arXiv subjects

Tirthankar Dasgupta

Publications and source records attributed to Tirthankar Dasgupta.

At least 19 recordsLinked to original sources

arXiv2026

Causal Inference of Ordinal Outcomes: A Bayesian Solution

Randomized experiments with ordinal outcomes are common in many scientific applications, but conventional causal estimands such as the average treatment effect are difficult to interpret because ordinal categories lack meaningful numerical spacing. We develop a Bayesian latent variable framework for drawing coherent super population and finite population inference on two interpretable causal estimands that quantify the probabilities that treatment is beneficial and strictly beneficial. By modeling the joint distribution of potential outcomes through an ordered probit model, the proposed approach overcomes the identifiability limitations of existing methods and yields substantially sharper inference than nonparametric bounds. We also investigate the impact of the unknown association between potential outcomes and propose a sensitivity analysis to assess its influence. Simulation studies and an application to a randomized experiment on human scalp health demonstrate that the method provides precise and practically relevant assessments of treatment effectiveness.

stat.ME↗

arXiv2026

GAR: Carbon-Aware Routing for LLM Inference via Constrained Optimization

The growing deployment of large language models (LLMs) makes per-request routing essential for balancing response quality and computational cost across heterogeneous model pools. Current routing methods rarely consider sustainable energy use and CO2 emissions as optimization objectives, despite grid carbon intensity varying by time and region, and models differing significantly in energy consumption. To address this gap, we introduce Green-Aware Routing (GAR), a constrained multi-objective optimization framework that minimizes per-request CO2 emissions subject to explicit accuracy floors and p95-latency service-level objectives (SLOs). GAR employs adaptive constraint optimization through per-dataset floor tuning and incorporates lightweight estimators for correctness, tail latency, and carbon emissions, enabling real-time routing decisions without additional inference passes. We present GAR-PD, a practical online primal-dual routing algorithm for rolling carbon budgets, alongside heuristic variants that achieve high feasibility coverage while limiting accuracy degradation. Comprehensive experiments across standard NLP benchmarks with heterogeneous LLM pools (7B-70B) demonstrate that GAR achieves substantial carbon reductions while maintaining competitive accuracy and p95 latency guarantees, providing a practical, theoretically grounded approach to sustainable LLM inference.

cs.AI↗

arXiv2026

Design Stability in Adaptive Experiments: Implications for Treatment Effect Estimation

We study the problem of estimating the average treatment effect (ATE) under sequentially adaptive treatment assignment mechanisms. In contrast to classical completely randomized designs, we consider a setting in which the probability of assigning treatment to each experimental unit may depend on prior assignments and observed outcomes. Within the potential outcomes framework, we propose and analyze two natural estimators for the ATE: the inverse propensity weighted (IPW) estimator and an augmented IPW (AIPW) estimator. The cornerstone of our analysis is the concept of design stability, which requires that as the number of units grows, either the assignment probabilities converge, or sample averages of the inverse propensity scores and of the inverse complement propensity scores converge in probability to fixed, non-random limits. Our main results establish central limit theorems for both the IPW and AIPW estimators under design stability and provide explicit expressions for their asymptotic variances. We further propose estimators for these variances, enabling the construction of asymptotically valid confidence intervals. Finally, we illustrate our theoretical results in the context of Wei's adaptive coin design and Efron's biased coin design, highlighting the applicability of the proposed methods to sequential experimentation with adaptive randomization.

