arXiv subjects

Anirban Chatterjee

Publications and source records attributed to Anirban Chatterjee.

At least 37 records · Page 2Linked to original sources

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

Boosting the Power of Kernel Two-Sample Tests

The kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. In this paper we propose a method to boost the power of the kernel test by combining MMD estimates over multiple kernels using their Mahalanobis distance. We derive the asymptotic null distribution of the proposed test statistic and use a multiplier bootstrap approach to efficiently compute the rejection region. The resulting test is universally consistent and, since it is obtained by aggregating over a collection of kernels/bandwidths, is more powerful in detecting a wide range of alternatives in finite samples. We also derive the distribution of the test statistic for both fixed and local contiguous alternatives. The latter, in particular, implies that the proposed test is statistically efficient, that is, it has non-trivial asymptotic (Pitman) efficiency. The consistency properties of the Mahalanobis and other natural aggregation methods are also explored when the number of kernels is allowed to grow with the sample size. Extensive numerical experiments are performed on both synthetic and real-world datasets to illustrate the efficacy of the proposed method over single kernel tests. The computational complexity of the proposed method is also studied, both theoretically and in simulations. Our asymptotic results rely on deriving the joint distribution of MMD estimates using the framework of multiple stochastic integrals, which is more broadly useful, specifically, in understanding the efficiency properties of recently proposed adaptive MMD tests based on kernel aggregation and also in developing more computationally efficient (linear time) tests that combine multiple kernels. We conclude with an application of the Mahalanobis aggregation method for kernels with diverging scaling parameters.

stat.ME↗

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

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

Dynamical analysis of coupled curvature-matter scenario in viable $f(R)$ dark energy models at de Sitter phase

We explore the interaction between dark matter and curvature-driven dark energy within viable $f(R)$ gravity models, employing the phase-space analysis approach of linear stability theory. By incorporating an interacting term, denoted as $\mathcal{Q}=αH \tildeρ_{\rm m}\left(\frac{κ^2 }{3H^2}ρ_{\rm curv} + 1 \right)$, into the continuity equations of both sectors, we examine dynamics of two $f(R)$ gravity models that adhere to local gravity constraints and fulfill cosmological viability criteria. In de Sitter phase, our investigation reveals modifications of critical points compared to the conventional form, attributed to the introduced interaction. Through a comprehensive phase-space analysis, we illustrate the trajectories near critical points and outline the constraints on the phase space based on cosmological and cosmographic parameters. Furthermore, we can also observe stable behavior of this interacting system during the de Sitter phase of the universe.

gr-qc↗

arXiv2024

Dynamics of viable $f(R)$ dark energy models in the presence of Curvature-Matter interactions

In this study, we analyze the dynamics of the interaction between dark matter and curvature-driven dark energy in viable $f(R)$ gravity models using the framework of dynamical system analysis. We incorporate this interaction by introducing a source term in their respective continuity equations, given by $Q = \frac{κ^2 α}{3H}\tildeρ_{\rm m}ρ_{\rm curv}$, and examine two $f(R)$ gravity models that comply with local gravity constraints and cosmological viability criteria. Our findings reveal subtle modifications to fixed points and their stability criteria when compared to the conventional dynamical analysis of $f(R)$ gravity models without matter-curvature interactions as proposed and examined in prior literature. We determine the parameter limits associated with the stability criteria of critical points of the dynamical system for both the models. Additionally, the introduction of interaction reveals variations in the dynamical aspects of cosmic evolution, contingent on the range of values for the relevant model parameters. These results are consistent with the observed features of cosmic evolution within specific limits of the $f(R)$ models parameters and the coupling parameter $α$. We also examine the evolutionary dynamics of the universe in the interacting scenario through cosmological and cosmographic parameters. Our analysis demonstrates that the interacting scenario comprehensively accounts for all the observed phases of the universe's evolution and also results in a stable late-time cosmic acceleration. Additionally, we've studied how the coupling parameter affects evolutionary dynamics, particularly its impact on the matter-to-curvature energy density ratio. Our findings suggest that the chosen form of interaction can also address the cosmic coincidence problem.

