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Dalia Chakrabarty

Dalia Chakrabarty appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Applicationsastro-ph.GAastro-phastro-ph.IMastro-ph.COastro-ph.SRcond-mat.mtrl-sciMachine LearningMethodology

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Published work

15 published item(s)

preprint2026arXiv

Interpretable Machine Learning for Spatial Science: A Lie-Algebraic Kernel for Rotationally Anisotropic Gaussian Processes

Many three-dimensional spatial fields are anisotropic, with directions of rapid and slow variation that need not align with the coordinate axes. Standard Gaussian process kernels with Automatic Relevance Determination (ARD) capture only axis-aligned anisotropy, while generic full symmetric positive definite (SPD) metrics can represent rotated anisotropy but do not parameterise principal length-scales and directions directly. We introduce an interpretable rotationally anisotropic GP kernel that parameterises a three-dimensional SPD covariance metric using three principal length-scales and an explicit SO(3) rotation. The rotation is represented by an axis-angle vector and mapped to SO(3) via the Lie-algebra exponential map, giving unconstrained Euclidean coordinates for inference while always inducing a valid SPD metric. The construction spans the same family of three-dimensional SPD covariance metrics as a generic full-SPD parameterisation, but exposes the geometry differently: length-scales and orientation are explicit, interpretable, and directly available for prior specification and posterior summaries. We perform Bayesian inference on these quantities using Markov Chain Monte Carlo (MCMC), and characterise the resulting symmetries and weakly identified regimes. On synthetic data with rotated anisotropy, the posterior recovers the generating metric and improves prediction relative to an axis-aligned ARD baseline, while matching the predictive performance of a generic full SPD baseline. When the ground truth is axis-aligned, posterior mass concentrates near the identity rotation and predictive performance matches ARD. On a material-density dataset from a laboratory-fabricated nano-brick, the inferred metric reveals rotated anisotropy that is not captured by axis-aligned kernels.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Soft Random Graphs in Probabilistic Metric Spaces & Inter-graph Distance

We present a new method for learning Soft Random Geometric Graphs (SRGGs), drawn in probabilistic metric spaces, with the connection function of the graph defined as the marginal posterior probability of an edge random variable, given the correlation between the nodes connected by that edge. In fact, this inter-node correlation matrix is itself a random variable in our learning strategy, and we learn this by identifying each node as a random variable, measurements of which comprise a column of a given multivariate dataset. We undertake inference with Metropolis with a 2-block update scheme. The SRGG is shown to be generated by a non-homogeneous Poisson point process, the intensity of which is location-dependent. Given the multivariate dataset, likelihood of the inter-column correlation matrix is attained following achievement of a closed-form marginalisation over all inter-row correlation matrices. Distance between a pair of graphical models learnt given the respective datasets, offers the absolute correlation between the given datasets; such inter-graph distance computation is our ultimate objective, and is achieved using a newly introduced metric that resembles an uncertainty-normalised Hellinger distance between posterior probabilities of the two learnt SRGGs, given the respective datasets. Two sets of empirical illustrations on real data are undertaken, and application to simulated data is included to exemplify the effect of incorporating measurement noise in the learning of a graphical model.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A New Bayesian Test to test for the Intractability-Countering Hypothesis

We present a new test of hypothesis in which we seek the probability of the null conditioned on the data, where the null is a simplification undertaken to counter the intractability of the more complex model, that the simpler null model is nested within. With the more complex model rendered intractable, the null model uses a simplifying assumption that capacitates the learning of an unknown parameter vector given the data. Bayes factors are shown to be known only up to a ratio of unknown data-dependent constants--a problem that cannot be cured using prescriptions similar to those suggested to solve the problem caused to Bayes factor computation, by non-informative priors. Thus, a new test is needed in which we can circumvent Bayes factor computation. In this test, we undertake generation of data from the model in which the null hypothesis is true and can achieve support in the measured data for the null by comparing the marginalised posterior of the model parameter given the measured data, to that given such generated data. However, such a ratio of marginalised posteriors can confound interpretation of comparison of support in one measured data for a null, with that in another data set for a different null. Given an application in which such comparison is undertaken, we alternatively define support in a measured data set for a null by identifying the model parameters that are less consistent with the measured data than is minimally possible given the generated data, and realising that the higher the number of such parameter values, less is the support in the measured data for the null. Then, the probability of the null conditional on the data is given within an MCMC-based scheme, by marginalising the posterior given the measured data, over parameter values that are as, or more consistent with the measured data, than with the generated data.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Bayesian Covariance Modelling of Large Tensor-Variate Data Sets $\&$ Inverse Non-parametric Learning of the Unknown Model Parameter Vector

