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Large epidemiological studies such as the UK Biobank (UKBB) or German National Cohort (NAKO) provide unprecedented health-related data of the general population aiming to better understand determinants of health and disease. As part of these studies, Magnetic Resonance Imaging (MRI) is performed in a subset of participants allowing for phenotypical and functional characterization of different organ systems. Due to the large amount of imaging data, automated image analysis is required, which can be performed using deep learning methods, e. g. for automated organ segmentation. In this paper we describe a computational pipeline for automated segmentation of abdominal organs on MRI data from 20,000 participants of UKBB and NAKO and provide results of the quality control process. We found that approx. 90% of data sets showed no relevant segmentation errors while relevant errors occurred in a varying proportion of data sets depending on the organ of interest. Image-derived features based on automated organ segmentations showed relevant deviations of varying degree in the presence of segmentation errors. These results show that large-scale, deep learning-based abdominal organ segmentation on MRI data is feasible with overall high accuracy, but visual quality control remains an important step ensuring the validity of down-stream analyses in large epidemiological imaging studies.

When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly improving state-of-the-art models. While new improved models develop at a fast pace, downstream tasks vary more slowly or stay constant. Assume that we have a large unlabelled data set for which we want to maintain accurate predictions. Whenever a new and presumably better ML models becomes available, we encounter two problems: (i) given a limited budget, which data points should be re-evaluated using the new model?; and (ii) if the new predictions differ from the current ones, should we update? Problem (i) is about compute cost, which matters for very large data sets and models. Problem (ii) is about maintaining consistency of the predictions, which can be highly relevant for downstream applications; our demand is to avoid negative flips, i.e., changing correct to incorrect predictions. In this paper, we formalize the Prediction Update Problem and present an efficient probabilistic approach as answer to the above questions. In extensive experiments on standard classification benchmark data sets, we show that our method outperforms alternative strategies along key metrics for backward-compatible prediction updates.

Modern neural network architectures can leverage large amounts of data to generalize well within the training distribution. However, they are less capable of systematic generalization to data drawn from unseen but related distributions, a feat that is hypothesized to require compositional reasoning and reuse of knowledge. In this work, we present Neural Interpreters, an architecture that factorizes inference in a self-attention network as a system of modules, which we call \emph{functions}. Inputs to the model are routed through a sequence of functions in a way that is end-to-end learned. The proposed architecture can flexibly compose computation along width and depth, and lends itself well to capacity extension after training. To demonstrate the versatility of Neural Interpreters, we evaluate it in two distinct settings: image classification and visual abstract reasoning on Raven Progressive Matrices. In the former, we show that Neural Interpreters perform on par with the vision transformer using fewer parameters, while being transferrable to a new task in a sample efficient manner. In the latter, we find that Neural Interpreters are competitive with respect to the state-of-the-art in terms of systematic generalization, Comment: NeurIPS 2021

Large-scale testing is considered key to assessing the state of the current COVID-19 pandemic, yet interpreting such data remains elusive. We modeled competing hypotheses regarding the underlying testing mechanisms, thereby providing different prevalence estimates based on case numbers, and used them to predict SARS-CoV-2-attributed death rate trajectories. Assuming that individuals were tested based solely on a predefined risk of being infectious implied the absolute case numbers reflected prevalence, but turned out to be a poor predictor. In contrast, models accounting for testing capacity, limiting the pool of tested individuals, performed better. This puts forward the percentage of positive tests as a robust indicator of epidemic dynamics in absence of country-specific information. We next demonstrated this strongly affects data interpretation. Notably absolute case numbers trajectories consistently overestimated growth rates at the beginning of two COVID-19 epidemic waves. Overall, this supports non-trivial testing mechanisms can be inferred from data and should be scrutinized.

