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44                        Mikio L. Braun
45                    </a>
46                    <p class="text-sm text-gray-500 mt-1">ML and AI expert</p>
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64<div class="max-w-3xl">
65    <h1 class="text-3xl font-bold mb-6">Publications</h1>
66
67    
68    
69    
70    <section class="mb-10">
71        <h2 class="text-xl font-bold mb-2 text-gray-800">General Machine Learning</h2>
72        
73
74        <div class="space-y-4">
75            
76            <div class="border-l-2 border-gray-200 pl-4 py-2">
77                <p class="font-medium text-gray-900">Fast Cross-Validation via Sequential Analysis</p>
78                <p class="text-sm text-gray-600">T. Krüger, D. Panknin, M. Braun</p>
79                <p class="text-sm text-gray-500 mt-1">
80                    <p>NIPS BigLearning Workshop, 2011</p>
81                </p>
82                
83                <a href="https://www.scribd.com/doc/76134303"
84                   class="text-blue-600 hover:text-blue-800 text-sm"
85                   target="_blank">
86                    View paper
87                </a>
88                
89                
90                <details class="mt-2">
91                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
92                        Show abstract
93                    </summary>
94                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
95                        With the increasing size of today’s data sets, finding the right
96parameter configuration via cross-validation can be an extremely
97time-consuming task. In this paperwe propose an improved
98cross-validation procedure which uses non-parametrictesting
99coupled with sequential analysis to determine the best parameter
100set on linearly increasing subsets of the data. By eliminating
101underperforming candidatesquickly and keeping promising candidates
102as long as possible the method speedsup the computation while
103preserving the capability of the full cross-validation.The
104experimental evaluation shows that our method reduces the
105computation timeby a factor of up to 70 compared to a full
106cross-validation with a negligible impacton the accuracy.
107
108                    </p>
109                </details>
110                
111            </div>
112            
113        </div>
114    </section>
115    
116    
117    
118    
119    <section class="mb-10">
120        <h2 class="text-xl font-bold mb-2 text-gray-800">Social Media Analysis</h2>
121        
122        <p class="text-gray-600 text-sm mb-4">Analysis of Twitter data; Impact Analysis; Big Data, Real-Time;
123Stream Mining.
124</p>
125        
126
127        <div class="space-y-4">
128            
129            <div class="border-l-2 border-gray-200 pl-4 py-2">
130                <p class="font-medium text-gray-900">Real-time social media analysis with TWIMPACT</p>
131                <p class="text-sm text-gray-600">M. Braun, M. Jugel, K.-R. Müller</p>
132                <p class="text-sm text-gray-500 mt-1">
133                    <p>Demonstration at NIPS 2011.</p>
134                </p>
135                
136                <a href="https://twimpact.tumblr.com/post/14164936717/preview-of-our-nips-poster-come-to-our-demo-on"
137                   class="text-blue-600 hover:text-blue-800 text-sm"
138                   target="_blank">
139                    View paper
140                </a>
141                
142                
143                <details class="mt-2">
144                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
145                        Show abstract
146                    </summary>
147                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
148                        Social media analysis has attracted quite some interest
149recently. Typical questions are identifying current trends, rating
150the impact or influence of users, summarizing what people are
151saying on some topic or brand, and so on. One challenge is the
152enormous amount of data you need to process. Current approaches
153often need to filter the data first and then do the actual
154analysis after the event. However, ideally you would want to be
155able to look into the stream of social media updates in real-time
156as the event unfolds, and not a few days or weeks later when
157you&#39;ve processed your data. We will showcase the real-time social
158media analysis engine developed by TWIMPACT in cooperation with
159the TU Berlin. You will be able to look at the current trends on
160Twitter in real-time, in addition to being able to have a look at
161the last year which we will bring in a pre-analyzed form, such
162that you can zoom in on the historic events of this year like the
163revolutions in Egypt, or Libya, and so on.
164
165                    </p>
166                </details>
167                
168            </div>
169            
170        </div>
171    </section>
172    
173    
174    
175    
176    <section class="mb-10">
177        <h2 class="text-xl font-bold mb-2 text-gray-800">(Deep) Neural Networks</h2>
178        
179        <p class="text-gray-600 text-sm mb-4">Studying how representations are built in (deep) neural networks
180using the techniques developed for kernel methods.