gr-qc↗

arXiv2024

PrIsing: Privacy-Preserving Peer Effect Estimation via Ising Model

The Ising model, originally developed as a spin-glass model for ferromagnetic elements, has gained popularity as a network-based model for capturing dependencies in agents' outputs. Its increasing adoption in healthcare and the social sciences has raised privacy concerns regarding the confidentiality of agents' responses. In this paper, we present a novel $(\varepsilon,δ)$-differentially private algorithm specifically designed to protect the privacy of individual agents' outcomes. Our algorithm allows for precise estimation of the natural parameter using a single network through an objective perturbation technique. Furthermore, we establish regret bounds for this algorithm and assess its performance on synthetic datasets and two real-world networks: one involving HIV status in a social network and the other concerning the political leaning of online blogs.

stat.ME↗

arXiv2023

Dynamical stability in models where dark matter and dark energy are non-minimally coupled to curvature

This work explores the dynamical stability of cosmological models where dark matter and dark energy can non-minimally couple to spacetime (scalar) curvature. Two different scenarios are presented here. In the initial case, only dark matter sector is coupled to curvature in the presence of a quintessence scalar field. In the second case both dark matter and the quintessence field are coupled to curvature. It is shown that one can get an accelerating expansion phase of the universe in both the cases. The nature of the fixed points show that there can be stable or unstable phases where the curvature coupling vanishes and dark energy and dark matter evolve independently. On the other hand there can be stable accelerating expansion phases where both the components are coupled to curvature.

gr-qc↗

arXiv2023

Observational constraints on non-minimally coupled curvature-matter models of gravity from the analysis of Pantheon data

We considered non-minimally coupled curvature-matter models of gravity in a FRW universe filled with perfect fluid and investigated its cosmological implications in the light of Pantheon compilation of 1048 Supernovae Ia data points along with 54 data points from Observed Hubble Data. The non-minimal curvature-matter coupling has been introduced by adding a term $\int \left[λR^n \mathcal{L}_m\right] \sqrt{-g}d^4x$ to the usual action for Einstein gravity involving the Einstein Hilbert action and minimally coupled matter action. We investigate the observational constraints on the non-minimal models by choosing two different kinds of parametrization of fluid-pressure profiles using a dimensionless parameter $k$. The interplay of the three parameters $λ,n,k$ plays a pivotal role in testing the consistency of non-minimally coupled fluid-curvature scenarios with the observed data. We found there exist large domains in the ($λ,n,k$)-parameter space for which models with non-minimal curvature-matter mixing stand as viable cosmological models reproducing the observed features of late-time cosmic evolution. We also commented on the possibility of `gravitationally induced particle creation' in the context of SNe Ia data.

gr-qc↗

arXiv2023

Realizing late-time cosmology in the context of Dynamical Stability Approach

We examine the scenario of non-minimally coupled relativistic fluid and $k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker universe. By adding a non-minimal coupling term in the Lagrangian level, we study the variation of Lagrangian with respect to independent variables, which produces modified scalar field and Friedmann equations. Using dynamical stability approach in different types of interaction models with two types of scalar field potential, we explore this coupled framework. Implementing detailed analysis, we can conclude our models can able to produce stable late-time cosmic acceleration.

gr-qc↗

arXiv2023

Investigating the accelerated expansion of the Universe through updated constraints on viable $f(R)$ models within the metric formalism