Structural causal models (SCMs), also known as (non-parametric) structural equation models (SEMs), are widely used for causal modeling purposes. In particular, acyclic SCMs, also known as recursive SEMs, form a well-studied subclass of SCMs that generalize causal Bayesian networks to allow for latent confounders. In this paper, we investigate SCMs in a more general setting, allowing for the presence of both latent confounders and cycles. We show that in the presence of cycles, many of the convenient properties of acyclic SCMs do not hold in general: they do not always have a solution; they do not always induce unique observational, interventional and counterfactual distributions; a marginalization does not always exist, and if it exists the marginal model does not always respect the latent projection; they do not always satisfy a Markov property; and their graphs are not always consistent with their causal semantics. We prove that for SCMs in general each of these properties does hold under certain solvability conditions. Our work generalizes results for SCMs with cycles that were only known for certain special cases so far. We introduce the class of simple SCMs that extends the class of acyclic SCMs to the cyclic setting, while preserving many of the convenient properties of acyclic SCMs. With this paper we aim to provide the foundations for a general theory of statistical causal modeling with SCMs.

Dexterous object manipulation remains an open problem in robotics, despite the rapid progress in machine learning during the past decade. We argue that a hindrance is the high cost of experimentation on real systems, in terms of both time and money. We address this problem by proposing an open-source robotic platform which can safely operate without human supervision. The hardware is inexpensive (about \SI{5000}[\$]{}) yet highly dynamic, robust, and capable of complex interaction with external objects. The software operates at 1-kilohertz and performs safety checks to prevent the hardware from breaking. The easy-to-use front-end (in C++ and Python) is suitable for real-time control as well as deep reinforcement learning. In addition, the software framework is largely robot-agnostic and can hence be used independently of the hardware proposed herein. Finally, we illustrate the potential of the proposed platform through a number of experiments, including real-time optimal control, deep reinforcement learning from scratch, throwing, and writing.

Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the architecture of such model reflect a causal graph of the true data generating process, such that one can intervene on each node independently of the others. However, the nodes of this graph are usually unobserved, leading to overparameterization and lack of identifiability of the causal structure. We develop a theoretical framework to address this challenging situation by defining a weaker form of identifiability, based on the principle of independence of mechanisms. We demonstrate on toy examples that classical stochastic gradient descent can hinder the model's extrapolation capabilities, suggesting independence of mechanisms should be enforced explicitly during training. Experiments on deep generative models trained on real world data support these insights and illustrate how the extrapolation capabilities of such models can be leveraged., 21 pages

Intelligent agents should be able to learn useful representations by observing changes in their environment. We model such observations as pairs of non-i.i.d. images sharing at least one of the underlying factors of variation. First, we theoretically show that only knowing how many factors have changed, but not which ones, is sufficient to learn disentangled representations. Second, we provide practical algorithms that learn disentangled representations from pairs of images without requiring annotation of groups, individual factors, or the number of factors that have changed. Third, we perform a large-scale empirical study and show that such pairs of observations are sufficient to reliably learn disentangled representations on several benchmark data sets. Finally, we evaluate our learned representations and find that they are simultaneously useful on a diverse suite of tasks, including generalization under covariate shifts, fairness, and abstract reasoning. Overall, our results demonstrate that weak supervision enables learning of useful disentangled representations in realistic scenarios., We updated the description of the generation of the dataset compared to the ICML version

Reinforcement learning (RL) algorithms usually require a substantial amount of interaction data and perform well only for specific tasks in a fixed environment. In some scenarios such as healthcare, however, usually only few records are available for each patient, and patients may show different responses to the same treatment, impeding the application of current RL algorithms to learn optimal policies. To address the issues of mechanism heterogeneity and related data scarcity, we propose a data-efficient RL algorithm that exploits structural causal models (SCMs) to model the state dynamics, which are estimated by leveraging both commonalities and differences across subjects. The learned SCM enables us to counterfactually reason what would have happened had another treatment been taken. It helps avoid real (possibly risky) exploration and mitigates the issue that limited experiences lead to biased policies. We propose counterfactual RL algorithms to learn both population-level and individual-level policies. We show that counterfactual outcomes are identifiable under mild conditions and that Q- learning on the counterfactual-based augmented data set converges to the optimal value function. Experimental results on synthetic and real-world data demonstrate the efficacy of the proposed approach., Comment: Neural Information Processing Systems Workshop on Offline Reinforcement Learning