181</p>
182        
183
184        <div class="space-y-4">
185            
186            <div class="border-l-2 border-gray-200 pl-4 py-2">
187                <p class="font-medium text-gray-900">Deep Boltzmann Machines as Feed-Forward Hierarchies</p>
188                <p class="text-sm text-gray-600">G. Montavon, M. Braun, K.-R. Müller</p>
189                <p class="text-sm text-gray-500 mt-1">
190                    <p>International Conference on Artificial Intelligence and Statistics
191(AISTATS), 2012</p>
192                </p>
193                
194                <a href="https://gregoire.montavon.name/publications/montavon-aistats12.pdf"
195                   class="text-blue-600 hover:text-blue-800 text-sm"
196                   target="_blank">
197                    View paper
198                </a>
199                
200                
201                <details class="mt-2">
202                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
203                        Show abstract
204                    </summary>
205                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
206                        The deep Boltzmann machine is a powerful model that extracts the
207hierarchical structure of observed data. While inference is
208typically slow due to its undirected nature, we argue that the
209emerging feature hierarchy is still explicit enough to be
210traversed in a feed-forward fashion. The claim is corroborated by
211training a set of deep neural networks on real data and measuring
212the evolution of the representation layer after layer. The
213analysis reveals that the deep Boltzmann machine produces a
214feed-forward hierarchy of increasingly invariant representations
215that clearly surpasses the layer-wise approach.
216
217                    </p>
218                </details>
219                
220            </div>
221            
222            <div class="border-l-2 border-gray-200 pl-4 py-2">
223                <p class="font-medium text-gray-900">Importance of Cross-Layer Cooperation for Learning Deep Feature Hierarchies</p>
224                <p class="text-sm text-gray-600">G. Montavon, M. Braun, K.-R. Müller</p>
225                <p class="text-sm text-gray-500 mt-1">
226                    <p>NIPS Workshop on Deep Learning and Unsupervised Feature Learning, 2011</p>
227                </p>
228                
229                <a href="Importance of Cross-Layer Cooperation for Learning Deep Feature Hierarchies"
230                   class="text-blue-600 hover:text-blue-800 text-sm"
231                   target="_blank">
232                    View paper
233                </a>
234                
235                
236                <details class="mt-2">
237                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
238                        Show abstract
239                    </summary>
240                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
241                        A common property of hierarchical models of the brain is their
242capacity to integrate bottom-up and top-down information in order
243to distill the task-relevant information from the sensory
244noise. In this paper, we argue that such cooperation between upper
245and lower layers is not only useful at prediction time but also at
246learning time in order to build a successful feature
247hierarchy. The claim is corroborated by training a set of deep
248networks on real data and measuring the evolution of the
249representation layer after layer. The analysis reveals that
250crosslayer cooperation enables the emergence of a sequence of
251increasingly invariant representations.
252
253                    </p>
254                </details>
255                
256            </div>
257            
258            <div class="border-l-2 border-gray-200 pl-4 py-2">
259                <p class="font-medium text-gray-900">Kernel Analysis of Deep Networks</p>
260                <p class="text-sm text-gray-600">G. Montavon, M. Braun, K.-R. Müller</p>
261                <p class="text-sm text-gray-500 mt-1">
262                    <p>Journal of Machine Learning Research (JMLR), 12, pp. 2563-2581, 2011</p>
263                </p>
264                
265                <a href="https://jmlr.csail.mit.edu/papers/v12/montavon11a.html"
266                   class="text-blue-600 hover:text-blue-800 text-sm"
267                   target="_blank">
268                    View paper
269                </a>
270                
271                
272                <details class="mt-2">
273                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
274                        Show abstract
275                    </summary>
276                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
277                        When training deep networks it is common knowledge that an
278efficient and well generalizing representation of the problem is
279formed. In this paper we aim to elucidate what makes the emerging
280representation successful. We analyze the layer-wise evolution of
281the representation in a deep network by building a sequence of
282deeper and deeper kernels that subsume the mapping performed by
283more and more layers of the deep network and measuring how these
284increasingly complex kernels fit the learning problem. We observe
285that deep networks create increasingly better representations of
286the learning problem and that the structure of the deep network
287controls how fast the representation of the task is formed layer
288after layer.
289
290                    </p>
291                </details>
292                
293            </div>
294            
295            <div class="border-l-2 border-gray-200 pl-4 py-2">
296                <p class="font-medium text-gray-900">Layer-wise analysis of deep networks with Gaussian kernels</p>
297                <p class="text-sm text-gray-600">G. Montavon, M. Braun, K.-R. Müller</p>
298                <p class="text-sm text-gray-500 mt-1">
299                    <p>Advances in Neural Information Processing Systems 23 (NIPS
3002010), pp. 1678-1686, 2010</p>
301                </p>
302                
303                <a href="https://books.nips.cc/papers/files/nips23/NIPS2010_0206.pdf"
304                   class="text-blue-600 hover:text-blue-800 text-sm"
305                   target="_blank">
306                    View paper
307                </a>
308                
309                
310                <details class="mt-2">
311                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
312                        Show abstract
313                    </summary>
314                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
315                        Deep networks can potentially express a learning problem more
316efficiently than local learning machines. While deep networks
317outperform local learning machines on some problems, it is still
318unclear how their nice representation emerges from their complex
319structure. We present an analysis based on Gaussian kernels that
320measures how the representation of the learning problem evolves
321layer after layer as the deep network builds higher-level abstract
322representations of the input. We use this analysis to show
323empirically that deep networks build progressively bet- ter
324representations of the learning problem and that the best
325representations are obtained when the deep network discriminates
326only in the last layers.
