arXiv subjects

Anirban Chatterjee

Publications and source records attributed to Anirban Chatterjee.

At least 19 recordsLinked to original sources

arXiv2026

Scaling Limits for Ising Models on Inhomogeneous Random Graphs and Applications

In this paper, we derive quenched scaling limits for linear functionals and the empirical spin field of Ising models on inhomogeneous random graphs generated by a graphon (encompassing both dense and sparse graphs), in the high-temperature regime. We first prove a joint central limit theorem (CLT) for finite collections of linear statistics of the spin configurations, where the limiting covariance is characterized by the resolvent of the associated graphon integral operator. Building on this result, we establish functional CLTs for the average magnetization and for the spin field indexed by suitable classes of regular test functions. We further prove convergence of the full empirical spin field, viewed as a random generalized function in negative Sobolev spaces. These scaling limits provide applications to both Bayesian neural networks and causal inference. Specifically, for the former, we derive infinite-width Gaussian-process limits for two-layer Bayesian neural networks with Ising-dependent output-layer signs, while for the latter, we establish the asymptotic normality of H\'{a}jek estimators for average treatment effects under network interference.

math.PR↗

arXiv2026

Adversarial Prompting Framework for AI Safety Assessment

Artificial Intelligence (AI), especially Generative AI (GenAI), adoption has increased in industries significantly in recent years. However, the use of these models may also expose systems to new forms of cyberattacks by different malicious actors -- adversarial prompt attack (APA) being one of the most prominent examples of such threats. This paper presents the implementation of an Adversarial Prompting Framework (APF) for a comprehensive assessment of AI safety. The framework systematically evaluates the resilience of the AI model through the generation of structured adversarial prompts at multiple sophistication levels, from direct harmful requests to advanced encoding-based attacks. Our implementation demonstrates the practical application of this methodology in enterprise environments, providing automated testing capabilities with quantitative security assessment metrics. The results indicate significant variations in the model vulnerabilities across different attack vectors, with encoded prompts presenting the highest success rates in bypassing safety mechanisms.

cs.CR↗

arXiv2026

Conditional Mean Independence and Global Sensitivity Analysis using Nearest Neighbor Graphs

Quantifying how well a conditional mean function explains a response is central to many statistical tasks, such as model evaluation and feature screening. A basic nonparametric measure of such dependence is the proportion of variation in the response explained by the regression function, which can also be interpreted as a multivariate Sobol' index, a fundamental notion in global sensitivity analysis. In this paper, we propose a consistent estimator of this measure based on nearest neighbor graphs that can be computed in near-linear time. We also derive its rate of convergence and show that a studentized version of the estimator is asymptotically standard normal under the null hypothesis of conditional mean independence. This leads to a computationally efficient test for conditional mean independence that attains the correct asymptotic level and is universally consistent, without requiring bootstrap calibration or sample splitting. Next, we use the proposed estimator to develop a model-free variable screening algorithm that is provably consistent. We also discuss extensions of the framework to measuring interaction effects using higher-order Sobol' indices. The benefits of the proposed methods are demonstrated through simulation studies and a real-data example.

stat.ME↗

arXiv2026

Ising Models on Inhomogeneous Random Graphs: Inference, Local Asymptotic Minimaxity, and Limit of Experiments

In this paper, we develop an inferential framework with sharp asymptotic optimality guarantees for Ising models on inhomogeneous random graphs in the subcritical parameter regime. We begin by characterizing the asymptotic distribution of the maximum likelihood (ML) estimate of the natural parameter, based on a single sample from the underlying model, covering both sparse and dense network regimes. Next, to overcome the computational intractability of the ML method, we propose a simple closed-form estimate obtained from a one-step approximation to the likelihood equation. We show that this estimate attains the same asymptotic distribution and variance as the ML estimate, thereby yielding a computationally efficient and asymptotically valid confidence interval for the natural parameter. We complement these inferential results by establishing a H\'ajek--Le Cam-type local asymptotic minimax theorem, showing that the proposed estimate achieves the smallest possible asymptotic maximum risk, both in rate and in leading constant, over shrinking neighborhoods of the true parameter. We also derive the corresponding limit of experiments. To the best of our knowledge, these are among the first sharp asymptotic optimality results for network-dependent data. Finally, we study goodness-of-fit testing for the natural parameter, deriving the local power of the likelihood ratio test and minimax detection rates. Our analysis relies on new fluctuation results for the sufficient statistic (Hamiltonian) and for the random partition function of Ising models on inhomogeneous random graphs, which are of independent interest.

