Mathematical Sciences

Department staff

Dr Dalia Chakrabarty

Photo of Dr Dalia Chakrabarty

Lecturer in Statistics

My D.Phil (from St. Cross College, Oxford) was in Theoretical Astrophysics, and I was examined by Prof. James Binney. My doctoral thesis was dedicated to the development of a novel Bayesian learning method that I used to learn the gravitational mass of the black hole in the centre of the Milky Way, (along with the Galactic phase space density), and to the computational modelling of non-linear dynamical phenomena in galaxies. Thereafter, I continued to develop probabilistic learning methods, and undertake Bayesian inference, in astronomical contexts, till 2009, when I moved to Warwick Statistics, and started developing Bayesian methodologies, to apply to diverse areas. After Warwick, I was a Lecturer in Statistics, in Leicester Maths, for about 4 years, and moved to Loughborough on the 1st of March, 2017. My current interest is strongly focused on the development of learning methodologies, given different challenging data situations, such as data that is shaped as a hyper-cuboid; is diversely correlated; absent training data; data that is discontinuous and/or changing with time. I am also interested in the development of Bayesian tests of hypotheses, and recently, have started work on learning the mis-specified parameters of a parametric model. My current applications include areas such as healthcare, vino-chemistry, astronomy, test theory, petrology, etc. 

  • Bayesian Supervised learning given high-dimensional discontinuous, and/or non-stationary data, using the Compounding of Tensor-variate GP with Scalar-variate GPs.
  • Graphical models of multivariate data, distance between learnt pair of graphical models, and inter-data correlation .
  • Novel Bayesian learning when training data is absent.
  • Tests of hypotheses given intractable alternatives.
  • Novel identification of model mis-specification parameters.
  • Supervised learning using hierarchical regression & supervised classification. 
  • Applications to Astrophysics, Materials Science, Chemistry, Healthcare, Petrophysics, Testing Theory, etc.

My research focuses upon the development of methodologies within Computational & Mathematical Statistics, including Bayesian supervised and unsupervised learning methods — given different data situations, such as high-dimensional data, temporally-evolving and/or discontinuous data, absent training data, large in size or under-abundant. This has resulted in

--supervised learning methodologies given hypercuboidally-shaped, discontinuous and/or non-stationary data, using high-dimensional Compounding of 
Gaussian Processes;
--pursuit of graphical models of multivariate data, followed by computing distance between learnt graphical models, to inform on the inter-data correlation.
--an unsupervised learning method in which the unknown is embedded within support of the state space density, where the aim is to learn such an unknown
in the absence of training data.
--Sometimes, in pursuit of this latterly mentioned unsupervised learning method, intractability is encountered, and I am interested in developing new tests of
hypotheses in which we seek the probability of a simplifying model, conditioned on the data, where said simplification is undertaken to counter the intractability.
--Have recently started work on the identification of model mis-specification parameter vector, using a new 5-step methodology that is an optimisation scheme, with MCMC-based learning embedded within.                                                                                                                                                                                                                                                                                                     In addition, I have worked on developing a novel classification technique in lieu of training data, and on another occasion, trained the model for the causal relationship between the observable and covariates, using hierarchical regression.

Applications of these methods are in Astronomy, Materials Science, Chemistry, Petrophysics, Testing theory, etc.

If you are a prospective Ph.D student or postdoctoral fellow,  with an interest in mathematical/computational statistics, please feel free to contact me; I have multiple projects in

  • Bayesian methodology development: high-dimensional supervised learning; learning in the absence of training data; Bayesian tests; dynamical inhomogeneous graphical models,
  • applications: Bayesian learning approaches in Material Sc; unsupervised learning in Astronomy; graphical models of data from assorted disciplines, and computationally intensive projects. 

Research - publication of developed methods+undertaken applications; attending conferences; applying or grants; Ph.D student supervision--currently working with two Ph.D students, Georgios Stagakis, and Cedric Spire, (and co-supervising another student); my first Ph.D student Kangrui Wang finished in 2018.

