization, we allow clients to learn \textit{compressed personalized models} with different quantization parameters and model dimensions/structures. Towards this, first we propose an algorithm for learning quantized models through a relaxed optimization problem, where quantization values are also optimized over. When each client participating in the (federated) learning process has different requirements for the compressed model (both in model dimension and precision), we formulate a compressed personalization framework by introducing knowledge distillation loss for local client objectives collaborating through a global model. We develop an alternating proximal gradient update for solving this compressed personalization problem, and analyze its convergence properties. Numerically, we validate that QuPeD outperforms competing personalized FL methods, FedAvg, and local training of clients in various heterogeneous settings.

Chaoqi Yang, Cheng Qian, Navjot Singh et al.

Tensor decompositions are powerful tools for dimensionality reduction and feature interpretation of multidimensional data such as signals. Existing tensor decomposition objectives (e.g., Frobenius norm) are designed for fitting raw data under statistical assumptions, which may not align with downstream classification tasks. In practice, raw input tensors can contain irrelevant information while data augmentation techniques may be used to smooth out class-irrelevant noise in samples. This paper addresses the above challenges by proposing augmented tensor decomposition (ATD), which effectively incorporates data augmentations and self-supervised learning (SSL) to boost downstream classification. To address the non-convexity of the new augmented objective, we develop an iterative method that enables the optimization to follow an alternating least squares (ALS) fashion. We evaluate our proposed ATD on multiple datasets. It can achieve 0.8% - 2.5% accuracy gain over tensor-based baselines. Also, our ATD model shows comparable or better performance (e.g., up to 15% in accuracy) over self-supervised and autoencoder baselines while using less than 5% of learnable parameters of these baseline models

Chaoqi Yang, Navjot Singh, Cao Xiao et al.

Existing tensor completion formulation mostly relies on partial observations from a single tensor. However, tensors extracted from real-world data are often more complex due to: (i) Partial observation: Only a small subset (e.g., 5%) of tensor elements are available. (ii) Coarse observation: Some tensor modes only present coarse and aggregated patterns (e.g., monthly summary instead of daily reports). In this paper, we are given a subset of the tensor and some aggregated/coarse observations (along one or more modes) and seek to recover the original fine-granular tensor with low-rank factorization. We formulate a coupled tensor completion problem and propose an efficient Multi-resolution Tensor Completion model (MTC) to solve the problem. Our MTC model explores tensor mode properties and leverages the hierarchy of resolutions to recursively initialize an optimization setup, and optimizes on the coupled system using alternating least squares. MTC ensures low computational and space complexity. We evaluate our model on two COVID-19 related spatio-temporal tensors. The experiments show that MTC could provide 65.20% and 75.79% percentage of fitness (PoF) in tensor completion with only 5% fine granular observations, which is 27.96% relative improvement over the best baseline. To evaluate the learned low-rank factors, we also design a tensor prediction task for daily and cumulative disease case predictions, where MTC achieves 50% in PoF and 30% relative improvements over the best baseline.

Kaan Ozkara, Navjot Singh, Deepesh Data et al.

Traditionally, federated learning (FL) aims to train a single global model while collaboratively using multiple clients and a server. Two natural challenges that FL algorithms face are heterogeneity in data across clients and collaboration of clients with {\em diverse resources}. In this work, we introduce a \textit{quantized} and \textit{personalized} FL algorithm QuPeL that facilitates collective training with heterogeneous clients while respecting resource diversity. For personalization, we allow clients to learn \textit{compressed personalized models} with different quantization parameters depending on their resources. Towards this, first we propose an algorithm for learning quantized models through a relaxed optimization problem, where quantization values are also optimized over. When each client participating in the (federated) learning process has different requirements of the quantized model (both in value and precision), we formulate a quantized personalization framework by introducing a penalty term for local client objectives against a globally trained model to encourage collaboration. We develop an alternating proximal gradient update for solving this quantized personalization problem, and we analyze its convergence properties. Numerically, we show that optimizing over the quantization levels increases the performance and we validate that QuPeL outperforms both FedAvg and local training of clients in a heterogeneous setting.

Navjot Singh, Deepesh Data, Jemin George et al.

In this paper, we propose and analyze SQuARM-SGD, a communication-efficient algorithm for decentralized training of large-scale machine learning models over a network. In SQuARM-SGD, each node performs a fixed number of local SGD steps using Nesterov's momentum and then sends sparsified and quantized updates to its neighbors regulated by a locally computable triggering criterion. We provide convergence guarantees of our algorithm for general (non-convex) and convex smooth objectives, which, to the best of our knowledge, is the first theoretical analysis for compressed decentralized SGD with momentum updates. We show that the convergence rate of SQuARM-SGD matches that of vanilla SGD. We empirically show that including momentum updates in SQuARM-SGD can lead to better test performance than the current state-of-the-art which does not consider momentum updates.

Navjot Singh, Deepesh Data, Jemin George et al.

In this paper, we propose and analyze SPARQ-SGD, which is an event-triggered and compressed algorithm for decentralized training of large-scale machine learning models. Each node can locally compute a condition (event) which triggers a communication where quantized and sparsified local model parameters are sent. In SPARQ-SGD each node takes at least a fixed number ($H$) of local gradient steps and then checks if the model parameters have significantly changed compared to its last update; it communicates further compressed model parameters only when there is a significant change, as specified by a (design) criterion. We prove that the SPARQ-SGD converges as $O(\frac{1}{nT})$ and $O(\frac{1}{\sqrt{nT}})$ in the strongly-convex and non-convex settings, respectively, demonstrating that such aggressive compression, including event-triggered communication, model sparsification and quantization does not affect the overall convergence rate as compared to uncompressed decentralized training; thereby theoretically yielding communication efficiency for "free". We evaluate SPARQ-SGD over real datasets to demonstrate significant amount of savings in communication over the state-of-the-art.