math.ST↗

arXiv2026

Thinking in Latents: Adaptive Anchor Refinement for Implicit Reasoning in LLMs

Token-level Chain-of-Thought (CoT) prompting has become a standard way to elicit multi-step reasoning in large language models (LLMs), especially for mathematical word problems. However, generating long intermediate traces increases output length and inference cost, and can be inefficient when the model could arrive at the correct answer without extensive verbalization. This has motivated latent-space reasoning approaches that shift computation into hidden representations and only emit a final answer. Yet, many latent reasoning methods depend on a fixed number of latent refinement steps at inference, adding another hyperparameter that must be tuned across models and datasets to balance accuracy and efficiency. We introduce AdaAnchor, a latent reasoning framework that performs silent iterative computation by refining a set of latent anchor vectors attached to the input. AdaAnchor further incorporates an adaptive halting mechanism that monitors anchor stability across iterations and terminates refinement once the anchor dynamics converge, allocating fewer steps to easier instances while reserving additional refinement steps for harder ones under a shared maximum-step budget. Our empirical evaluation across three mathematical word-problem benchmarks shows that AdaAnchor with adaptive halting yields accuracy gains of up to 5% over fixed-step latent refinement while reducing average latent refinement steps by 48-60% under the same maximum-step budget. Compared to standard reasoning baselines, AdaAnchor achieves large reductions in generated tokens (92-93%) by moving computation into silent latent refinement, offering a different accuracy-efficiency trade-off with substantially lower output-token usage.

cs.CL↗

arXiv2025

Decoding Plastic Toxicity: An Intelligent Framework for Conflict-Aware Relational Metapath Extraction from Scientific Abstracts

The widespread use of plastics and their persistence in the environment have led to the accumulation of micro- and nano-plastics across air, water, and soil, posing serious health risks including respiratory, gastrointestinal, and neurological disorders. We propose a novel framework that leverages large language models to extract relational metapaths, multi-hop semantic chains linking pollutant sources to health impacts, from scientific abstracts. Our system identifies and connects entities across diverse contexts to construct structured relational metapaths, which are aggregated into a Toxicity Trajectory Graph that traces pollutant propagation through exposure routes and biological systems. Moreover, to ensure consistency and reliability, we incorporate a dynamic evidence reconciliation module that resolves semantic conflicts arising from evolving or contradictory research findings. Our approach demonstrates strong performance in extracting reliable, high-utility relational knowledge from noisy scientific text and offers a scalable solution for mining complex cause-effect structures in domain-specific corpora.

cs.AI↗

arXiv2025

StayLTC: A Cost-Effective Multimodal Framework for Hospital Length of Stay Forecasting

Accurate prediction of Length of Stay (LOS) in hospitals is crucial for improving healthcare services, resource management, and cost efficiency. This paper presents StayLTC, a multimodal deep learning framework developed to forecast real-time hospital LOS using Liquid Time-Constant Networks (LTCs). LTCs, with their continuous-time recurrent dynamics, are evaluated against traditional models using structured data from Electronic Health Records (EHRs) and clinical notes. Our evaluation, conducted on the MIMIC-III dataset, demonstrated that LTCs significantly outperform most of the other time series models, offering enhanced accuracy, robustness, and efficiency in resource utilization. Additionally, LTCs demonstrate a comparable performance in LOS prediction compared to time series large language models, while requiring significantly less computational power and memory, underscoring their potential to advance Natural Language Processing (NLP) tasks in healthcare.

cs.AI↗

arXiv2025

Analysis and sample-size determination for $2^K$ audit experiments with binary response and application to identification of effect of racial discrimination on access to justice

Social scientists have increasingly turned to audit experiments to investigate discrimination in the market for jobs, loans, housing and other opportunities. In a typical audit experiment, researchers assign ``signals'' (the treatment) to subjects at random and compare success rates across treatment conditions. In the recent past there has been increased interest in using randomized multifactor designs for audit experiments, popularly called factorial experiments, in which combinations of multiple signals are assigned to subjects. Although social scientists have manipulated multiple factors like race, gender and income, the analyses have been mostly exploratory in nature. In this paper we lay out a comprehensive methodology for design and analysis of $2^K$ factorial designs with binary response using model-free, randomization-based Neymanian inference and demonstrate its application by analyzing the audit experiment reported in Libgober (2020). Specifically, we integrate and extend several sections of the randomization-based, finite-population literature for binary outcomes, including sample size and power calculations, and non-linear factorial estimators, extending results.

stat.ME↗

arXiv2024

PICS: A sequential approach to obtain optimal designs for non-linear models leveraging closed-form solutions for faster convergence

