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Ritwik Bhattacharya

Publications and source records attributed to Ritwik Bhattacharya.

11 recordsLinked to original sources

DP-FlogTinyLLM: Differentially private federated log anomaly detection using Tiny LLMs

Modern distributed systems generate massive volumes of log data that are critical for detecting anomalies and cyber threats. However, in real world settings, these logs are often distributed across multiple organizations and cannot be centralized due to privacy and security constraints. Existing log anomaly detection methods, including recent large language model (LLM) based approaches, largely rely on centralized training and are not suitable for such environments. In this paper, we propose DP-FLogTinyLLM, a privacy preserving federated framework for log anomaly detection using parameter efficient LLMs. Our approach enables collaborative learning without sharing raw log data by integrating federated optimization with differential privacy. To ensure scalability in resource constrained environments, we employ low rank adaptation (LoRA) for efficient fine tuning of Tiny LLMs at each client. Empirical results on the Thunderbird and BGL datasets show that the proposed framework matches the performance of centralized LLM based methods, while incurring additional computational overhead due to privacy mechanisms. Compared to existing federated baselines, DP-FLogTinyLLM consistently achieves higher precision and F1-score, with particularly strong gains on the Thunderbird dataset, highlighting its effectiveness in detecting anomalies while minimizing false positives.

cs.CR

Bayesian Optimum Warranty Region for Right Censored Two Dimensional Dependent Data

Warranty policies play a crucial role in balancing customer satisfaction and cost of the manufacturer. Traditional one-dimensional warranty frameworks, based solely on either age or usage, often fail to capture the joint effect of product life factors. This article investigates two-dimensional warranty policies by combining Free Replacement Warranty, Pro-Rata Warranty, and Combination FRW-PRW Warranty schemes across both age and usage scales. A dissatisfaction cost function is proposed alongside the economic benefit and warranty cost functions, and the expected utility framework is employed to derive optimal warranty parameters. The expectation is taken with respect to the posterior predictive distribution of product lifetime and usage data, ensuring a data-driven approach. Finally, the methodology is validated using an open-source dataset, and a new two-dimensional starter motor dataset is introduced to demonstrate the practical advantages of adopting two-dimensional warranty policies.

stat.AP

Computation of Optimal Type-II Progressing Censoring Scheme Using Genetic Algorithm Approach

The experimenter must perform a legitimate search in the entire set of feasible censoring schemes to identify the optimal type II progressive censoring scheme, when applied to a life-testing experiment. Current recommendations are limited to small sample sizes. Exhaustive search strategies are not practically feasible for large sample sizes. This paper proposes a meta-heuristic algorithm based on the genetic algorithm for large sample sizes. The algorithm is found to provide optimal or near-optimal solutions for small sample sizes and large sample sizes. Our suggested optimal criterion is based on the cost function and is scale-invariant for both location-scale and log-location-scale distribution families. To investigate how inaccurate parameter values or cost coefficients may affect the optimal solution, a sensitivity analysis is also taken into account.

stat.AP

LogTinyLLM: Tiny Large Language Models Based Contextual Log Anomaly Detection

Log anomaly detection using traditional rule based or deep learning based methods is often challenging due to the large volume and highly complex nature of log sequence. So effective way of detection of anomalous sequence of logs is crucial for system maintenance and development. This paper proposes parameter efficient finetuning specifically low rank adaptation (LoRA) and adapter based approaches for finding contextual anomalies in sequence of logs in large log data set. It compares different tiny large language models (LLMs) on the Thunderbird dataset. The results show that LoRA based finetuning provides substantial performance improvements of 18 to 19 percentage over LogBert based full finetuning approach, achieving accuracy scores between 97.76% and 98.83% compared to 79.37%.