math.ST↗

arXiv2026

Dispersion of multiple charged species in an axially symmetric slowly varying channel

The transport and dispersion of multiple species of charged ions are central to many biological and physical processes, including electrokinetic ion separation. However, most theoretical studies of dispersion in channels have focused on neutral solutes, leaving the transport of multiple charged species comparatively unexplored. Differences in ionic diffusivities in a multispecies electrolyte solution generate an self-induced electric fields that drive electromigration. To capture these effects at the macroscopic scale, we combine the lubrication approximation with homogenization theory, under electroneutrality and zero-current constraints, to derive an effective transport equation governing the cross-sectionally averaged concentrations. We apply our model framework to a range of channel geometries and compute the resulting effective dispersion coefficients. Finally, we investigate how channel geometry can be tuned to enhance ionic separation. We observe a geometry-induced electro-diffusive coupling that inhibits solute dispersion in certain channels, leading to a non-monotonic Number of Theoretical Plates (NTP) and making such channels ideal for separation processes.

cond-mat.soft↗

arXiv2026

Electrohydrodynamic lubrication theory for an immersed cylinder moving near wall

The free motion of charged colloids within ionic solutions and in the vicinity of charged boundaries, is a phenomenon that occurs in various natural, biological and industrial settings. Here, we develop an electrohydrodynamic lubrication theoretical framework, in order to characterize such a motion in the case of an infinite rigid cylinder near a rigid wall. Combining hydrodynamic lubrication theory, Debye-H\''uckel electrostatics, and Nernst-Planck electrokinetics, we derive the three coupled equations of motion for the normal, longitudinal and rotational degrees of freedom of the cylinder, which are then investigated numerically and through asymptotic analysis. Our results reveal complex behaviours, beyond existing asymptotic electroviscous-lift expressions, and extend the classical Faxen-Brenner-like mobility matrix when surface charges and dissolved ions are incorporated.

cond-mat.soft↗

arXiv2026

Observational and Thermodynamic aspects of one-dimensional Dark Energy EoS parametrization models

We investigate the observational and thermodynamic viability of Gong-Zhang (GZ) Type~I (GZ1) and Type~II (GZ2) dark-energy parametrizations using late-time cosmological probes including Type~Ia supernovae (Union3, Pantheon+SH0ES, and DES-SN5YR), DESI baryon acoustic oscillations, cosmic chronometer $H(z)$ measurements, and growth-rate data. Using Bayesian Markov Chain Monte Carlo analysis together with Akaike and Bayesian information criteria, we show that both parametrizations provide observationally consistent and phenomenologically competitive late-time alternatives to $\Lambda$CDM, while the GZ2 model generally provides tighter constraints and reduced parameter degeneracies. The reconstructed evolution of the dark-energy equation of state and coincidence parameter demonstrates that both models recover the standard matter-dominated behaviour at high redshift while producing controlled late-time deviations from the cosmological-constant scenario. A complementary cosmographic, sound-speed, and growth analysis further confirms stable late-time accelerated expansion together with physically viable perturbative behaviour. Finally, using configuration entropy as a thermodynamic probe, we show that the entropy-production rate sensitively captures the influence of dynamical dark energy on late-time structure formation while remaining consistent with standard early-time cosmology.