327
328                    </p>
329                </details>
330                
331            </div>
332            
333        </div>
334    </section>
335    
336    
337    
338    
339    <section class="mb-10">
340        <h2 class="text-xl font-bold mb-2 text-gray-800">Machine Learning Open Source Software</h2>
341        
342
343        <div class="space-y-4">
344            
345            <div class="border-l-2 border-gray-200 pl-4 py-2">
346                <p class="font-medium text-gray-900">The Need for Open Source Software in Machine Learning</p>
347                <p class="text-sm text-gray-600">S. Sonnenburg, M. L. Braun, C. S. Ong, S. Bengio, L. Bottou,
348G. Holmes, Y. LeCun, K.-R. M&amp;uuml;ller, F. Pereira, C. E. Rasmussen,
349G. R&amp;auml;tsch, B.  Sch&amp;ouml;lkopf, A. Smola, P. Vincent, J. Weston,
350R. Williamson
351</p>
352                <p class="text-sm text-gray-500 mt-1">
353                    <p>Journal of Machine Learning Research, 8(Oct):2443-2466, 2007</p>
354                </p>
355                
356                <a href="https://jmlr.csail.mit.edu/papers/v8/sonnenburg07a.html"
357                   class="text-blue-600 hover:text-blue-800 text-sm"
358                   target="_blank">
359                    View paper
360                </a>
361                
362                
363                <details class="mt-2">
364                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
365                        Show abstract
366                    </summary>
367                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
368                        Open source tools have recently reached a level of maturity
369which makes them suitable for building large-scale real-world
370systems. At the same time, the field of machine learning has
371developed a large body of powerful learning algorithms for diverse
372applications. However, the true potential of these methods is not
373used, since existing implementations are not openly shared,
374resulting in software with low usability, and weak
375interoperability. We argue that this situation can be
376significantly improved by increasing incentives for researchers to
377publish their software under an open source model. Additionally,
378we outline the problems authors are faced with when trying to
379publish algorithmic implementati
379ons of machine learning
380methods. We believe that a resource of peer reviewed software
381accompanied by short articles would be highly valuable to both the
382machine learning and the general scientific community.
383
384                    </p>
385                </details>
386                
387            </div>
388            
389        </div>
390    </section>
391    
392    
393    
394    
395    <section class="mb-10">
396        <h2 class="text-xl font-bold mb-2 text-gray-800">Kernel Methods</h2>
397        
398        <p class="text-gray-600 text-sm mb-4">Eigenstructure of the Kernel Matrix; Kernel PLS; Kernel Methods</p>
399        
400
401        <div class="space-y-4">
402            
403            <div class="border-l-2 border-gray-200 pl-4 py-2">
404                <p class="font-medium text-gray-900">Lanczos Approximations for the Speedup of Kernel Partial
405Least Squares Regression
406</p>
407                <p class="text-sm text-gray-600">N. Kr&amp;auml;mer, M. Sugiyama, M.L. Braun</p>
408                <p class="text-sm text-gray-500 mt-1">
409                    <p>JMLR Workshop and Conference Proceedings, Volume 5: AISTATS 2009</p>
410                </p>
411                
412                <a href="https://jmlr.csail.mit.edu/proceedings/papers/v5/kramer09a/kramer09a.pdf"
413                   class="text-blue-600 hover:text-blue-800 text-sm"
414                   target="_blank">
415                    View paper
416                </a>
417                
418                
419                <details class="mt-2">
420                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
421                        Show abstract
422                    </summary>
423                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
424                        The runtime for Kernel Partial Least Squares (KPLS) to compute the
425fit is quadratic in the number of examples. However, the necessity
426of obtaining sensitivity measures as degrees of freedom for model
427selection or confidence intervals for more detailed analysis
428requires cubic runtime, and thus constitutes a computational
429bottleneck in real-world data analysis. We propose a novel
430algorithm for KPLS which not only computes (a) the fit, but also
431(b) its approximate degrees of freedom and (c) error bars in
432quadratic runtime. The algorithm exploits a close connection
433between Kernel PLS and the Lanczos algorithm for approximating the
434eigenvalues of symmetric matrices, and uses this approximation to
435compute the trace of powers of the kernel matrix in quadratic runtime.
