Dr Franz Kiraly


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+44 (0) 20 7679 1259

+44 (0) 20 3108 3105



Department of Statistical Science
University College London
Gower Street
London WC1E 6BT
United Kingdom

Franz Király (September 2013, small version)
Themes Computational Statistics
Stochastic Modelling and Time Series
General Theory and Methodology
Curriculum Vitae (2014/02)

 Franz Kiraly @
Google Scholar
UCL Centre for Inverse Problems
 Quick links
Core interests Current projects PhD applications Upcoming events
Short CV Publications Slides and videos  

Core interests

Statistics - the study of data and its properties

Algebraic Combinatorics - the study of structure and its properties
(whenever operations/relations and/or discrete structure is involved)

Machine Learning - learning structure from data and drawing conclusions
(using machines/computers)

My primary research interest consists of using Algebra and Combinatorics to find practically relevant structure in data. Naturally this includes the study of interactions between

Algebra and Algebraic Geometry, Discrete Geometry and Probabilistic Combinatorics, and Statistical Modelling.

My research aims at finding novel algebraic and combinatorial methods which can be applied in

Statistics and Machine Learning,

that is, to construct methods and algorithms for real world data. In particular, I am interested in understanding, and solving

Ill-Posed and Inverse Problems,

by finding and using the structure therein.

Current projects

Currently, I am working on:

Kernel Learning with Ideals, on estimating the structure of the data manifold, using a combination of kernel methods and algebraic techniques
(read more)

Estimation with Algebraic Combinatorial Structure, exploiting hidden algebraic structure in the model for accurate estimation and error prediction
(read more)

Matrix Completion, studying the the combinatorial algebraic structure imposed by constraints and its relation to convex relaxation methods and spectral phenomena
(read more)

Compressed Sensing, in particular when an inverse problem can be described by combinatorial algebraic compression constraints
(read more)

Tensor Factorization, and blind source separation, by algebraic properties of the tensors in question
(read more)

PhD applications

I am currently accepting PhD applications. If you would like to do your PhD with me as your advisor, please contact me initially, preferably by email, so we can discuss the feasibility of working together. Please include a CV, a short description of your research interests and why you would like to pursue your PhD with me. You are also advised to consult the UCL guidelines on formal requirements for obtaining a graduate research degree. Possible (not mutually exclusive) topic areas are:

Statistics and Machine Learning. This is were my core research interests lie. Please have a look at my personal interests, the institute's research foci, or the EPSRC Computational Statistics and Machine Learning network.

Inverse Problems. I am a member of the newly founded Inverse Problems Centre at UCL, which is devoted to a wide spectrum of inverse problems occurring in different scientific disciplines.

Interdisciplinary Applications. There are a variety of data-driven applications I am currently working on or I am potentially interested in, for example in medical statistics, finance, sports science, or networks.

Additionally, if you have your own innovative idea you would like to do research on (assuming it makes sense and our interests match), I would be happy to help you to pursue that goal even if it is not specifically something I am currently working on.

Depending on your interests, there are different opportunities for funding with different deadlines and conditions (see here for UCL scholarships).

For formal inquiries please contact our graduate tutor, Dr Afzal Siddiqui.
(please contact me first and/or read through the UCL guidelines before doing so)

Upcoming Talks and Conferences

(times are local time and in 24h format)

2014, December 11-20, Universidad de la República, Montevideo
Foundations of Computational Mathematics 2014

2015, February 16, University of Oxford
Stochastic Analysis Group Seminar

Short Curriculum Vitae

At the University of Ulm, I have obtained my Diplomae (equivalent to MSc or MD, as regards content) in Computer Science, Mathematics, Medicine and Physics in the years 2003, 2005, 2006 and 2011; in 2008, I recieved my PhD in Medicine.

From 2007 to 2010, I have completed my PhD thesis in Mathematics on the topic of Arithmetic Geometry, under supervision of and in cooperation with Prof. Werner Lütkebohmert in Ulm.

