Klaus-Robert Müller

Bio: Klaus-Robert Müller is an academic researcher from Technical University of Berlin. The author has contributed to research in topics: Artificial neural network & Support vector machine. The author has an hindex of 129, co-authored 764 publications receiving 79391 citations. Previous affiliations of Klaus-Robert Müller include Korea University & University of Tokyo.

Noninvasive Estimates of Local Field Potentials for Brain-Computer Interfaces

Abstract: Recent experiments have shown the possibility to use the brain electrical activity to directly control the movement of robots or prosthetic devices in real time. Such neuroprostheses can be invasive or non-invasive, depending on how the brain signals are recorded. In principle, invasive approaches will provide a more natural and flexible control of neuroprostheses, but their use in humans is debatable given the inherent medical risks. Non-invasive approaches mainly use scalp electroencephalogram (EEG) signals and their main disadvantage is that these signals represent the noisy spatiotemporal overlapping of activity arising from very diverse brain regions; i.e., a single scalp electrode picks up and mixes the temporal activity of myriads of neurons at very different brain areas. In order to combine the benefits of both approaches, we propose to rely on the non-invasive estimation of local field potentials (eLFP) in the whole human brain from the scalp measured EEG data using a recently developed inverse solution (ELECTRA) to the EEG inverse problem. The goal of a linear inverse procedure is to deconvolve or unmix the scalp signals attributing to each brain area its own temporal activity. To illustrate the advantage of this approach we compare, using identical set of spectral features, classification of rapid voluntary finger self-tapping with left and right hands based on scalp EEG and eLFP on three subjects using different number of electrodes. It is shown that the eLFP-based Gaussian classifier outperforms the EEG-based Gaussian classifier for the three subjects.

Reconstructing Kernel-based Machine Learning Force Fields with Super-linear Convergence

Abstract: Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances due to physical symmetries can be incorporated into the kernel function to compensate for much larger data sets. So far, the scalability of kernel machines has however been hindered by its quadratic memory and cubical runtime complexity in the number of training points. While it is known that iterative Krylov subspace solvers can overcome these burdens, their convergence crucially relies on effective preconditioners, which are elusive in practice. Effective preconditioners need to partially presolve the learning problem in a computationally cheap and numerically robust manner. Here, we consider the broad class of Nyström-type methods to construct preconditioners based on successively more sophisticated low-rank approximations of the original kernel matrix, each of which provides a different set of computational trade-offs. All considered methods aim to identify a representative subset of inducing (kernel) columns to approximate the dominant kernel spectrum.

Pitfalls in EEG-based brain effective connectivity analysis

Abstract: We consider the problem of estimating brain effective connectivity from electroencephalographic (EEG) measurements, which is challenging due to instantaneous correlations in the sensor data caused by volume conduction in the head. We present selected results of a larger realistic simulation study in which we tested the ability of various measures of effective connectivity to recover the information flow between the underlying sources, as well as the ability of linear and nonlinear inverse source reconstruction approaches to improve the estimation. It turns out that factors related to volume conduction dramatically limit the neurophysiological interpretability of sensor-space connectivity maps and may even (depending on the connectivity measure used) lead to conflicting results. The success of connectivity estimation on inverse source estimates crucially depends on the correctness of the source demixing. This in turn depends on the capability of the method to model (multiple) interacting sources, which is in general not achievable by linear inverses.

Analysis of Drifting Dynamics with Competing Predictors

Abstract: A method for the analysis of nonstationary time series with multiple modes of behaviour is presented. In particular, it is not only possible to detect a switching of dynamics but also a less abrupt, time consuming drift from one mode to another. This is achieved by an unsupervised algorithm for segmenting the data according to the modes and a subsequent search through the space of possible drifts. Applications to speech and physiological data demonstrate that analysis and modeling of real world time series can be improved when the drift paradigm is taken into account.

Deep Residual Learning for Image Recognition

Abstract: Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

Deep Residual Learning for Image Recognition

Abstract: Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers---8x deeper than VGG nets but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

Deep Learning

Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Abstract: Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization, and in some cases eliminates the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.82% top-5 test error, exceeding the accuracy of human raters.