436
437                    </p>
438                </details>
439                
440            </div>
441            
442            <div class="border-l-2 border-gray-200 pl-4 py-2">
443                <p class="font-medium text-gray-900">On Relevant Dimensions in Kernel Feature Spaces</p>
444                <p class="text-sm text-gray-600">M.L. Braun, J. Buhmann, K.-R. M&amp;uuml;ller</p>
445                <p class="text-sm text-gray-500 mt-1">
446                    <p>JMLR 9(Aug):1875--1908, 2008. (<a href="software.html#rdetools">software</a>)
447(<a href="research.html#rde">more information</a>)</p>
448                </p>
449                
450                <a href="https://www.jmlr.org/papers/volume9/braun08a/braun08a.pdf"
451                   class="text-blue-600 hover:text-blue-800 text-sm"
452                   target="_blank">
453                    View paper
454                </a>
455                
456                
457                <details class="mt-2">
458                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
459                        Show abstract
460                    </summary>
461                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
462                        We show that the relevant information of a supervised learning
463problem is contained up to negligible error in a finite number of
464leading kernel PCA components if the kernel matches the underlying
465learning problem in the sense that it can asymptotically represent
466the function to be learned and is sufficiently smooth. Thus,
467kernels do not only transform data sets such that good
468generalization can be achieved using only linear discriminant
469functions, but this transformation is also performed in a manner
470which makes economical use of feature space dimensions. In the
471best case, kernels provide efficient implicit representations of
472the data for supervised learning problems. Practically, we propose
473an algorithm which enables us to recover the number of leading
474kernel PCA components relevant for good classification. Our
475algorithm can therefore be applied (1) to analyze the interplay of
476data set and kernel in a geometric fashion, (2) to aid in model
477selection, and (3) to denoise in feature space in order to yield
478better classification results.
479
480                    </p>
481                </details>
482                
483            </div>
484            
485            <div class="border-l-2 border-gray-200 pl-4 py-2">
486                <p class="font-medium text-gray-900">Kernelizing PLS, Degress of Freedom, and Efficient Model Selection</p>
487                <p class="text-sm text-gray-600">N. Kr&amp;auml;mer, M.L. Braun</p>
488                <p class="text-sm text-gray-500 mt-1">
489                    <p>ICML 2007</p>
490                </p>
491                
492                <a href="https://ml.cs.tu-berlin.de/~nkraemer/papers/icml_kernelpls.pdf"
493                   class="text-blue-600 hover:text-blue-800 text-sm"
494                   target="_blank">
495                    View paper
496                </a>
497                
498                
499                <details class="mt-2">
500                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
501                        Show abstract
502                    </summary>
503                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
504                        Kernelizing partial least squares (PLS), an algorithm which has
505been particularly popular in chemometrics, leads to kernel PLS
506which has several interesting properties, including a sub-cubic
507runtime for learning, and an iterative construction of directions
508which are relevant for predicting the outputs. We show that the
509kernelization of PLS introduces interesting properties not found
510in ordinary PLS, giving novel insights into the workings of kernel
511PLS and the connections to kernel ridge regression and conjugate
512gradient descent methods. Furthermore, we show how to correctly
513define the degrees of freedom for kernel PLS and how to
514efficiently compute an unbiased estimate. Finally, we address the
515practical problem of model selection. We demonstrate how to use
516the degrees of freedom estimate to perform effective model
517selection, and discuss how to implement cross-validation schemes
518efficiently.
519
520                    </p>
521                </details>
522                
523            </div>
524            
525            <div class="border-l-2 border-gray-200 pl-4 py-2">
526                <p class="font-medium text-gray-900">Accurate bounds for the eigenvalues of the kernel matrix</p>
527                <p class="text-sm text-gray-600">M. L. Braun</p>
528                <p class="text-sm text-gray-500 mt-1">
529                    <p>Journal of Machine Learning Research, Vol. 7(Nov) 2303-2328, 2006</p>
530                </p>
531                
532                <a href="https://jmlr.csail.mit.edu/papers/v7/braun06a.html"
533                   class="text-blue-600 hover:text-blue-800 text-sm"
534                   target="_blank">
535                    View paper
536                </a>
537                
538                
539                <details class="mt-2">
540                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
541                        Show abstract
542                    </summary>
543                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
544                        The eigenvalues of the kernel matrix play an important role in a
545number of kernel methods, in particular, in kernel principal
546component analysis. It is well known that the eigenvalues of the
547kernel matrix converge as the number of samples tends to
548infinity. We derive probabilistic finite sample size bounds on the
549approximation error of individual eigenvalues which have the
550important property that the bounds scale with the eigenvalue under
551consideration, reflecting the actual behavior of the approximation
552errors as predicted by asymptotic results and observed in
553numerical simulations. Such scaling bounds have so far only been
554known for tail sums of eigenvalues. Asymptotically, the bounds
555presented here have a slower than stochastic rate, but the number
556of sample points necessary to make this disadvantage noticeable is
557often unrealistically large. Therefore, under practical
558conditions, and for all but the largest few eigenvalues, the
559bounds presented here form a significant improvement over existing
560non-scaling bounds.