From 2010 to 2013, I have worked as a postdoctoral researcher in Prof. Klaus-Robert Müller's Machine Learning Group, at the Technische Universität Berlin, and I have been an associate member of Prof. Günter Ziegler's Discrete Geometry Group, at the Freie Universität Berlin.

In 2012 I was appointed Leibniz Fellow at the Mathematisches Forschungsinstitut Oberwolfach where I spent a total of six months, split over 2012, 2013 and 2014.

Since August 2013, I am working as a lecturer (comparable to assistant professor) at University College London.

In 2015, I will be visiting the Aalto Science Institute as an AScI Visiting Fellow.

[Download Curriculum Vitae] (2014/02)


(the arXiv versions are usually the most up-to-date)


Király FJ, Ziehe A, Müller K-R. Learning with Algebraic Invariances, and the Invariant Kernel Trick. Preprint, 17 pages, arXiv 1411.7817. 2014.

Blythe DAJ, Király FJ, Theran L. Algebraic combinatorial methods for low-rank matrix completion with application to athletic performance prediction. Preprint, 13 pages, arXiv 1406.2864. 2014.

Király FJ, Kreuzer M, Theran L. Learning with cross-kernels and Ideal PCA. Preprint, 14 pages, arXiv 1406.2646. 2014.

Király FJ, Theran L. Matroid Regression. Preprint, 16 pages, arXiv 1403.0873. 2014.

Király FJ, Ehler M. The algebraic approach to phase retrieval and explicit inversion at the identifiability threshold. Preprint, 26 pages, arXiv 1402.4053. 2014.

Király FJ, Kreuzer M, Theran L. Dual-to-kernel learning with ideals. Preprint, 15 pages, arXiv 1402.0099. 2014.

Király FJ, Rosen Z, Theran L. Algebraic matroids with graph symmetry. Preprint, 70 pages, arXiv 1312.3777. 2013.

Király FJ. Efficient orthogonal tensor decomposition, with an application to latent variable model learning. Preprint, 14 pages, arXiv 1309.3233. 2013.

Király FJ, Theran L. Coherence and sufficient sampling densities for reconstruction in compressed sensing. Preprint, 18 pages, arXiv 1302.2767. 2013.
[arXiv 1302.2767]

Király FJ, Theran L, Tomioka R, Uno T. The algebraic combinatorial approach for low-rank matrix completion. Preprint, 102 pages, arXiv 1211.4116. 2013.
[arXiv 1211.4116]
Preprint published in the Oberwolfach Preprint Series as
[OWP 2013-05]

Refereed conference publications

Király FJ, Ehler M. Algebraic reconstruction bounds and explicit inversion for phase retrieval at the identifiability threshold. Journal of Machine Learning Research Workshop & Conference Proceedings Vol.24 – Proceedings on the Seventeenth International Conference on Artificial Intelligence and Statistics. To appear, 9 pages. 2014.

Király FJ, Theran L. Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion. Neural Information Processing Systems 2013, to appear in Proceedings. Preprint version available as arXiv 1302.5337, 14 pages. 2013.
[arXiv 1302.5337] [code, mloss]

Király FJ, Ziehe A. Approximate rank-detecting factorization of low-rank tensors. IEEE Internatioal Conference of Acoustics, Speech, and Signal Processing 2013, to appear in Proceedings. Preprint version available as arXiv 1211.7369, 5 pages. 2013.
[arXiv 1211.7369] [code, mloss]

Király FJ, Tomioka R. A combinatorial algebraic approach for the identifiability of low-rank matrix completion. International Conference on Machine Learning 2012. Published in ICML Proceedings, made available by ICML as arXiv 1206.4670, 8 pages. 2012.
[arXiv 1206.6470]
[ICML 2012-510]

Király FJ, Von Buenau P, Müller JS, Blythe DAJ, Meinecke FC, Müller K-R. Regression for sets of polynomial equations. Journal of Machine Learning Research Workshop & Conference Proceedings Vol.22 – Proceedings on the Fifteenth International Conference on Artificial Intelligence and Statistics, 22:628-637. 2012.
[arXiv 1110.4531] [code] (ZIP, 17,4 KB)
[JMLR W&CP 2012-22]