Modified theories of gravity encompass a class of $f(R)$-models that seek to elucidate the observed late time accelerated expansion of the universe. In this study, we examine a set of viable $f(R)$ models (Hu-Sawicki: two cases, Satrobinsky, Tsujikawa, exponential and arcTanh models) in metric formalism, using recent cosmological data sets: type Ia supernovae data, cosmic chronometer observations, baryonic acoustic oscillations data, data from H\textsc{ii} starburst galaxies, and local measurements of the Hubble parameter $H_0$. The model parameters are constrained using a Bayesian analysis with the Monte Carlo Markov Chain method. We employ statistical tools such as the Akaike Information Criterion, Bayesian Information Criterion, and reduced chi-square statistics to conduct a comparative investigation of these models. We determine the transition redshift, the evolution of total equation-of-state (EoS) parameter, and the EoS for the component responsible for current accelerated expansion to characterize the expansion's evolution. Taking into account the ``Hubble tension," we perform the study with and without a Gaussian prior for $H_0$ from local measurements. Our findings are as follows: (i) in many cases the $f(R)$ models are strongly favored over the standard $Λ$CDM model, (ii) the deviation parameter ($b$) significantly deviates from zero in several cases, (iii) the inclusion of local $H_0$ not only increases the fitted value of $H_0$ (as expected) but also affects the gap between predictions of $f(R)$ models and the $Λ$CDM model, and (iv) the relevant quantities characterizing the (accelerated) expansion of the universe obtained in our models are consistent with those obtained in a model-independent way by others. Our investigation and results present a compelling case for pursuing further research on $f(R)$ models with future observations to come.

astro-ph.CO↗

arXiv2023

Exploring maverick top partner decays at the LHC

In this work, we have considered an extension of the standard model (SM) with a $SU(2)_L$ singlet vectorlike quark (VLQ) with electric charge $Q=+2/3$. The model also contains an additional local $U(1)_d$ symmetry group and the corresponding gauge boson is the dark photon. The VLQ is charged while all the SM particles are neutral under the new $U(1)_d$ gauge group. Even though in this model the VLQ possesses many properties qualitatively similar to that of the traditional top partner ($T_p$), there are some compelling differences as well. In particular, its branching ratio to the traditional modes ($T_p \to bW, tZ, th$) are suppressed which in turn helps to evade many of the existing bound, mainly coming from the LHC experiments. In an earlier work, such a VLQ is referred to as ``maverick top partner". It has been shown that the top partner in this model predominantly decays to a top quark and a dark photon/dark higgs pair ($T_p \to tγ_d ,~th_d$) over a large region of the parameter space. The dark photon can be made invisible and consequently, it gives rise to the missing transverse energy ($\not\!\!{E} _{T}$) signature at the LHC detector. We have mainly focused on the LHC signatures and future prospects of such top partners. In particular, we have studied the $t\bar{t}+\not\!\!{E}_{T}$ and $t+\not\!\!{E}_{T}$ signatures in the context of the LHC via pair and single productions of the top partner, respectively at 13 and 14 TeV LHC center of mass energies assuming that the dark photon either decays into an invisible mode or it is invisible at the length scale of the detector. We have shown that one can exclude $\sinθ_L \sim 0.025$ (0.05) for $m_{_{T_p}} \leq $ 2.0 (2.6) TeV at $\sqrt{s}=14$ TeV with an integrated luminosity of 3 ab$^{-1}$ using the single top partner production channel.

hep-ph↗

arXiv2023

Dynamical Stability in presence of non-minimal derivative dependent coupling of $k$-essence field with a relativistic fluid

In this paper we investigate a non-minimal, space-time derivative dependent, coupling between the $k$-essence field and a relativistic fluid using a variational approach. The derivative coupling term couples the space-time derivative of the $k$-essence field with the fluid 4-velocity via an inner product. The inner product has a coefficient whose form specifies the various models of interaction. By introducing a coupling term at the Lagrangian level and using the variational technique we obtain the $k$-essence field equation and the Friedmann equations in the background of a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. Explicitly using the dynamical analysis approach we analyze the dynamics of this coupled scenario in the context of two kinds of interaction models. The models are distinguished by the form of the coefficient multiplying the derivative coupling term. In the simplest approach we work with an inverse square law potential of the $k$-essence field. Both of the models are not only capable of producing a stable accelerating solution, they can also explain different phases of the evolutionary universe.

gr-qc↗

arXiv2023

Ghost condensates and pure kinetic $k$-essence condensates in presence of field-fluid non-minimal coupling in the dark sector

