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 (2016/01)

 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

Lucky is the man who's able
to see structure in a table
since this might be useful later
when there's nosie and missing        
Matrix und Moritz

I am a practical statistician and machine learner, seeking for data analysis methods that find and make use of structure in data.

My favourite methods are those which are useful, my favourite problems are those which are relevant. I am currently working on data analytics applications in

the medical sciences, physics and sports science,

close to my methodological expertise in

non-linear methods for dimension reduction, denoising, prediction, and missing data,

with a trajectory in the vicinity of

kernel learning, compressed sensing and low-rank matrix completion.

I also have a faible for malappropriating ideas from pure mathematics, particularly algebra and combinatorics, to an impure context.

Current projects

Recently, I have been doing research on these applications:

Quantification and Prediction in Running Sports. Characterizing the training state of running athletes, and making predictions for race planning and training. We can predict Marathon times with an error in the order of a few minutes, and we are able to accurately summarize an athlete by three characteristic numbers (work in progress).
(read more)

My current work on data analysis methodology includes:

Non-linear prediction and dimension reduction with series-valued samples. We propose a new learning framework for the situation where the data samples are time series or otherwise sequentially ordered, based on kernels whose features are ordered variants of sample moments.
(read more)

Single-Entry Matrix Completion and Local Matrix Completion. Our new methods can (i) reliably impute or predict single missing entries in a numerical data table, with error bars, and (ii) do so without necessarily reading in all entries in a big data table. They are the first of their kind under the common low-rank assumption.
(read more)

Kernel Learning with Invariances. Encoding known invariances of the data, say sign/mirror symmetry, scaling or phase invariance, efficiently with a kernel (work in progress).
(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)

Upcoming events will be announced here.

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

In 2015, I have been visiting the Aalto Science Institute as an AScI Visiting Fellow.

Since 2016, I am also a faculty fellow at the newly founded Alan Turing Institute whose vision is to bundle and catalyze the UK's efforts in modern data science.

[Download Curriculum Vitae] (2016/01)


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


Király FJ, Oberhauser H. Kernels for sequentially ordered data. Preprint, 48 pages, arXiv 1601.08169. 2016.

Ehler M, Graef M, Király FJ. Phase retrieval using random cubatures and fusion frames of semidefinite matrices. Preprint, 21 pages, arXiv 1505.05003. 2015.

Blythe DAJ, Király FJ. Prediction and Quantification of Individual Athletic Performance. Preprint, 27 pages, arXiv 1505.01147. 2015.

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]

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

Király FJ, Theran L, Tomioka R. The algebraic combinatorial approach for low-rank matrix completion. Preprint, 42 pages, arXiv 1211.4116. Accepted for publication in the Journal of Machine Learning Research, 2015.
[arXiv 1211.4116]
Preprint published in the Oberwolfach Preprint Series as
[OWP 2013-05]

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]


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