--Kangrui is working on high-dimensional Bayesian supervised learning methodologies and graphical models of large/small multivariate data using tensor-variate Gaussian Processes; he is interested in exploring kernel parametrisation. Kangrui has made applications of his methods to astronomical data, to the learning of vino-chemical networks of wine samples, learning the disease-symptom network in humans, and in computing reliability of large tests. He was examined in the summer of 2018, and bagged a postdoctoral position in the Alan Turing Institute thereafter.

-- Cedric is pursuing a novel Bayesian unsupervised learning methodology that works by embedding the sought model parameter into the support of the likelihood. He is making applications to learn the probability density of phase spaces of distant galaxies, and the total gravitational mass density in these systems. He is currently in his third year. 

-- Georgios Stagakis joined me as my Ph.D student, in 2018.

In addition, I regularly work with final year project students in the Department, and offer Small Group Tutorials to my 1st Year personal tutees enrolled on the Mathematics BSc degree.

Teaching -

--MAB270: Statsitical Modelling.
--MAB280: Introduction to Stochastic Analysis (second half of module); 
--assessment of presentations of various project modules in Statistics and Mathematics.

Pastoral -

          --Induction Coordinator in Mathematics.
          --tutor to a small group of 1st and 2nd year tutees, 2 placement students

Enterprise - contributing towards impact case studies; industrial collaborations.

Recently  published & communicated:

 

  • Cedric Spire & Dalia Chakrabarty, "Learning in the Absence of Training Data -- a Galactic Application", proceedings for the BAYSM, 2018 conference.
  • Kangrui Wang & Dalia Chakrabarty, " 2 Layers Suffice: Bayesian Supervised Learning given Hypercuboidally-shaped, Discontinuous Data, using Compound Tensor-Variate $\&$ Scalar-Variate Gaussian Processes", arXiv:1803.04582
  • Kangrui Wang & Dalia Chakrabarty, "Correlation between Multivariate Datasets, from Inter-Graph Distance computed using Graphical Models Learnt With Uncertainties",arXiv:1710.11292
  • Dalia Chakrabarty, ``A New Bayesian Test to test for the Intractability-Countering Hypothesis'', 2017, Jl. of American Statistical Association; 112, pg.561--577.
  • Dalia Chakrabarty et. al, ``Bayesian Density Estimation via Multiple Sequential Inversions of 2-D Images with Application in Electron Microscopy'', 2015, Technometrics, 57, 2, pg. 217–233.
  • Dalia Chakrabarty, M. Biswas & Sourabh Bhattacharya,``Bayesian Nonparametric Estimation of Milky Way Model Parameters Using a New Matrix-Variate Gaussian Process Based Method'', Electronic Journal of Statistics, 2015, 9, 1, pg. 1378–1403.
  • S. Banerjee, A. Basu, S. Bhattacharya, S. Bose, Dalia Chakrabarty, and S.S. Mukherjee, ``Minimum Distance Estimation of  Milky Way Model Parameters and Related Inference'', 2015, SIAM/ASA Jl. of Uncertainty Quantification, 3, 1, pg. 91–115.
  • Dalia Chakrabarty & S. Paul, ``Bayesian Learning of Material Density Function by Multiple Sequential Inversions of 2-D Images in Electron Microscopy'', 2015, Springer Proceedings in Mathematics and Statistics, 118, pg. 35–48.

 Upcoming publications:

  • Satyendra Nath Chakrabartty, Kangrui Wang, Dalia Chakrabarty, "A New, Fast Method of Computing Reliability of Very-Large Sets of Test Score Data, applied to the Yelp Review Data".
  • Cedric Spire & Dalia Chakrabarty, ``Learning of State Space Density & Static Model Parameter by Embedding the Latter into the Support of the Former''.
  • Dalia Chakrabarty, "A New Method for Learning the Mis-specified Vector of Parameters in a Parametric Model".