In this article we try to find out the conditions when a ghost field in conjunction with a barotropic fluid produces a stable accelerating expansion phase of the universe. It is seen that in many cases the ghost field produces a condensate and drives the fluid energy density to zero in the final accelerating phase, but there can be other possibilities. We have shown that a pure kinetic $k$-essence field (which is not a ghost field) interacting with a fluid can also form an interaction induced condensate and produce a stable accelerating phase of the universe. In the latter case the fluid energy density does not vanish in the stable phase.

gr-qc↗

arXiv2022

Modified scaling in $k$-essence model in interacting dark energy - dark matter scenario

It has been shown by \textit{Scherrer and Putter et.al} that, when dynamics of dark energy is driven by a homogeneous $k-$essence scalar field $ϕ$, with a Lagrangian of the form $L = V_0F(X)$ with a constant potential $V_0$ and $X = \frac{1}{2}\nabla^μϕ\nabla_μϕ= \frac{1}{2}\dotϕ^2$, one obtains a scaling relation $X(dF/dX)^2 = Ca^{-6}$ , where $C$ is a constant and $a$ is the FRW scale factor of the universe. The separate energy conservation in the dark energy sector and the constancy of $k-$essence potential are instrumental in obtaining such a scaling. In this paper, we have shown that even when considering time-dependent interactions between dark energy and dark matter, the constancy of $k-$essence potential may lead to a modified form of scaling. We have obtained such a scaling relation for a particular class of parametrisation of the source term occurring in the continuity equation of dark energy and dark matter in the interacting scenario. We used inputs from the JLA analysis of luminosity distance and redshift data from Supernova Ia observations, to obtain the modified form of the scaling.

gr-qc↗

arXiv2022

The nature of cosmological metric perturbations in presence of gravitational particle production

The present paper tries to answer the question: Can a de Sitter phase in presence of radiation be a competitor of the standard inflationary paradigm for the early universe? This kind of a de Sitter phase can exist in cosmological models where gravitational particle production takes place. To address the issue the metric perturbations in the de Sitter phase in presence of radiation must be known. The evolution of metric perturbations are explicitly calculated in the paper. It is seen that the evolution of scalar and vector perturbations are considerably different from standard inflationary models. These differences arise due to the particle production mechanism. The scalar perturbation power spectrum grows exponentially at small length scales. However, one cannot uniquely specify the scale at which this exponential growth starts because of the dependence of the power spectrum on the initial perturbation value. The time slice on which the initial perturbation starts is arbitrary. The arbitrariness of the initial time slice is related to the problem of setting the initial condition on the perturbations in the present model. The paper briefly opines on vector and tensor perturbations in the de Sitter space filled with radiation. It is seen that quantization of the perturbation modes in the present model is considerably difficult. One has to modify the present model to provide a consistent scheme of quantization of the perturbation modes.

gr-qc↗

arXiv2022

Detecting Concept Drift in the Presence of Sparsity -- A Case Study of Automated Change Risk Assessment System

Missing values, widely called as \textit{sparsity} in literature, is a common characteristic of many real-world datasets. Many imputation methods have been proposed to address this problem of data incompleteness or sparsity. However, the accuracy of a data imputation method for a given feature or a set of features in a dataset is highly dependent on the distribution of the feature values and its correlation with other features. Another problem that plagues industry deployments of machine learning (ML) solutions is concept drift detection, which becomes more challenging in the presence of missing values. Although data imputation and concept drift detection have been studied extensively, little work has attempted a combined study of the two phenomena, i.e., concept drift detection in the presence of sparsity. In this work, we carry out a systematic study of the following: (i) different patterns of missing values, (ii) various statistical and ML based data imputation methods for different kinds of sparsity, (iii) several concept drift detection methods, (iv) practical analysis of the various drift detection metrics, (v) selecting the best concept drift detector given a dataset with missing values based on the different metrics. We first analyze it on synthetic data and publicly available datasets, and finally extend the findings to our deployed solution of automated change risk assessment system. One of the major findings from our empirical study is the absence of supremacy of any one concept drift detection method across all the relevant metrics. Therefore, we adopt a majority voting based ensemble of concept drift detectors for abrupt and gradual concept drifts. Our experiments show optimal or near optimal performance can be achieved for this ensemble method across all the metrics.

cs.LG↗