Data Analysis, Probability and Statistics

Directions of research:

  • Limit theorems and asymptotic methods in probability and statistics.
  • Bayesian nonparametric learning methodologies; applications to Astrophysics, Material Science and Item Response Theory.
  • Pattern recognition techniques including development of supervised shape classifier and hierarchical non-linear regression models.
  • Dimensionality reduction, principal components, principal graphs and manifolds, data visualization
  • Maximum Entropy methods with applications in statistics, economics and natural sciences
  • Gaussian process regression and non-parametric statistics.
  • Artificial and natural neural networks

 

Current members

Press Releases

Breakthrough study discovers six changing faces of 'global killer' bacteria (September 30, 2014)
New hope for beloved family pets: New blood test for canine cancer (September 23, 2014)
Genetic evidence for single bacteria cause of sepsis identified for the first time by academic team (March 21, 2014)
Mathematicians Solve Decade-Old Debate On Regulation of Protein Production by microRNAs in Cells (July 31, 2012)
Plants and Animals Under Stress May Provide the Key to Better Stock Market Predications (Nov. 3, 2010)
Brain power- breakthrough in mathematical modelling (September 2007)

Some recent publications

  1. A.N. Gorban, I.Y. Tyukin, I. Romanenko,
    The Blessing of Dimensionality: Separation Theorems in the Thermodynamic Limit, IFAC-PapersOnLine 49-24 (2016), 064–069.
  2. Moczko, E.M. Mirkes, C. Ceceres, A.N. Gorban, S. Piletsky,  Fluorescence-based assay as a new screening tool for toxic chemicals, Scientific Reports 6, Article number: 33922 (2016)
  3. Kajero OT, Thorpe RB, Chen T, Wang B, Yao Y. Kriging meta‐model assisted calibration of computational fluid dynamics models, AIChE Journal. 2016 Dec 1;62(12):4308-20.
  4. A.N. Gorban, E.M. Mirkes, A. Zinovyev, Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning, Neural Networks 84 (2016), 28-38
  5.  Grechuk B, Zabarankin M. Inverse portfolio problem with coherent risk measures. European Journal of Operational Research. 2016 Mar 1;249(2):740-50.
  6. E.M. Mirkes, T.J. Coats, J. Levesley, A.N. Gorban, Handling missing data in large healthcare dataset: a case study of unknown trauma outcomes, Computers in Biology and Medicine 75 (2016), 203-216.
  7.  Peligrad M, Utev S. On the invariance principle for reversible Markov chains. Journal of Applied Probability. 2016 Jun 1;53(02):593-9.
  8.  A.N. Gorban, I.Yu. Tyukin, D.V. Prokhorov, K.I. Sofeikov, Approximation with random bases: Pro et Contra, Information Sciences 364-365, (2016), 129-145.
  9. A. N. Gorban,·A. Zinovyev, Fast and user-friendly non-linear principal manifold learning by method of elastic maps, in Proceedings DSAA 2015 -- IEEE International Conference on Data Science and Advanced Analytics, Paris; 10/2015.
  10.   
  11. A.S. Manso, M.H. Chai, J.M. Atack, L. Furi, M. De Ste Croix, R. Haigh, C. Trappetti, A.D. Ogunniyi, L.K. Shewell, M. Boitano, T.A. Clark, J. Korlach, M. Blades, E. Mirkes, A.N. Gorban, J.C. Paton, M.P. Jennings, M.R. Oggioni, A random six-phase switch regulates pneumococcal virulence via global epigenetic changes, Nature Communications 5 (2014), Article number: 5055.
  12. S. Utev, S. R. Mudakkar, Rademacher Inequalities with Applications. Journal of Theoretical Probability, 27(1), 301-314 (2014).
  13. D. Chakrabarty, F. Rigat, N. Gabrielyan, R. Beanland, S. Paul, Bayesian Density Estimation via Multiple Sequential Inversions of 2-D Images with Application in Electron Microscopy, Technometrics (2014), DOI:10.1080/00401706.2014.923789.
  14. E.M. Mirkes, I. Alexandrakis, K. Slater, R. Tuli, A.N. Gorban,  Computational diagnosis and risk evaluation for canine lymphoma,  Computers in Biology and Medicine 53, 279-290 (2014).
  15.  A. Gerlini, L. Colomba, L. Furi, T. Braccini, A.S. Manso, A. Pammolli, Bo Wang, A. Vivi, M. Tassini, N. van Rooijen, G. Pozzi, S. Ricci, P.W. Andrew, U. Koedel, E.R. Moxon, M.R. Oggioni, The role of host and microbial factors in the pathogenesis of pneumococcal bacteraemia arising from a single bacterial cell bottleneck, PLoS Pathogens 03/2014; 10(3):e1004026.
  16. IY Tyukin, E Steur, H Nijmeijer, C Van Leeuwen, Adaptive observers and parameter estimation for a class of systems nonlinear in the parameters. Automatica 49 (8), 2409–2423 (2013),
  17. P Jurica, S Gepshtein, I Tyukin, C van Leeuwen, Sensory optimization by stochastic tuning. Psychological review 120 (4), 798 (2013).
  18. A Zinovyev, E Mirkes, Data complexity measured by principal graphs,  Computers & Mathematics with Applications 65 (10), 1471-1482 (2013)
  19. C. Lefèvre, S. Utev, Convolution property and exponential bounds for symmetric monotone densities. ESAIM: Probability and Statistics, 17, 605-613 (2013).
  20. G. Deligiannidis, S. Utev, Variance of partial sums of stationary sequences. The Annals of Probability, 41(5), 3606-3616 (2013).
  21. A.N. Gorban, Maxallent: Maximizers of all entropies and uncertainty of uncertainty, Computers & Mathematics with Applications 65 (10) (2013), 1438-1456. arXiv:1212.5142 [physics.data-an] http://arxiv.org/pdf/1212.5142
  22. V Kazantsev, I Tyukin, Adaptive and phase selective spike timing dependent plasticity in synaptically coupled neuronal oscillators, PloS One 7 (3), e30411
  23. A.N. Gorban, A. Zinovyev. Principal manifolds and graphs in practice: from molecular biology to dynamical systems, International Journal of Neural Systems, Vol. 20, No. 3 (2010) 219–232.
  24. Taeryon Choi, J.Q. Shi and Bo Wang. A Gaussian process regression approach to a single-index model. Journal of Nonparametric Statistics 23, 21-36, 2011. (The winning paper of JNPS 2011 Best Paper Award)
  25. RK Beatson, J Levesley, CT Mouat, Better bases for radial basis function interpolation problems, Journal of Computational and Applied Mathematics 236 (4), 434-446
  26. A.N. Gorban, P.A. Gorban, G. Judge, Entropy: The Markov Ordering Approach. Entropy. 12(5), 1145-193 (2010). (Entropy best paper award, 2014).
  27. G. Deligiannidis, H. Le and S. Utev, Optimal stopping for processes with independent increments, and applications, J. Appl. Probab. 46 (4) (2009), 1130-1145.
  28. B Grechuk, A Molyboha, M Zabarankin, Maximum entropy principle with general deviation measures, Mathematics of Operations Research 34 (2), 445-467 (2009).
  29. R. Johnson, D. Chakrabarty, E. O'Sullivan, & S. Raychaudhury, Comparing X-ray and dynamical mass profiles in the early-type galaxy NGC 4636. The Astrophysical Journal, 706(2), 980–994  (2009).
  30. J. Dubinski, & D. Chakrabarty, Warps and Bars from the External Tidal Torques of Tumbling Dark Halos. The Astrophysical Journal, 703(2), 2068–2081 (2009).
  31. D. Chakrabarty,  & L. Ferrarese, DOPING: a new Non-parametric Deprojection Scheme. International Journal of Modern Physics D, 17(02), 195-201 (2008).
  32. A. Gorban, B. Kegl, D. Wunsch, A. Zinovyev  (Eds.), Principal Manifolds for Data Visualisation and Dimension Reduction, Lecture Notes in Computational Science and Engineering, Vol. 58, Springer, Berlin – Heidelberg – New York, 2008.

