Dr Franz Kiraly
+44 (0) 20 7679 1259
+44 (0) 20 3108 3105
Department of Statistical Science
Stochastic Modelling and Time Series
General Theory and Methodology
Curriculum Vitae (2014/02)
|Franz Kiraly @|
UCL Centre for Inverse Problems
|Core interests||Current projects||PhD applications||Upcoming events|
|Short CV||Publications||Slides and videos|
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
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.
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
Estimation with Algebraic Combinatorial Structure, exploiting hidden algebraic structure in the model for accurate estimation and error prediction
Matrix Completion, studying the the combinatorial algebraic
structure imposed by constraints and its relation to convex relaxation
methods and spectral phenomena
Compressed Sensing, in particular when an inverse problem can be described by combinatorial algebraic compression constraints
Tensor Factorization, and blind source separation, by algebraic properties of the tensors in question
If you would like to do your PhD with me as your advisor, please contact me initially, preferably by email, so we can discuss your interests. 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. 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. The CoMPLEX research centre offers opportunities for PhDs spanning interdisciplinary topics in the life sciences, physics and mathematics/statistics.
Depending on your interests, there are different opportunities for funding with different deadlines and conditions (see here for UCL scholarships, and the links above).
(times are local time and in 24h format)
2014, July 3-4, Universität Ulm
Conference on Rigid and Algebraic Geometry
2014, July 16-20, NIMS, Korea
Optimization and Algebraic Geometry
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.
Since August 2013, I am working as a lecturer (comparable to assistant professor) at University College London.
[Download Curriculum Vitae] (2014/02)
(the arXiv versions are usually the most up-to-date)
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.
Király FJ, Larsen P.
Fano schemes of generic intersections and machine learning. Preprint, 9 pages, arXiv
Király FJ, Theran L, Tomioka R, Uno T. The algebraic
combinatorial approach for low-rank matrix completion. Preprint, 102
pages, arXiv 1211.4116. 2013.
Preprint published in the Oberwolfach Preprint Series as
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.
[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.
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.
[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.
Refereed journal publications
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)
Preprint published in the Oberwolfach Preprint Series as
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.
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.
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.
Von Bünau P, Meinecke FC, Király
FJ, Müller K-R. Finding stationary subspaces in multivariate
Physics Review Letters. 103, 214101. 2009.
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]
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
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 16 jun 14 13:09