arXiv subjects

Bernhard Schölkopf

Publications and source records attributed to Bernhard Schölkopf.

At least 397 records · Page 22Linked to original sources

arXiv2019

Kernel Stein Tests for Multiple Model Comparison

We address the problem of non-parametric multiple model comparison: given $l$ candidate models, decide whether each candidate is as good as the best one(s) or worse than it. We propose two statistical tests, each controlling a different notion of decision errors. The first test, building on the post selection inference framework, provably controls the number of best models that are wrongly declared worse (false positive rate). The second test is based on multiple correction, and controls the proportion of the models declared worse but are in fact as good as the best (false discovery rate). We prove that under appropriate conditions the first test can yield a higher true positive rate than the second. Experimental results on toy and real (CelebA, Chicago Crime data) problems show that the two tests have high true positive rates with well-controlled error rates. By contrast, the naive approach of choosing the model with the lowest score without correction leads to more false positives.

cs.LG↗

arXiv2019

Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks

We study the problem of causal discovery through targeted interventions. Starting from few observational measurements, we follow a Bayesian active learning approach to perform those experiments which, in expectation with respect to the current model, are maximally informative about the underlying causal structure. Unlike previous work, we consider the setting of continuous random variables with non-linear functional relationships, modelled with Gaussian process priors. To address the arising problem of choosing from an uncountable set of possible interventions, we propose to use Bayesian optimisation to efficiently maximise a Monte Carlo estimate of the expected information gain.

stat.ML↗

arXiv2019

Convolutional neural networks: a magic bullet for gravitational-wave detection?

In the last few years, machine learning techniques, in particular convolutional neural networks, have been investigated as a method to replace or complement traditional matched filtering techniques that are used to detect the gravitational-wave signature of merging black holes. However, to date, these methods have not yet been successfully applied to the analysis of long stretches of data recorded by the Advanced LIGO and Virgo gravitational-wave observatories. In this work, we critically examine the use of convolutional neural networks as a tool to search for merging black holes. We identify the strengths and limitations of this approach, highlight some common pitfalls in translating between machine learning and gravitational-wave astronomy, and discuss the interdisciplinary challenges. In particular, we explain in detail why convolutional neural networks alone cannot be used to claim a statistically significant gravitational-wave detection. However, we demonstrate how they can still be used to rapidly flag the times of potential signals in the data for a more detailed follow-up. Our convolutional neural network architecture as well as the proposed performance metrics are better suited for this task than a standard binary classifications scheme. A detailed evaluation of our approach on Advanced LIGO data demonstrates the potential of such systems as trigger generators. Finally, we sound a note of caution by constructing adversarial examples, which showcase interesting "failure modes" of our model, where inputs with no visible resemblance to real gravitational-wave signals are identified as such by the network with high confidence.

astro-ph.IM↗

arXiv2019

Reliable Real Time Ball Tracking for Robot Table Tennis

Robot table tennis systems require a vision system that can track the ball position with low latency and high sampling rate. Altering the ball to simplify the tracking using for instance infrared coating changes the physics of the ball trajectory. As a result, table tennis systems use custom tracking systems to track the ball based on heuristic algorithms respecting the real time constrains applied to RGB images captured with a set of cameras. However, these heuristic algorithms often report erroneous ball positions, and the table tennis policies typically need to incorporate additional heuristics to detect and possibly correct outliers. In this paper, we propose a vision system for object detection and tracking that focus on reliability while providing real time performance. Our assumption is that by using multiple cameras, we can find and discard the errors obtained in the object detection phase by checking for consistency with the positions reported by other cameras. We provide an open source implementation of the proposed tracking system to simplify future research in robot table tennis or related tracking applications with strong real time requirements. We evaluate the proposed system thoroughly in simulation and in the real system, outperforming previous work. Furthermore, we show that the accuracy and robustness of the proposed system increases as more cameras are added. Finally, we evaluate the table tennis playing performance of an existing method in the real robot using the proposed vision system. We measure a slight increase in performance compared to a previous vision system even after removing all the heuristics previously present to filter out erroneous ball observations.

cs.RO↗

arXiv2019

The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA

We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available.