gr-qc↗

arXiv2025

Asymptotic Normality of Subgraph Counts in Sparse Inhomogeneous Random Graphs

In this paper, we derive the asymptotic distribution of the number of copies of a fixed graph $H$ in a random graph $G_n$ sampled from a sparse graphon model. Specifically, we provide a refined analysis that separates the contributions of edge randomness and vertex-label randomness, allowing us to identify distinct sparsity regimes in which each component dominates or both contribute jointly to the fluctuations. As a result, we establish asymptotic normality for the count of any fixed graph $H$ in $G_n$ across the entire range of sparsity (above the containment threshold for $H$ in $G_n$). These results provide a complete description of subgraph count fluctuations in sparse inhomogeneous networks, closing several gaps in the existing literature that were limited to specific motifs or suboptimal sparsity assumptions.

math.PR↗

arXiv2025

A Martingale Kernel Two-Sample Test

The Maximum Mean Discrepancy (MMD) is a widely used multivariate distance metric for two-sample testing. The standard MMD test statistic has an intractable null distribution typically requiring costly resampling or permutation approaches for calibration. In this work we leverage a martingale interpretation of the estimated squared MMD to propose martingale MMD (mMMD), a quadratic-time statistic which has a limiting standard Gaussian distribution under the null. Moreover we show that the test is consistent against any fixed alternative and for large sample sizes, mMMD offers substantial computational savings over the standard MMD test, with only a minor loss in power.

stat.ME↗

arXiv2025

One-shot Conditional Sampling: MMD meets Nearest Neighbors

How can we generate samples from a conditional distribution that we never fully observe? This question arises across a broad range of applications in both modern machine learning and classical statistics, including image post-processing in computer vision, approximate posterior sampling in simulation-based inference, and conditional distribution modeling in complex data settings. In such settings, compared with unconditional sampling, additional feature information can be leveraged to enable more adaptive and efficient sampling. Building on this, we introduce Conditional Generator using MMD (CGMMD), a novel framework for conditional sampling. Unlike many contemporary approaches, our method frames the training objective as a simple, adversary-free direct minimization problem. A key feature of CGMMD is its ability to produce conditional samples in a single forward pass of the generator, enabling practical one-shot sampling with low test-time complexity. We establish rigorous theoretical bounds on the loss incurred when sampling from the CGMMD sampler, and prove convergence of the estimated distribution to the true conditional distribution. In the process, we also develop a uniform concentration result for nearest-neighbor based functionals, which may be of independent interest. Finally, we show that CGMMD performs competitively on synthetic tasks involving complex conditional densities, as well as on practical applications such as image denoising and image super-resolution.

stat.ML↗

arXiv2025

A comprehensive dynamical and phenomenological analysis of structure growth in curvature-modulated coupled quintessence scenario

We investigate an interacting dark energy-dark matter model within the quintessence framework, characterized by the coupling term $Q_0 = \alpha \kappa \rho_m \dot{\phi} \left[1 - \beta R/(6H^2) \right]$, and the scalar field evolves under an exponential potential $V(\phi) = V_0 e^{-\lambda \kappa \phi}$, with parameters $\alpha$, $\lambda$, and $\beta$. Recasting the cosmological equations into a first-order autonomous system using dimensionless variables, we perform a phase space analysis to identify conditions for stable, non-phantom accelerating attractors. The Ricci scalar term, controlled by $\beta$, significantly affects the stability of critical points, with attractors transitioning to repellers for higher values of $\beta$. We also analyze linear scalar perturbations, focusing on the matter density contrast $\delta_m$ and the growth index $\gamma$. Additionally, we compute the deceleration and jerk parameters, the Hubble rate, and the distance modulus $\mu(z)$, showing good agreement with observational data. The model naturally addresses the cosmic coincidence problem through scalar field tracking behavior. For moderate parameter values, matter perturbations continue to grow into the future, capturing both background and perturbative dynamics effectively. This framework thus offers a consistent and observationally viable approach to interacting dark energy.

gr-qc↗

arXiv2024

Understanding curvature-matter interaction in viable $f(R)$ dark energy models: A dynamical analysis approach