Király FJ, Ziehe A, Müller K-R. An algebraic method for approximate rank one factorization of rank deficient matrices. Latent Variable Analysis and Signal Separation 2012 Conference Proceedings, 272-279. 2012.
[LVAASS 2012-7191]

Refereed journal publications

Larsen P, Király FJ. Fano schemes of generic intersections and machine learning. International Journal of Algebra and Computation, Vol.24, No.17, 923-933. 2014.
[IJAC 10.1142]
[arXiv 1301.3078]

Király FJ, Lütkebohmert W. Invariants of regular local rings by p-cyclic group actions. Algebra and Number Theory, Vol.7, No.1, 63-74. 2013.
[arXiv 1001.1945]
[ANT 2913.7.63]

Király FJ, Von Buenau P, Blythe DAJ, Meinecke FC, Müller K-R. Algebraic geometric comparison of probability distributions. Journal of Machine Learning Research 13(Mar):855-903. 2012.
[JMLR 2012-13] [code] (ZIP, 3,8 KB)
[arXiv 1108.1483]
Preprint published in the Oberwolfach Preprint Series as
[OWP 2011-30]

Müller JS, von Bünau P, Meinecke FC, Király FJ, Müller K-R. The Stationary Subspace Analysis Toolbox. Journal of Machine Learning Research 12(Oct):3065−3069. 2011.
[JMLR 2011-12]

Kilian H-G, Kazda M, Király FJ, Kaufmann D, Kemkemer R, Bartkowiak D. On the structure-bounded growth processes in plant population. Cell Biochemistry and Biophysics 57:87-100. 2010.
[CBB 1559-0283]

Schlenk RF, Döhner K, Mack S, Stoppel M, Király F, Götze K, Hartmann F, Horst HA, Koller E, Petzer A, Grimminger W, Kobbe G, Glasmacher A, Salwender H, Kirchen H, Haase D, Kremers S, Matzdorff A, Benner A, Döhner H. Prospective evaluation of allogeneic hematopoietic stem-cell transplantation from matched related and matched unrelated donors in younger adults with high-risk Acute Myeloid Leukemia: German-Austrian trial AMLHD98A. Journal of Clinical Oncology 20;28(30):4642-4648. 2010.
[Weblink JCO]

Von Bünau P, Meinecke FC, Király FJ, Müller K-R. Finding stationary subspaces in multivariate time series. Physics Review Letters. 103, 214101. 2009.
[PRL 103.214101]

Király FJ, Kletting P, Reske SN, Glatting G. Modelling radioimmunotherapy (RIT) with anti-CD45 antibody to obtain a more favourable biodistribution. Nuklearmedizin 48:113-119. 2009.


Király FJ. Wild quotient singularities of surfaces and their regular models. Doctoral dissertation, Ulm. 2010.
[e-print VTS Univ. Ulm]

Király FJ. Vergleich verschiedener Postremissionsstrategien bei der akuten myeloischen Leukämie mit normalem Karyotyp. Doctoral dissertation, Ulm. 2008.
[e-print VTS Univ. Ulm]

Past Talks: Slides and Videos

2012, September 29, 14:00-14:45, Algebraic Statistics in Europe
IST Austria, Mondi Conference Center, Mondi 2
Low-Rank Matrix Completion

2012, June 29, 14:00-14:20, ICML 2012
University of Edinburgh, Appleton Tower, Room AT LT 2

A Combinatorial Algebraic Approach for the Identifiability of Matrix Completion

2012, June 13, 15:30-16:00, Algebraic Statistics 2012
Penn State University, Berg Auditorium
Ideal Regression

2012, April 23, 19:35-20:00, AISTATS 2012
La Palma, Los Cancajos, H10 Taburiente Playa, Las Nieves/Tenguía room

Regression for sets of polynomial equations
[Video, unfortunately incomplete]

Page last modified on 11 dec 14 15:57