stat.ML↗

arXiv2019

Neural Signatures of Motor Skill in the Resting Brain

Stroke-induced disturbances of large-scale cortical networks are known to be associated with the extent of motor deficits. We argue that identifying brain networks representative of motor behavior in the resting brain would provide significant insights for current neurorehabilitation approaches. Particularly, we aim to investigate the global configuration of brain rhythms and their relation to motor skill, instead of learning performance as broadly studied. We empirically approach this problem by conducting a three-dimensional physical space visuomotor learning experiment during electroencephalographic (EEG) data recordings with thirty-seven healthy participants. We demonstrate that across-subjects variations in average movement smoothness as the quantified measure of subjects' motor skills can be predicted from the global configuration of resting-state EEG alpha-rhythms (8-14 Hz) recorded prior to the experiment. Importantly, this neural signature of motor skill was found to be orthogonal to (independent of) task -- as well as to learning-related changes in alpha-rhythms, which we interpret as an organizing principle of the brain. We argue that disturbances of such configurations in the brain may contribute to motor deficits in stroke, and that reconfiguring stroke patients' brain rhythms by neurofeedback may enhance post-stroke neurorehabilitation.

q-bio.NC↗

arXiv2019

Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations

The key idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train more than 12000 models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on seven different data sets. We observe that while the different methods successfully enforce properties ``encouraged'' by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, increased disentanglement does not seem to lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.

cs.LG↗

arXiv2019

First-order Adversarial Vulnerability of Neural Networks and Input Dimension

Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisingly, vulnerability does not depend on network topology: for many standard network architectures, we prove that at initialization, the $\ell_1$-norm of these gradients grows as the square root of the input dimension, leaving the networks increasingly vulnerable with growing image size. We empirically show that this dimension dependence persists after either usual or robust training, but gets attenuated with higher regularization.

stat.ML↗

arXiv2019

Disentangled State Space Representations

Sequential data often originates from diverse domains across which statistical regularities and domain specifics exist. To specifically learn cross-domain sequence representations, we introduce disentangled state space models (DSSM) -- a class of SSM in which domain-invariant state dynamics is explicitly disentangled from domain-specific information governing that dynamics. We analyze how such separation can improve knowledge transfer to new domains, and enable robust prediction, sequence manipulation and domain characterization. We furthermore propose an unsupervised VAE-based training procedure to implement DSSM in form of Bayesian filters. In our experiments, we applied VAE-DSSM framework to achieve competitive performance in online ODE system identification and regression across experimental settings, and controlled generation and prediction of bouncing ball video sequences across varying gravitational influences.

stat.ML↗

arXiv2019

On Matching Pursuit and Coordinate Descent

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear $\mathcal{O}(1/t)$ rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate $\mathcal{O}(1/t^2)$ for matching pursuit and steepest coordinate descent on convex objectives.

stat.ML↗

arXiv2019

Quantum Mean Embedding of Probability Distributions

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance measure between probability distributions, called maximum mean discrepancy (MMD). In this work, we propose to represent probability distributions in a pure quantum state of a system that is described by an infinite dimensional Hilbert space. This enables us to work with an explicit representation of the mean embedding, whereas classically one can only work implicitly with an infinite dimensional Hilbert space through the use of the kernel trick. We show how this explicit representation can speed up methods that rely on inner products of mean embeddings and discuss the theoretical and experimental challenges that need to be solved in order to achieve these speedups.

quant-ph↗

arXiv2019

AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.

cs.LG↗

arXiv2019

Kernel Mean Matching for Content Addressability of GANs

We propose a novel procedure which adds "content-addressability" to any given unconditional implicit model e.g., a generative adversarial network (GAN). The procedure allows users to control the generative process by specifying a set (arbitrary size) of desired examples based on which similar samples are generated from the model. The proposed approach, based on kernel mean matching, is applicable to any generative models which transform latent vectors to samples, and does not require retraining of the model. Experiments on various high-dimensional image generation problems (CelebA-HQ, LSUN bedroom, bridge, tower) show that our approach is able to generate images which are consistent with the input set, while retaining the image quality of the original model. To our knowledge, this is the first work that attempts to construct, at test time, a content-addressable generative model from a trained marginal model.