We present a method for modelling the covariance structure of tensor-variate data, with the ulterior aim of learning an unknown model parameter vector using such data. We express the high-dimensional observable as a function of this sought model parameter vector, and attempt to learn such a high-dimensional function given training data, by modelling it as a realisation from a tensor-variate Gaussian Process (GP). The likelihood of the unknowns given training data, is then tensor-normal. We choose vague priors on the unknown GP parameters (mean tensor and covariance matrices) and write the posterior probability density of these unknowns given the data. We perform posterior sampling using Random-Walk Metropolis-Hastings. Thereafter we learn the aforementioned unknown model parameter vector by performing posterior sampling in two different ways, given test and training data, using MCMC, to generate 95$\%$ HPD credible region on each unknown. We make an application of this method to the learning of the location of the Sun in the Milky Way disk.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Bayesian Covariance Modelling of Large Tensor-Variate Data Sets $\&$ Inverse Non-parametric Learning of the Unknown Model Parameter Vector

Tensor-valued data are being encountered increasingly more commonly, in the biological, natural as well as the social sciences. The learning of the unknown model parameter vector given such data, involves covariance modelling of such data, though this can be difficult owing to the high-dimensional nature of the data, where the numerical challenge of such modelling can only be compounded by the largeness of the available data set. Assuming such data to be modelled using a correspondingly high-dimensional Gaussian Process (${\cal GP}$), the joint density of a finite set of such data sets is then a tensor normal distribution, with density parametrised by a mean tensor $\boldsymbol{M}$ (that is of the same dimensionality as the $k$-tensor valued observable), and the $k$ covariance matrices $\boldsymbolΣ_1,...,\boldsymbolΣ_k$. When aiming to model the covariance structure of the data, we need to estimate/learn $\{\boldsymbolΣ_1,...,\boldsymbolΣ_k \}$ and $\boldsymbol{M}$, given tha data. We present a new method in which we perform such covariance modelling by first expressing the probability density of the available data sets as tensor-normal. We then invoke appropriate priors on these unknown parameters and express the posterior of the unknowns given the data. We sample from this posterior using an appropriate variant of Metropolis Hastings. Since the classical MCMC is time and resource intensive in high-dimensional state spaces, we use an efficient variant of the Metropolis-Hastings algorithm--Transformation based MCMC--employed to perform efficient sampling from a high-dimensional state space. Once we perform the covariance modelling of such a data set, we will learn the unknown model parameter vector at which a measured (or test) data set has been obtained, given the already modelled data (training data), augmented by the test data.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Bayesian Nonparametric Estimation of Milky Way Model Parameters Using a New Matrix-Variate Gaussian Process Based Method

In this paper we develop an inverse Bayesian approach to find the value of the unknown model parameter vector that supports the real (or test) data, where the data comprises measurements of a matrix-variate variable. The method is illustrated via the estimation of the unknown Milky Way feature parameter vector, using available test and simulated (training) stellar velocity data matrices. The data is represented as an unknown function of the model parameters, where this high-dimensional function is modelled using a high-dimensional Gaussian Process (${\cal GP}$). The model for this function is trained using available training data and inverted by Bayesian means, to estimate the sought value of the model parameter vector at which the test data is realised. We achieve a closed-form expression for the posterior of the unknown parameter vector and the parameters of the invoked ${\cal GP}$, given test and training data. We perform model fitting by comparing the observed data with predictions made at different summaries of the posterior probability of the model parameter vector. As a supplement, we undertake a leave-one-out cross validation of our method.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Uncertainty in Test Score Data and Classically Defined Reliability of Tests and Test Batteries, using a New Method for Test Dichotomisation

As with all measurements, the measurement of examinee ability, in terms of scores that the examinee obtains in a test, is also error-ridden. The quantification of such error or uncertainty in the test score data--or rather the complementary test reliability--is pursued within the paradigm of Classical Test Theory in a variety of ways, with no existing method of finding reliability, isomorphic to the theoretical definition that parametrises reliability as the ratio of the true score variance and observed (i.e. error-ridden) score variance. Thus, multiple reliability coefficients for the same test have been advanced. This paper describes a much needed method of obtaining reliability of a test as per its theoretical definition, via a single administration of the test, by using a new fast method of splitting of a given test into parallel halves, achieving near-coincident empirical distributions of the two halves. The method has the desirable property of achieving splitting on the basis of difficulty of the questions (or items) that constitute the test, thus allowing for fast computation of reliability even for very large test data sets, i.e. test data obtained by a very large examinee sample. An interval estimate for the true score is offered, given an examinee score, subsequent to the determination of the test reliability. This method of finding test reliability as per the classical definition can be extended to find reliability of a set or battery of tests; a method for determination of the weights implemented in the computation of the weighted battery score is discussed. We perform empirical illustration of our method on real and simulated tests, and on a real test battery comprising two constituent tests.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Bayesian Density Estimation via Multiple Sequential Inversions of 2-D Images with Application in Electron Microscopy