561
562                    </p>
563                </details>
564                
565            </div>
566            
567            <div class="border-l-2 border-gray-200 pl-4 py-2">
568                <p class="font-medium text-gray-900">Denoising and Dimension Reduction in Feature Space</p>
569                <p class="text-sm text-gray-600">M.L. Braun, J. Buhmann, K.-R. M&amp;uuml;ller</p>
570                <p class="text-sm text-gray-500 mt-1">
571                    <p>Advances in Neural Information Processing Systems 19 (NIPS 2006), 
572B. Sch&ouml;lkopf, J. Platt, and T. Hoffman (eds.), MIT Press, 
573Cambridge, MA, 185-192, 2007</p>
574                </p>
575                
576                <a href="https://books.nips.cc/papers/files/nips19/NIPS2006_0407.pdf"
577                   class="text-blue-600 hover:text-blue-800 text-sm"
578                   target="_blank">
579                    View paper
580                </a>
581                
582                
583                <details class="mt-2">
584                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
585                        Show abstract
586                    </summary>
587                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
588                        We show that the relevant information about a classification
589problem in feature space is contained up to negligible error in a
590finite number of leading kernel PCA components if the kernel
591matches the underlying learning problem. Thus, ker- nels not only
592transform data sets such that good generalization can be achieved
593even by linear discriminant functions, but this transformation is
594also performed in a manner which makes economic use of feature
595space dimensions. In the best case, kernels provide efficient
596implicit representations of the data to perform
597classification. Practically, we propose an algorithm which enables
598us to recover the subspace and dimensionality relevant for good
599classification. Our algorithm can therefore be applied (1) to
600analyze the interplay of data set and kernel in a geo- metric
601fashion, (2) to help in model selection, and to (3) de-noise in
602feature space in order to yield better classification
603results.
604
605                    </p>
606                </details>
607                
608            </div>
609            
610            <div class="border-l-2 border-gray-200 pl-4 py-2">
611                <p class="font-medium text-gray-900">Model Selection in Kernel Methods based on a Spectral Analysis of
612Label Information
613</p>
614                <p class="text-sm text-gray-600">M.L. Braun, T. Lange, J. Buhmann</p>
615                <p class="text-sm text-gray-500 mt-1">
616                    <p>DAGM 2006, LNCS 4174, pp. 344-353</p>
617                </p>
618                
619                <a href="https://www.springerlink.com/content/48481751l288w5q0/"
620                   class="text-blue-600 hover:text-blue-800 text-sm"
621                   target="_blank">
622                    View paper
623                </a>
624                
625                
626                <details class="mt-2">
627                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
628                        Show abstract
629                    </summary>
630                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
631                        We propose a novel method for addressing the model selection
632problem in the context of kernel methods. In contrast to existing
633methods which rely on hold-out testing or try to compensate for
634the optimism of the generalization error, our method is based on a
635structural analysis of the label information using the
636eigenstructure of the kernel matrix. In this setting, the label
637vector can be transformed into a representation in which the
638smooth information is easily discernible from the noise. This
639permits to estimate a cut-off dimension such that the leading
640coefficients in that representation contains the learnable
641information, discarding the noise. Based on this cut-off
642dimension, the regularization parameter is estimated for kernel
643ridge regression.
644
645                    </p>
646                </details>
647                
648            </div>
649            
650            <div class="border-l-2 border-gray-200 pl-4 py-2">
651                <p class="font-medium text-gray-900">Spectral Properties of the Kernel Matrix and their Relation 
652to Kernel Methods in Machine Learning
653</p>
654                <p class="text-sm text-gray-600">M. L. Braun</p>
655                <p class="text-sm text-gray-500 mt-1">
656                    <p>Ph.D. thesis, University of Bonn, 2005. Published electronically.</p>
657                </p>
658                
659                <a href="https://hss.ulb.uni-bonn.de/diss_online/math_nat_fak/2005/braun_mikio"
660                   class="text-blue-600 hover:text-blue-800 text-sm"
661                   target="_blank">
662                    View paper
663                </a>
664                
665                
666                <details class="mt-2">
667                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
668                        Show abstract
669                    </summary>
670                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
671                        Machine learning is an area of research concerned with the
672construction of algorithms which are able to learn from
673examples. Among such algorithms, so-called kernel methods form an
674important family of algorithms which have proven to be powerful
675and versatile for a large number of problem areas. Central to
676these approaches is the kernel matrix which summarizes the
677information contained in the training examples. The goal of this
678thesis is to analyze machine learning kernel methods based on
679properties of the kernel matrix. The algorithms considered are
680kernel principal component analysis and kernel ridge
681regression. This thesis is divided into two parts: a theoretical
682part devoted to studying the spectral properties of the kernel
683matrix, and an application part which analyzes the kernel
684principal component analysis method and kernel based regression
685based on these theoretical results.