cs.LG↗

arXiv2019

Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness

The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards this goal have been proposed in recent times, a commonly accepted definition and validation procedure is missing. We provide a causal perspective on representation learning which covers disentanglement and domain shift robustness as special cases. Our causal framework allows us to introduce a new metric for the quantitative evaluation of deep latent variable models. We show how this metric can be estimated from labeled observational data and further provide an efficient estimation algorithm that scales linearly in the dataset size.

stat.ML↗

arXiv2019

Consequential Ranking Algorithms and Long-term Welfare

Ranking models are typically designed to provide rankings that optimize some measure of immediate utility to the users. As a result, they have been unable to anticipate an increasing number of undesirable long-term consequences of their proposed rankings, from fueling the spread of misinformation and increasing polarization to degrading social discourse. Can we design ranking models that understand the consequences of their proposed rankings and, more importantly, are able to avoid the undesirable ones? In this paper, we first introduce a joint representation of rankings and user dynamics using Markov decision processes. Then, we show that this representation greatly simplifies the construction of consequential ranking models that trade off the immediate utility and the long-term welfare. In particular, we can obtain optimal consequential rankings just by applying weighted sampling on the rankings provided by models that maximize measures of immediate utility. However, in practice, such a strategy may be inefficient and impractical, specially in high dimensional scenarios. To overcome this, we introduce an efficient gradient-based algorithm to learn parameterized consequential ranking models that effectively approximate optimal ones. We showcase our methodology using synthetic and real data gathered from Reddit and show that ranking models derived using our methodology provide ranks that may mitigate the spread of misinformation and improve the civility of online discussions.

cs.LG↗

arXiv2019

Perceptual Video Super Resolution with Enhanced Temporal Consistency

With the advent of perceptual loss functions, new possibilities in super-resolution have emerged, and we currently have models that successfully generate near-photorealistic high-resolution images from their low-resolution observations. Up to now, however, such approaches have been exclusively limited to single image super-resolution. The application of perceptual loss functions on video processing still entails several challenges, mostly related to the lack of temporal consistency of the generated images, i.e., flickering artifacts. In this work, we present a novel adversarial recurrent network for video upscaling that is able to produce realistic textures in a temporally consistent way. The proposed architecture naturally leverages information from previous frames due to its recurrent architecture, i.e. the input to the generator is composed of the low-resolution image and, additionally, the warped output of the network at the previous step. Together with a video discriminator, we also propose additional loss functions to further reinforce temporal consistency in the generated sequences. The experimental validation of our algorithm shows the effectiveness of our approach which obtains images with high perceptual quality and improved temporal consistency.

cs.CV↗

arXiv2019

Beta Power May Mediate the Effect of Gamma-TACS on Motor Performance

Transcranial alternating current stimulation (tACS) is becoming an important method in the field of motor rehabilitation because of its ability to non-invasively influence ongoing brain oscillations at arbitrary frequencies. However, substantial variations in its effect across individuals are reported, making tACS a currently unreliable treatment tool. One reason for this variability is the lack of knowledge about the exact way tACS entrains and interacts with ongoing brain oscillations. The present crossover stimulation study on 20 healthy subjects contributes to the understanding of cross-frequency effects of gamma (70 Hz) tACS over the contralateral motor cortex by providing empirical evidence which is consistent with a role of low- (12~-20 Hz) and high- (20-~30 Hz) beta power as a mediator of gamma-tACS on motor performance.

q-bio.NC↗

arXiv2019

Competitive Training of Mixtures of Independent Deep Generative Models

A common assumption in causal modeling posits that the data is generated by a set of independent mechanisms, and algorithms should aim to recover this structure. Standard unsupervised learning, however, is often concerned with training a single model to capture the overall distribution or aspects thereof. Inspired by clustering approaches, we consider mixtures of implicit generative models that ``disentangle'' the independent generative mechanisms underlying the data. Relying on an additional set of discriminators, we propose a competitive training procedure in which the models only need to capture the portion of the data distribution from which they can produce realistic samples. As a by-product, each model is simpler and faster to train. We empirically show that our approach splits the training distribution in a sensible way and increases the quality of the generated samples.

cs.LG↗