D-Optimal designs for estimating parameters of response models are derived by maximizing the determinant of the Fisher information matrix. For non-linear models, the Fisher information matrix depends on the unknown parameter vector of interest, leading to a weird situation that in order to obtain the D-optimal design, one needs to have knowledge of the parameter to be estimated. One solution to this problem is to choose the design points sequentially, optimizing the D-optimality criterion using parameter estimates based on available data, followed by updating the parameter estimates using maximum likelihood estimation. On the other hand, there are many non-linear models for which closed-form results for D-optimal designs are available, but because such solutions involve the parameters to be estimated, they can only be used by substituting "guestimates" of parameters. In this paper, a hybrid sequential strategy called PICS (Plug into closed-form solution) is proposed that replaces the optimization of the objective function at every single step by a draw from the probability distribution induced by the known optimal design by plugging in the current estimates. Under regularity conditions, asymptotic normality of the sequence of estimators generated by this approach are established. Usefulness of this approach in terms of saving computational time and achieving greater efficiency of estimation compared to the standard sequential approach are demonstrated with simulations conducted from two different sets of models.

stat.ME↗

arXiv2024

Mapping Patient Trajectories: Understanding and Visualizing Sepsis Prognostic Pathways from Patients Clinical Narratives

In recent years, healthcare professionals are increasingly emphasizing on personalized and evidence-based patient care through the exploration of prognostic pathways. To study this, structured clinical variables from Electronic Health Records (EHRs) data have traditionally been employed by many researchers. Presently, Natural Language Processing models have received great attention in clinical research which expanded the possibilities of using clinical narratives. In this paper, we propose a systematic methodology for developing sepsis prognostic pathways derived from clinical notes, focusing on diverse patient subgroups identified by exploring comorbidities associated with sepsis and generating explanations of these subgroups using SHAP. The extracted prognostic pathways of these subgroups provide valuable insights into the dynamic trajectories of sepsis severity over time. Visualizing these pathways sheds light on the likelihood and direction of disease progression across various contexts and reveals patterns and pivotal factors or biomarkers influencing the transition between sepsis stages, whether toward deterioration or improvement. This empowers healthcare providers to implement more personalized and effective healthcare strategies for individual patients.

cs.CL↗

arXiv2023

Optimal allocation of sample size for randomization-based inference from $2^K$ factorial designs

Optimizing the allocation of units into treatment groups can help researchers improve the precision of causal estimators and decrease costs when running factorial experiments. However, existing optimal allocation results typically assume a super-population model and that the outcome data comes from a known family of distributions. Instead, we focus on randomization-based causal inference for the finite-population setting, which does not require model specifications for the data or sampling assumptions. We propose exact theoretical solutions for optimal allocation in $2^K$ factorial experiments under complete randomization with A-, D- and E-optimality criteria. We then extend this work to factorial designs with block randomization. We also derive results for optimal allocations when using cost-based constraints. To connect our theory to practice, we provide convenient integer-constrained programming solutions using a greedy optimization approach to find integer optimal allocation solutions for both complete and block randomization. The proposed methods are demonstrated using two real-life factorial experiments conducted by social scientists.

stat.ME↗

arXiv2022

Causal inference from treatment-control studies having an additional factor with unknown assignment mechanism

Consider a situation with two treatments, the first of which is randomized but the second is not, and the multifactor version of this. Interest is in treatment effects, defined using standard factorial notation. We define estimators for the treatment effects and explore their properties when there is information about the nonrandomized treatment assignment and when there is no information on the assignment of the nonrandomized treatment. We show when and how hidden treatments can bias estimators and inflate their sampling variances.

stat.ME↗

arXiv2021

CLAIMED: A CLAssification-Incorporated Minimum Energy Design to explore a multivariate response surface with feasibility constraints

Motivated by the problem of optimization of force-field systems in physics using large-scale computer simulations, we consider exploration of a deterministic complex multivariate response surface. The objective is to find input combinations that generate output close to some desired or "target" vector. In spite of reducing the problem to exploration of the input space with respect to a one-dimensional loss function, the search is nontrivial and challenging due to infeasible input combinations, high dimensionalities of the input and output space and multiple "desirable" regions in the input space and the difficulty of emulating the objective function well with a surrogate model. We propose an approach that is based on combining machine learning techniques with smart experimental design ideas to locate multiple good regions in the input space.