We employ a linear stability analysis approach to explore the dynamics of matter and curvature-driven dark energy interactions within the framework of two types of viable $f(R)$ gravity models. The interaction is modeled via a source term in the continuity equations, $\mathcal{Q} = \alpha \tilde{\rho}_{\rm m} \Big{(}\frac{3H^3}{\kappa^2 \rho_{\rm curv}} + \frac{\kappa^2 }{3H}\rho_{\rm curv} \Big{)}$. Our results reveal significant modifications to the fixed points and their stability criteria compared to traditional $f(R)$ gravity analyses without matter-curvature coupling. We identify constraints on model and coupling parameters necessary for critical point stability, illustrating how the interaction influences cosmic dynamics within specific parameter ranges. The findings are consistent with observed cosmic evolution, supporting stable late-time acceleration. Moreover, we highlight the coupling parameter's potential role in addressing the cosmic coincidence problem.

gr-qc↗

arXiv2024

A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)

In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed in nearly linear time (for a fixed number of nearest neighbors). Moreover, when the two conditional distributions are the same, the estimate has a Gaussian limit and its asymptotic variance has a simple form that can be easily estimated from the data. The resulting test attains precise asymptotic level and is universally consistent for detecting differences between two conditional distributions. We also provide a resampling based test using our estimate that applies to the conditional goodness-of-fit problem, which controls Type I error in finite samples and is asymptotically consistent with only a finite number of resamples. A method to de-randomize the resampling test is also presented. The proposed methods can be readily applied to a broad range of problems, ranging from classical nonparametric statistics to modern machine learning. Specifically, we explore three applications: testing model calibration, regression curve evaluation, and validation of emulator models in simulation-based inference. We illustrate the superior performance of our method for these tasks, both in simulations as well as on real data. In particular, we apply our method to (1) assess the calibration of neural network models trained on the CIFAR-10 dataset, (2) compare regression functions for wind power generation across two different turbines, and (3) validate emulator models on benchmark examples with intractable posteriors and for generating synthetic `redshift' associated with galaxy images.

stat.ME↗

arXiv2024

Observational constraints on generic models of non-minimal curvature-matter coupling

We investigate two classes of non-minimally coupled curvature-matter models in the FLRW universe with a perfect fluid and analyze their cosmological implications using Supernova Ia, Observed Hubble Data, and Baryon Acoustic Oscillation measurements. Non-minimal coupling is introduced via an additional term $\int d^4x \sqrt{-g} \mathcal{G}({\cal L}_{m}) f_2(R)$ in the Einstein-Hilbert action. To obtain observational constraints, we use an exponential-type fluid-pressure profile $p = p_0e^{ak}$ characterized by the dimensionless parameter $k$ and parameterize $f_2(R)$ as $R^n$ with another dimensionless parameter $n$. Two additional parameters, $\alpha$ and $\beta$ in the functional form of $\mathcal{G}({\cal L}_{m})$ determine the coupling strength. We identify significant regions in the $(n, k)$-parameter space for fixed coupling strength values where non-minimally coupled models align with observed late-time cosmic evolution. Additionally, we explore and discuss features of energy transfer between the curvature and matter sectors using observational data.

gr-qc↗

arXiv2024

Pre-Trained Foundation Model representations to uncover Breathing patterns in Speech

The process of human speech production involves coordinated respiratory action to elicit acoustic speech signals. Typically, speech is produced when air is forced from the lungs and is modulated by the vocal tract, where such actions are interspersed by moments of breathing in air (inhalation) to refill the lungs again. Respiratory rate (RR) is a vital metric that is used to assess the overall health, fitness, and general well-being of an individual. Existing approaches to measure RR (number of breaths one takes in a minute) are performed using specialized equipment or training. Studies have demonstrated that machine learning algorithms can be used to estimate RR using bio-sensor signals as input. Speech-based estimation of RR can offer an effective approach to measure the vital metric without requiring any specialized equipment or sensors. This work investigates a machine learning based approach to estimate RR from speech segments obtained from subjects speaking to a close-talking microphone device. Data were collected from N=26 individuals, where the groundtruth RR was obtained through commercial grade chest-belts and then manually corrected for any errors. A convolutional long-short term memory network (Conv-LSTM) is proposed to estimate respiration time-series data from the speech signal. We demonstrate that the use of pre-trained representations obtained from a foundation model, such as Wav2Vec2, can be used to estimate respiration-time-series with low root-mean-squared error and high correlation coefficient, when compared with the baseline. The model-driven time series can be used to estimate $RR$ with a low mean absolute error (MAE) ~ 1.6 breaths/min.