Projects with Industry

Computational Diagnosis of Canine Lymphoma, with PetScreen and Avacta

Avacta Animal Health has developed new CRP and HAP tests and has secured exclusive rights to multivariate analytical algorithms developed by Leicester University that combine the APP test results to provide a unique and powerful tool capable of assisting in the non-invasive diagnosis of lymphoma in dogs and in remission monitoring. The generated software can be used as a diagnostic, monitoring and screening tool. For the differential diagnosis the best solution gave a sensitivity and specificity of 83.5% and 77%, respectively (using three input features, CRP, Haptoglobin and a standard clinical symptom). For the screening task, the decision tree method provided the best result, with sensitivity and specificity of 81.4% and >99%, respectively (using the same input features).

Press Release in ScienceDaily
New hope for beloved family pets: New blood test for canine cancer (September 23, 2014)

E.M. Mirkes, I. Alexandrakis, K. Slater, R. Tuli, A.N. Gorban, Computational diagnosis and risk evaluation for canine lymphoma, Computers in Biology and Medicine 53, 279-290 (2014).

 E M Mirkes, I Alexandrakis, K Slater, R Tuli and A N Gorban, Computational diagnosis of canine lymphoma, J. Phys.: Conf. Ser. 490 012135 (2014).

Detection and Tracking of Objects in Live Video Streams, with Apical LTD

 The project aims at developing classifiers for real-time and accurate tracking of objects (e.g. humans, cars, bicycles, pets etc) in live video streams. As a result of the project we now have a n Apical hardware capable of detecting and tracking  objects (represented by 2048-dimensional feature vectors) equipped by jointly developed learning models of these objects online and software library for intellectual analysis of video stream. In particular, we developed a technique for scene analysis and improving Automatic White Balance (AWB) settings in digital cameras on the basis automatic classification of image fragments.

K.I. Sofeikov, I. Romanenko, I. Tyukin, A.N. Gorban. Scene Analysis Assisting for AWB Using Binary Decision Trees and Average Image Metrics. In Proceedings of IEEE Conference on Consumer Electronics, 10-13 January, Las-Vegas, USA, 2014, pp. 488-491.

K.I. Sofeikov, I. Yu. Tyukin, A.N.Gorban, E.M.Mirkes, D.V. Prokhorov, and I.V.Romanenko, Learning Optimization for Decision Tree Classification of Non-categorical Data with Information Gain Impurity Criterion. In Proceedings of 2014 International Joint Conference on Neural Networks (IJCNN) July 6-11, 2014, Beijing, China, IEEE 2014, pp. 3548-3555

Presentation slides

A.N. Gorban, Geometry of data sets, an invited talk given at ESOF2010 (Euroscience Open Forum, Torino, July 2-7, 2010)

Teaching applets
The online Data Mining course (in preparation)

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Contact details

Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 252 3917
Fax: +44 (0)116 252 3915

Campus Based Courses

Undergraduate: mathsug@le.ac.uk
Postgraduate Taught: mathspg@le.ac.uk

Postgraduate Research: pgrmaths@le.ac.uk

Distance Learning Course  

Actuarial Science:

dlstudy@le.ac.uk  

 

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