We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the convolution of the density function with the unknown microscopy correction function that we also learn from the data. We invoke a novel design of experiment, involving imaging at multiple values of the parameter that controls the sub-surface depth from which information about the density structure is carried, to result in the image. Real-life material density functions are characterised by high density contrasts and typically are highly discontinuous, implying that they exhibit correlation structures that do not vary smoothly. In the absence of training data, modelling such correlation structures of real material density functions is not possible. So we discretise the material sample and treat values of the density function at chosen locations inside it as independent and distribution-free parameters. Resolution of the available image dictates the discretisation length of the model; three models pertaining to distinct resolution classes are developed. We develop priors on the material density, such that these priors adapt to the sparsity inherent in the density function. The likelihood is defined in terms of the distance between the convolution of the unknown functions and the image data. The posterior probability density of the unknowns given the data is expressed using the developed priors on the density and priors on the microscopy correction function as elicitated from the Microscopy literature. We achieve posterior samples using an adaptive Metropolis-within-Gibbs inference scheme. The method is applied to learn the material density of a 3-D sample of a real nano-structure and of simulated alloy samples.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Minimum Distance Estimation of Milky Way Model Parameters and Related Inference

We propose a method to estimate the location of the Sun in the disk of the Milky Way using a method based on the Hellinger distance and construct confidence sets on our estimate of the unknown location using a bootstrap based method. Assuming the Galactic disk to be two-dimensional, the sought solar location then reduces to the radial distance separating the Sun from the Galactic center and the angular separation of the Galactic center to Sun line, from a pre-fixed line on the disk. On astronomical scales, the unknown solar location is equivalent to the location of us earthlings who observe the velocities of a sample of stars in the neighborhood of the Sun. This unknown location is estimated by undertaking pairwise comparisons of the estimated density of the observed set of velocities of the sampled stars, with densities estimated using synthetic stellar velocity data sets generated at chosen locations in the Milky Way disk according to four base astrophysical models. The "match" between the pair of estimated densities is parameterized by the affinity measure based on the familiar Hellinger distance. We perform a novel cross-validation procedure to establish a desirable "consistency" property of the proposed method.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

Comparing X-ray and Dynamical Mass Profiles in the Early-Type Galaxy NGC 4636

We present the results of an X-ray mass analysis of the early-type galaxy NGC 4636, using Chandra data. We have compared the X-ray mass density profile with that derived from a dynamical analysis of the system's globular clusters (GCs). Given the observed interaction between the central active galactic nucleus and the X-ray emitting gas in NGC 4636, we would expect to see a discrepancy in the masses recovered by the two methods. Such a discrepancy exists within the central ~10kpc, which we interpret as the result of non-thermal pressure support or a local inflow. However, over the radial range ~10-30kpc, the mass profiles agree within the 1-sigma errors, indicating that even in this highly disturbed system, agreement can be sought at an acceptable level of significance over intermediate radii, with both methods also indicating the need for a dark matter halo. However, at radii larger than 30kpc, the X-ray mass exceeds the dynamical mass, by a factor of 4-5 at the largest disagreement. A Fully Bayesian Significance Test finds no statistical reason to reject our assumption of velocity isotropy, and an analysis of X-ray mass profiles in different directions from the galaxy centre suggests that local disturbances at large radius are not the cause of the discrepancy. We instead attribute the discrepancy to the paucity of GC kinematics at large radius, coupled with not knowing the overall state of the gas at the radius where we are reaching the group regime (>30kpc), or a combination of the two.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

Non-parametric Deprojection of Surface Brightness Profiles of Galaxies in Generalised Geometries

We present a new Bayesian non-parametric deprojection algorithm DOPING (Deprojection of Observed Photometry using and INverse Gambit), that is designed to extract 3-D luminosity density distributions $ρ$ from observed surface brightness maps $I$, in generalised geometries, while taking into account changes in intrinsic shape with radius, using a penalised likelihood approach and an MCMC optimiser. We provide the most likely solution to the integral equation that represents deprojection of the measured $I$ to $ρ$. In order to keep the solution modular, we choose to express $ρ$ as a function of the line-of-sight (LOS) coordinate $z$. We calculate the extent of the system along the ${\bf z}$-axis, for a given point on the image that lies within an identified isophotal annulus. The extent along the LOS is binned and density is held a constant over each such $z$-bin. The code begins with a seed density and at the beginning of an iterative step, the trial $ρ$ is updated. Comparison of the projection of the current choice of $ρ$ and the observed $I$ defines the likelihood function (which is supplemented by Laplacian regularisation), the maximal region of which is sought by the optimiser (Metropolis Hastings). The algorithm is successfully tested on a set of test galaxies, the morphology of which ranges from an elliptical galaxy with varying eccentricity to an infinitesimally thin disk galaxy marked by an abruptly varying eccentricity profile. Applications are made to faint dwarf elliptical galaxy Ic~3019 and another dwarf elliptical that is characterised by a central spheroidal nuclear component superimposed upon a more extended flattened component. The result of deprojection of the X-ray image of triaxial cluster A1413 is also presented.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