cs.SD↗

arXiv2024

Detecting Planted Partition in Sparse Multi-Layer Networks

Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the presence of planted partition among the nodes of a multi-layer network with additional nodewise covariate information and diverging average degree, Ma and Nandy (2023) introduced Multi-Layer Contextual Stochastic Block Model. In this paper, we consider the problem of detecting planted partitions in the Multi-Layer Contextual Stochastic Block Model, when the average node degrees for each network is greater than $1$. We establish the sharp phase transition threshold for detecting the planted bi-partition. Above the phase-transition threshold testing the presence of a bi-partition is possible, whereas below the threshold no procedure to identify the planted bi-partition can perform better than random guessing. We further establish that the derived detection threshold coincides with the threshold for weak recovery of the partition and provide a quasi-polynomial time algorithm to estimate it.

math.ST↗

arXiv2024

Higher-Order Graphon Theory: Fluctuations, Degeneracies, and Inference

Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a natural way to sample exchangeable random graphs. It is well known that network moments (motif/subgraph counts) identify a graphon (up to an isomorphism), hence, understanding the sampling distribution of subgraph counts in random graphs sampled from a graphon is pivotal for nonparametric network inference. In this paper, we derive the joint asymptotic distribution of any finite collection of network moments in random graphs sampled from a graphon, that includes both the non-degenerate case (where the distribution is Gaussian) as well as the degenerate case (where the distribution has both Gaussian or non-Gaussian components). This provides the higher-order fluctuation theory for subgraph counts in the graphon model. We also develop a novel multiplier bootstrap for graphons that consistently approximates the limiting distribution of the network moments (both in the Gaussian and non-Gaussian regimes). Using this and a procedure for testing degeneracy, we construct joint confidence sets for any finite collection of motif densities. This provides a general framework for statistical inference based on network moments in the graphon model. To illustrate the broad scope of our results we also consider the problem of detecting global structure (that is, testing whether the graphon is a constant function) based on small subgraphs. We propose a consistent test for this problem, invoking celebrated results on quasi-random graphs, and derive its limiting distribution both under the null and the alternative.

math.ST↗

arXiv2024

Exploring the evolution of structure growth in the universe with field-fluid interactions through dynamical stability analysis

We investigate an interacting quintessence dark energy - dark matter scenario and its impact on structure formation by analyzing the evolution of scalar perturbations. The interaction is introduced by incorporating a non-zero source term into the continuity equations of the two sectors (with opposite signs), modeled as $\bar{Q}_0 \equiv \alpha\bar{\rho}_{\rm m}(H + \kappa\dot{\phi})$. The coupling parameter $\alpha$ and the parameter $\lambda$ involved in quintessence potential $V(\phi) = V_0e^{-\lambda\kappa\phi}$, play crucial roles in governing the dynamics of evolution examined within the present framework. The cosmic evolution, within this context, is depicted as a first-order autonomous system of equations involving appropriately chosen dynamical variables. We analyzed the associated stability characteristics and growth rate of perturbations and obtained domains in the ($\alpha-\lambda$) parameter space for which fixed points can exhibit stable and non-phantom accelerating solutions. Depending on its magnitude, the coupling parameter $\alpha$ has the potential to change the characteristics of certain critical points, altering them from attractors to repellers. This model effectively captures the evolutionary features of the universe across its various phases at both the background and perturbation levels. The issue of cosmic coincidence can also be addressed within the framework of this model. We also observed that for a moderate strength of coupling, the growth rate of matter perturbation extends into the distant future.

gr-qc↗