686
687In the theoretical part, convergence properties of the
688eigenvalues and eigenvectors of the kernel matrix are studied. We
689derive accurate bounds on the approximation error which have the
690important property that the error bounds scale with the magnitude
691of the eigenvalue, predicting correctly that the approximation
692error of small eigenvalues is much smaller than that of large
693eigenvalues. In this respect, the results improve significantly on
694existing results. A similar result is proven for scalar products
695with eigenvectors of the kernel matrix. It is shown that the
696scalar products with eigenvectors corresponding to small
697eigenvalues are small a priori independently of the degree of
698approximation.
699
700In the application part, we discuss the following topics. For
701kernel principal component analysis, we show that the estimated
702eigenvalues approximate the true principal values with high
703precision. Next, we discuss the general setting of kernel based
704regression and show that the relevant information of the labels is
705contained in the first few coefficients of the label vector in the
706basis of eigenvectors of the kernel matrix, such that the
707information and the noise can be divided much more easily in this
708representation. Finally, we show that kernel ridge regression
709works by suppressing all but the leading coefficients, thereby
710extracting the relevant information of the label vectors. This
711interpretation suggests an estimate of the number of relevant
712coefficients in order to perform model selection. In an
713experimental evaluation, this approach proves to perform
714competitively to state-of-the-art methods.
715
716                    </p>
717                </details>
718                
719            </div>
720            
721        </div>
722    </section>
723    
724    
725    
726    
727    <section class="mb-10">
728        <h2 class="text-xl font-bold mb-2 text-gray-800">Brain Computer Interface</h2>
729        
730        <p class="text-gray-600 text-sm mb-4">Detecting conditions of high mental and auditory workload based on
731EEG recordings under real-world conditions.
732</p>
733        
734
735        <div class="space-y-4">
736            
737            <div class="border-l-2 border-gray-200 pl-4 py-2">
738                <p class="font-medium text-gray-900">Improving BCI performance by task-related trial pruning</p>
739                <p class="text-sm text-gray-600">C. Sannelli, M. Braun, and K.-R. Müller</p>
740                <p class="text-sm text-gray-500 mt-1">
741                    <p>Neural Networks, Volume 22, Issue 9, November 2009, Pages
7421295-1304, Special Issue on Brain-Machine Interface</p>
743                </p>
744                
745                <a href="https://dx.doi.org/10.1016/j.neunet.2009.08.006"
746                   class="text-blue-600 hover:text-blue-800 text-sm"
747                   target="_blank">
748                    View paper
749                </a>
750                
751                
752                <details class="mt-2">
753                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
754                        Show abstract
755                    </summary>
756                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
757                        Noise in electroencephalography data (EEG) is an ubiquitous
758problem that limits the performance of brain computer interfaces
759(BCI). While typical EEG artifacts are usually removed by trial
760rejection or by filtering, noise induced in the data by the subject&#39;s
761failure to produce the required mental state is very harmful. Such
762&#34;noise&#34; effects are rather common, especially for naive subjects
763in their training phase and, thus, standard artifact removal methods
764would inevitably fail. In this paper, we present a novel method
765which aims to detect such defected trials taking into account the
766intended task by use of Relevant Dimensionality Estimation (RDE), a
767new machine learning method for denoising in feature space. In this
768manner, our method effectively &#34;cleans&#34; the training data and thus
769allows better BCI classification. Preliminary results conducted on a
770data set of 43 naive subjects show a significant improvement for 74%
771of the subjects.
772
773                    </p>
774                </details>
775                
776            </div>
777            
778            <div class="border-l-2 border-gray-200 pl-4 py-2">
779                <p class="font-medium text-gray-900">Estimating Noise and Dimensionality in BCI Data Sets: Towards BCI
780Illiteracy Comprehension
781</p>
782                <p class="text-sm text-gray-600">C. Sannelli, M. Braun, M. Tangermann, and K.-R. Müller</p>
783                <p class="text-sm text-gray-500 mt-1">
784                    <p>In Proceedings of the <a href="https://bci.tugraz.at/BCI08/index.html">4th International Brain-Computer Interface
785Workshop and Training Course 2008</a>. Verlag der Technischen
786Universität Graz, 2008 (won the young scientists best talk award)</p>
787                </p>
788                
789                
790            </div>
791            
792            <div class="border-l-2 border-gray-200 pl-4 py-2">
793                <p class="font-medium text-gray-900">Improving Human Performance in a Real Operating Environment
794through Real-Time Mental Workload Detection
795</p>
796                <p class="text-sm text-gray-600">J. Kohlmorgen, G. Dornhege, M.L. Braun, B. Blankertz,
797K.-R. M&amp;uuml;ller, G. Curio, K. Hagemann, A. Bruns, M. Schrauf,
798W.E. Kincses
799</p>
800                <p class="text-sm text-gray-500 mt-1">
801                    <p>in <em>Towards Brain-Computer Interfacing</em>, G. Dornhege, 
802J. del R. Milli&aacute;n, T. Hinterberger, D. McFarland, 
803K.-R. Müller (Eds), MIT Press, 2007</p>
804                </p>
805                
806                <a href="https://mitpress.mit.edu/catalog/item/default.asp?ttype=2&amp;tid=11237"
807                   class="text-blue-600 hover:text-blue-800 text-sm"
808                   target="_blank">
809                    View paper
810                </a>
811                
812                
813            </div>
814            
815        </div>
816    </section>
817    
818    
819    
820    
821    <section class="mb-10">
822        <h2 class="text-xl font-bold mb-2 text-gray-800">Stability Based Model Selection</h2>
823        
824        <p class="text-gray-600 text-sm mb-4">
824A general framework for estimating the right number of clusters
825based on the stability of the clustering solutions.