cs.LG

Determination of Optimum Warranty Region for Two Dimensional Dependent Data

This paper presents a method for determining the optimal two-dimensional warranty region for age and mileage scales across all possible combinations of free replacement warranty (FRW), prorata warranty (PRW), and FRW-PRW combined policies. The operational time or lifetime and usage of the products are modeled using a bivariate Gumbel copula with Weibull as the marginal distribution. The optimal warranty region is derived by maximizing an expected utility function, which incorporates two cost components: the economic benefit function and the warranty cost function, specifically constructed for the two-dimensional warranty scenario. To obtain the optimal warranty region, a real-world dataset of traction motors, including age and mileage information, is analyzed. The results show that considering a two-dimensional warranty cost function yields the highest utility compared to all other scenarios.

stat.AP

Simultaneous best linear invariant prediction of future order statistics for location-scale and scale families and associated optimality properties

In this article, we first derive an explicit expression for the marginal best linear invariant predictor (BLIP) of an unobserved future order statistic based on a set of early observed ordered statistics. We then derive the joint BLIPs of two future order statistics and prove that the joint predictors are trace-efficient as well as determinant-efficient linear invariant predictors. More generally, the BLIPs are shown to possess complete mean squared predictive error matrix dominance property in the class of all linear invariant predictors of two future unobserved order statistics. Finally, these results are extended to the case of simultaneous BLIPs of any $\ell$ future order statistics. Both scale and location-scale families of distributions are considered as the parent distribution for the development of results.

math.ST

On simultaneous best linear unbiased prediction of future order statistics and associated properties

In this article, the joint best linear unbiased predictors (BLUPs) of two future unobserved order statistics, based on a set of observed order statistics, are developed explicitly. It is shown that these predictors are trace-efficient as well as determinant-efficient BLUPs. More generally, the BLUPs are shown to possess complete mean squared predictive error matrix dominance in the class of all linear unbiased predictors of two future unobserved order statistics. Finally, these results are extended to the case of simultaneous BLUPs of any $l$ future order statistics.

stat.AP

A MCMC-type simple probabilistic approach for determining optimal progressive censoring schemes

We present here a simple probabilistic approach for determining an optimal progressive censoring scheme by defining a probability structure on the set of feasible solutions. Given an initial solution, the new updated solution is computed within the probabilistic structure. This approach will be especially useful when the cardinality of the set of feasible solutions is large. The validation of the proposed approach is demonstrated by comparing the optimal scheme with these obtained by exhaustive numerical search.

stat.AP

D-optimal joint best linear unbiased prediction of order statistics

In life-testing experiments, it is often of interest to predict unobserved future failure times based on observed early failure times. A point best linear unbiased predictor (BLUP) has been developed in this context by Kaminsky and Nelson (1975). In this article, we develop joint BLUPs of two future failure times based on early failure times by minimizing the determinant of the variance-covariance matrix of the predictors. The advantage of applying joint prediction is demonstrated by using a real data set. The non-existence of joint BLUPs in certain setups is also discussed.

stat.AP

Determination of Bayesian optimal warranty length under Type-II unified hybrid censoring scheme

Determination of an appropriate warranty length for the lifetime of the product is an important issue to the manufacturer. In this article, optimal warranty length of the product for the combined free replacement and the pro-rata warranty policy is computed based on the Type-II unified hybrid censored data. A non-linear pro-rata warranty policy is proposed in this context. The optimal warranty length is obtained by maximizing an expected utility function. The expectation is taken with respect to the posterior predictive model for the time-to-failure data. It is observed that the non-linear pro-rata warranty policy gives a larger warranty length with maximum profit as compared to linear warranty policy. Finally, a real-data set is analyzed in order to illustrate the advantage of using non-linear pro-rata warranty policy.

econ.GN

Statistical inference and Bayesian optimal life-testing plans under Type-II unified hybrid censoring scheme

This article describes the inferential procedures and Bayesian optimal life-testing issues under Type-II unified hybrid censoring scheme. First, the explicit expressions of expected number of failures, expected duration of testing and Fisher information matrix for the unknown parameters of the underlying lifetime model are derived. Then, using these quantities, the Bayesian optimal life-testing plans are computed in subsequent section. A cost constraint D-optimal optimization problem has been formulated and the corresponding solution algorithm is provided to obtain optimal plans. Computational procedures are illustrated through numerical examples.

math.ST