stat.ML↗

arXiv2020

An Email Experiment to Identify the Effect of Racial Discrimination on Access to Lawyers: A Statistical Approach

We consider the problem of conducting an experiment to study the prevalence of racial bias against individuals seeking legal assistance, in particular whether lawyers use clues about a potential client's race in deciding whether to reply to e-mail requests for representations. The problem of discriminating between potential linear and non-linear effects of a racial signal is formulated as a statistical inference problem, whose objective is to infer a parameter determining the shape of a specific function. Various complexities associated with the design and analysis of this experiment are handled by applying a novel combination of rigorous, semi-rigorous and rudimentary statistical techniques. The actual experiment was attempted with a population of lawyers in Florida, but could not be performed with the desired sample size due to resource limitations. Nonetheless, it provides a nice demonstration of the proposed steps involved in conducting such a study.

stat.AP↗

arXiv2020

Leveraging the Fisher randomization test using confidence distributions: inference, combination and fusion learning

The flexibility and wide applicability of the Fisher randomization test (FRT) makes it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions Such a connection leads to development of (i) an unambiguous procedure for inversion of FRTs to generate confidence intervals with guaranteed coverage, (ii) generic and specific methods to combine FRTs from multiple independent experiments with theoretical guarantees and (iii) new insights on the effect of size of the Monte Carlo sample on the results of FRT. Our developments pertain to finite sample settings but have direct extensions to large samples. Simulations and a case example demonstrate the benefit of these new developments.

stat.ME↗

arXiv2019

Causal Inference from Possibly Unbalanced Split-Plot Designs: A Randomization-based Perspective

Split-plot designs find wide applicability in multifactor experiments with randomization restrictions. Practical considerations often warrant the use of unbalanced designs. This paper investigates randomization based causal inference in split-plot designs that are possibly unbalanced. Extension of ideas from the recently studied balanced case yields an expression for the sampling variance of a treatment contrast estimator as well as a conservative estimator of the sampling variance. However, the bias of this variance estimator does not vanish even when the treatment effects are strictly additive. A careful and involved matrix analysis is employed to overcome this difficulty, resulting in a new variance estimator, which becomes unbiased under milder conditions. A construction procedure that generates such an estimator with minimax bias is proposed.

stat.ME↗

arXiv2019

Sampling-based randomized designs for causal inference under the potential outcomes framework

We establish the inferential properties of the mean-difference estimator for the average treatment effect in randomized experiments where each unit in a population is randomized to one of two treatments and then units within treatment groups are randomly sampled. The properties of this estimator are well-understood in the experimental design scenario where first units are randomly sampled and then treatment is randomly assigned, but not for the aforementioned scenario where the sampling and treatment assignment stages are reversed. We find that the inferential properties of the mean-difference estimator under this experimental design scenario are identical to those under the more common sample-first-randomize-second design. This finding will bring some clarifications about sampling-based randomized designs for causal inference, particularly for settings where there is a finite super-population. Finally, we explore to what extent pre-treatment measurements can be used to improve upon the mean-difference estimator for this randomize-first-sample-second design. Unfortunately, we find that pre-treatment measurements are often unhelpful in improving the precision of average treatment effect estimators under this design, unless a large number of pre-treatment measurements that are highly associative with the post-treatment measurements can be obtained. We confirm these results using a simulation study based on a real experiment in nanomaterials.

math.ST↗

arXiv2018

Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes, and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes, and are directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.

stat.ME↗

arXiv2017

A randomization-based perspective of analysis of variance: a test statistic robust to treatment effect heterogeneity

Fisher randomization tests for Neyman's null hypothesis of no average treatment effects are considered in a finite population setting associated with completely randomized experiments with more than two treatments. The consequences of using the $F$ statistic to conduct such a test are examined both theoretically and computationally, and it is argued that under treatment effect heterogeneity, use of the $F$ statistic in the Fisher randomization test can severely inflate the type I error under Neyman's null hypothesis. An alternative test statistic is proposed, its asymptotic distributions under Fisher's and Neyman's null hypotheses are derived, and its advantages demonstrated.

math.ST↗