Total mass distributions of Sersic galaxies from photometry $&$ cent\ ral velocity dispersion

We develop a novel way of finding total mass density profiles in Sersic ellipticals, to about 3 times the major axis effective radius, using no other information other than what is typically available for distant galaxies, namely the observed surface brightness distribution and the central velocity dispersion $σ_0$. The luminosity density profile of the observed galaxy is extracted by deprojecting the measured brightness distribution and scaling it by a fiduciary, step-function shaped, $raw$ mass-to-light ratio profile ($M/L$). The resulting raw, discontinuous, total, 3-D mass density profile is then smoothed according to a proposed smoothing prescription. The parameters of this raw $M/L$ are characterised by implementing the observables in a model-based study. The complete characterisation of the formalism is provided as a function of the measurements of the brightness distribution and $σ_0$. The formalism, thus specified, is demonstrated to yield the mass density profiles of a suite of test galaxies and is successfully applied to extract the gravitational mass distribution in NGC 3379 and NGC 4499, out to about 3 effective radii.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

Warps and Bars from the External Tidal Torques of Tumbling Dark Halos

The dark matter halos in $Λ$CDM cosmological simulations are triaxial and highly flattened. In many cases, these triaxial equilibria are also tumbling slowly, typically about their short axes, with periods of order a Hubble time. Halos may therefore exert a slowly changing external torque on spiral galaxies that can affect their dynamical evolution in interesting ways. We examine the effect of the external torques exerted by a tumbling quadrupolar tidal field on the evolution of spiral galaxies using N-body simulations with realistic, disk galaxy models. We measure the amplitude of the external quadrupole moments of dark halos in cosmological simulations and use these to force disk galaxy models in a series of N-body experiments for a range of pattern speeds. We find that the torques are strong enough to induce long lived transient warps in disks similar to those observed in real spirals and also induce the bar instability at later times in some galaxy models that are otherwise stable for long periods of time in isolation. We also observe forced spiral structure near the edge of the disk where normally self-gravity is too weak to be responsible for such structure. This overlooked influence of dark halos may well be responsible for many of the peculiar aspects of disk galaxy dynamics.

0 citations0 reviewsNo code linkedOpen access
preprint2008arXiv

Cluster Geometry & Inclinations from Deprojection Uncertainties

{The determination of cluster masses is a complex problem that would be aided by information about the cluster shape and orientation (along the line-of-sight).} {It is in this context, that we have developed a scheme for identifying the intrinsic morphology and inclination of a cluster, by looking for the signature of the true cluster characteristics in the inter-comparison of the different deprojected emissivity profiles (that all project to the same X-ray brightness distribution) and by using SZe data when available.} {We deproject the cluster X-ray surface brightness profile under the assumptions of four different geometry and inclination configurations for the observed system; these 4 configurations correspond to four extreme geometry+inclination scenarios. The deprojection in question is performed by the non-parametric algorithm DOPING. The formalism is tested with model systems and then is applied to a sample of 24 clusters. While the shape determination is possible by implementing the X-ray brightness alone, the estimation of the inclination is usually markedly improved by the usage of SZe data that is available for the considered sample.}{We spot 8 prolate systems, 1 oblate and 15 of the clusters in our sample as triaxial. In fact, for systems identified as triaxial, we are able to discern how the three semi-axes lengths compare with each other. This, when compounded by the information about the line-of-sight extent, allows us to constrain the inclination quite tightly and offers the two intrinsic axial ratios of the triaxial systems.}{}

0 citations0 reviewsNo code linkedOpen access
preprint2008arXiv

Local Phase Space - Shaped by Chaos?

We attempt to understand the state of the local phase space by comparing simulated 2-D velocity distributions to the distribution that is constructed for the solar neighbourhood, from measurements of stellar radial and transverse velocities. The joint perurbation of the central bar in the Galaxy and the spiral pattern is found to be a must, in order to produce successful models of the local phase space. The existence of chaos is found to be an important ingredient in the formation of the observed phase space structure.

0 citations0 reviewsNo code linkedOpen access