826</p>
827        
828
829        <div class="space-y-4">
830            
831            <div class="border-l-2 border-gray-200 pl-4 py-2">
832                <p class="font-medium text-gray-900">Stability-Based Validation of Clustering Solutions</p>
833                <p class="text-sm text-gray-600">T. Lange, V. Roth, M. Braun and J. Buhmann</p>
834                <p class="text-sm text-gray-500 mt-1">
835                    <p>Neural Computation 16:6, June 2004.</p>
836                </p>
837                
838                <a href="https://www.mitpressjournals.org/doi/abs/10.1162/089976604773717621"
839                   class="text-blue-600 hover:text-blue-800 text-sm"
840                   target="_blank">
841                    View paper
842                </a>
843                
844                
845                <details class="mt-2">
846                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
847                        Show abstract
848                    </summary>
849                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
850                        Data clustering describes a set of frequently employed techniques
851in exploratory data analysis to extract &#34;natural&#34; group structure
852in data. Such groupings need to be validated to separate the
853signal in the data from spurious structure. In this context,
854finding an appropriate number of clusters is a particularly
855important model selection question. We introduce a measure of
856cluster stability to assess the validity of a cluster model. This
857stability measure quantifies the reproducibility of clustering
858solutions on a second sample, and it can be interpreted as a
859classification risk with regard to class labels produced by a
860clustering algorithm. The preferred number of clusters is
861determined by minimizing this classification risk as a function of
862the number of clusters. Convincing results are achieved on
863simulated as well as gene expression data sets. Comparisons to
864other methods demonstrate the competitive performance of our
865method and its suitability as a general validation tool for
866clustering solutions in real-world problems.
867
868                    </p>
869                </details>
870                
871            </div>
872            
873            <div class="border-l-2 border-gray-200 pl-4 py-2">
874                <p class="font-medium text-gray-900">Stability-Based Model Selection</p>
875                <p class="text-sm text-gray-600">T. Lange, M. Braun, V. Roth, and J. Buhmann</p>
876                <p class="text-sm text-gray-500 mt-1">
877                    <p>NIPS 2002</p>
878                </p>
879                
880                <a href="https://books.nips.cc/papers/files/nips15/AA17.pdf"
881                   class="text-blue-600 hover:text-blue-800 text-sm"
882                   target="_blank">
883                    View paper
884                </a>
885                
886                
887            </div>
888            
889            <div class="border-l-2 border-gray-200 pl-4 py-2">
890                <p class="font-medium text-gray-900">Stability-Based Model Order Selection in Clustering with
891Applications to Gene Expression Data
892</p>
893                <p class="text-sm text-gray-600">V. Roth, M. Braun, T. Lange, and J. Buhmann</p>
894                <p class="text-sm text-gray-500 mt-1">
895                    <p>ICANN 2002, pp. 607-612, Lecture Notes in Computer Science 
8962415, Jos&eacute; R. Dorronsoro (Ed.)</p>
897                </p>
898                
899                <a href="https://link.springer.de/link/service/series/0558/papers/2415/24150607.pdf"
900                   class="text-blue-600 hover:text-blue-800 text-sm"
901                   target="_blank">
902                    View paper
903                </a>
904                
905                
906            </div>
907            
908            <div class="border-l-2 border-gray-200 pl-4 py-2">
909                <p class="font-medium text-gray-900">A Resampling Approach to Cluster Validation</p>
910                <p class="text-sm text-gray-600">V. Roth, T. Lange, M. Braun, J. Buhmann</p>
911                <p class="text-sm text-gray-500 mt-1">
912                    <p>COMPSTAT 2002</p>
913                </p>
914                
915                <a href="compstat02.pdf"
916                   class="text-blue-600 hover:text-blue-800 text-sm"
917                   target="_blank">
918                    View paper
919                </a>
920                
921                
922            </div>
923            
924        </div>
925    </section>
926    
927    
928    
929    
930    <section class="mb-10">
931        <h2 class="text-xl font-bold mb-2 text-gray-800">Noisy TSP</h2>
932        
933        <p class="text-gray-600 text-sm mb-4">Applying methods from statistical physics to robustly sample good
934solutions for combinatorial optimization problems like the
935travelling salesman problem.
936</p>
937        
938
939        <div class="space-y-4">
940            
941            <div class="border-l-2 border-gray-200 pl-4 py-2">
942                <p class="font-medium text-gray-900">The Noisy Euclidian Traveling Salesman Problem and Learning</p>
943                <p class="text-sm text-gray-600">M. Braun, J. Buhmann</p>
944                <p class="text-sm text-gray-500 mt-1">
945                    <p>in: T. G. Diettrich, S. Becker, Z. Ghahramani (Eds.), Advances in
946Information Processing Systems 14, pp. 251-258, MIT Press</p>
947                </p>
948                
949                <a href="https://books.nips.cc/papers/files/nips14/LT11.pdf"
950                   class="text-blue-600 hover:text-blue-800 text-sm"
951                   target="_blank">
952                    View paper
953                </a>
954                
955                
956                <details class="mt-2">
957                    <summary class="text-sm text-gray-500 cursor-pointer hover:text-gray-700">
958                        Show abstract
959                    </summary>
960                    <p class="text-sm text-gray-600 mt-2 pl-2 border-l border-gray-200">
961                        We consider noisy Euclidean traveling salesman problems in the
962plane, whcih are random combinatorial problems with underlying
963structure. Gibbs sampling is sused to compute average
964trajectories, which estimate the underlying structure common to
965all instances. This procedure requires identifying the exact
966relationship between permutations and tours. In a learning
967setting, the average trajectory is used as a model to construct
968solutions to new instances sampled from the same
969source. Experimental results show that the average trajectory can
970in fact estimate the underlying structure and that overfitting
971effects occur if the trajectory adapts too closely to a single
972instance.
973
974                    </p>
975                </details>
976                
977            </div>
978            
979        </div>
980    </section>
981    
982    
983    
984    
985    <section class="mb-10">
986        <h2 class="text-xl font-bold mb-2 text-gray-800">Retina Implant</h2>
987        
988        <p class="text-gray-600 text-sm mb-4">From Mar. 1997 to Sept. 1999, I worked as a lab assitant in the &lt;a
989href=&#34;https://www.nero.uni-bonn.de/projekte/ri/ri-index-en.htm&#34;&gt;Retina
990Implant project&lt;/a&gt; (which was a registered project of the
991EXPO2000) with Michael Becker. The goal was to construct a retinal
992prosthesis for people with &lt;a
993href=&#34;https://en.wikipedia.org/wiki/Macular_degeneration&#34;&gt;macula
994degeneration&lt;/a&gt;.
995</p>
996        
997
998        <div class="space-y-4">
999            
1000            <div class="border-l-2 border-gray-200 pl-4 py-2">
1001                <p class="font-medium text-gray-900">Retina Implant Adjustment with Reinforcement Learning</p>
1002                <p class="text-sm text-gray-600">M. Becker, M. Braun, R. Eckmiller</p>
1003                <p class="text-sm text-gray-500 mt-1">
1004                    <p>Proc. ICASSP98, IEEE Press, 1998, Vol. II, pp. 1181-1184</p>
1005                </p>
1006                
1007                <a href="https://citeseer.ist.psu.edu/becker98retina.html"
1008                   class="text-blue-600 hover:text-blue-800 text-sm"
1009                   target="_blank">
1010                    View paper
1011                </a>
1012                
1013                
1014            </div>
1015            
1016            <div class="border-l-2 border-gray-200 pl-4 py-2">
1017                <p class="font-medium text-gray-900">Retina Encoder Inversion for Retina Implant Simulation</p>
1018                <p class="text-sm text-gray-600">M. Becker, M. Braun, R. Eckmiller</p>
1019                <p class="text-sm text-gray-500 mt-1">
1020                    <p>Niklasson L. et al (eds), Proc. ICANN98, Springer 1998, pp. 791-796</p>
1021                </p>
1022                
1023                <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.4726"
1024                   class="text-blue-600 hover:text-blue-800 text-sm"
1025                   target="_blank">
1026                    View paper
1027                </a>
1028                
1029                
1030            </div>
1031            
1032        </div>
1033    </section>
1034    
1035    
1036</div>
1037
1038    </main>
1039
1040    <!-- Footer -->
1041    <footer class="bg-white border-t border-gray-200 mt-auto">
1042        <div class="max-w-4xl mx-auto px-4 sm:px-6 py-6">
1043            <p class="text-sm text-gray-500 text-center">
1044                &copy; Mikio L. Braun &middot;
1045                <a href="/impressum" class="hover:text-gray-700">Impressum</a>
1046            </p>
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