Recent work has discussed the limitations of counterfactual explanations to recommend actions for algorithmic recourse, and argued for the need of taking causal relationships between features into consideration. Unfortunately, in practice, the true underlying structural causal model is generally unknown. In this work, we first show that it is impossible to guarantee recourse without access to the true structural equations. To address this limitation, we propose two probabilistic approaches to select optimal actions that achieve recourse with high probability given limited causal knowledge (e.g., only the causal graph). The first captures uncertainty over structural equations under additive Gaussian noise, and uses Bayesian model averaging to estimate the counterfactual distribution. The second removes any assumptions on the structural equations by instead computing the average effect of recourse actions on individuals similar to the person who seeks recourse, leading to a novel subpopulation-based interventional notion of recourse. We then derive a gradient-based procedure for selecting optimal recourse actions, and empirically show that the proposed approaches lead to more reliable recommendations under imperfect causal knowledge than non-probabilistic baselines., Comment: Camera ready version (NeurIPS 2020 spotlight)

Comunicació presentada al 36th Conference on Uncertainty in Artificial Intelligence (UAI), celebrat del 3 al 6 d'agost de 2020 de manera virtual. Ranking models are typically designed to 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 anticipate the consequences of their proposed rankings and 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 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 illustrate our methodology using synthetic and real data gathered from Reddit and show that our consequential rankings may mitigate the spread of misinformation and improve the civility of online discussions. V. Gomez has received funding from “la Caixa” Foundation (ID 100010434), under the agreement LCF/PR/PR16/51110009 and by the Volkswagen Foundation, Courage project (95.566).

The 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 over 14000 models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on eight 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, different evaluation metrics do not always agree on what should be considered “disentangled” and exhibit systematic differences in the estimation. Finally, increased disentanglement does not seem to necessarily 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., Journal of Machine Learning Research, 21, ISSN:1532-4435, ISSN:1533-7928

During the ongoing COVID-19 pandemic, there have been burgeoning efforts to develop and deploy smartphone apps to expedite contact tracing and risk notification. Most of these apps track pairwise encounters between individuals via Bluetooth and then use these tracked encounters to identify and notify those who might have been in proximity of a contagious individual. Unfortunately, these apps have not yet proven sufficiently effective, partly owing to low adoption rates, but also due to the difficult tradeoff between utility and privacy and the fact that, in COVID-19, most individuals do not infect anyone but a few superspreaders infect many in superspreading events. In this paper, we proposePanCast, a privacy-preserving and inclusive system for epidemic risk assessment and notification that scales gracefully with adoption rates, utilizes location and environmental information to increase utility without tracking its users, and can be used to identify superspreading events. To this end, rather than capturing pairwise encounters between smartphones, our system utilizes Bluetooth encounters between beacons placed in strategic locations where superspreading events are most likely to occur and inexpensive, zero-maintenance, small devices that users can attach to their keyring. PanCast allows healthy individuals to use the system in a purely passive "radio" mode, and can assist and benefit from other digital and manual contact tracing systems. Finally, PanCast can be gracefully dismantled at the end of the pandemic, minimizing abuse from any malevolent government or entity.

Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While data splitting results in a tractable null distribution, it suffers from a reduction in test power due to smaller test sample size. Inspired by the selective inference framework, we propose an approach that enables learning the hyperparameters and testing on the full sample without data splitting. Our approach can correctly calibrate the test in the presence of such dependency, and yield a test threshold in closed form. At the same significance level, our approach's test power is empirically larger than that of the data-splitting approach, regardless of its split proportion., Comment: 24 (11+13) pages, 10 figures. Camera-Ready version. Accepted to the Thirty-fourth Conference on Neural Information Processing Systems (NeurIPS 2020)

Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an \emph{unobserved} sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing the representations of more than \num{12600} trained state-of-the-art disentangled models, we observe that several disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.

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.

Deep generative models can emulate the perceptual properties of complex image datasets, providing a latent representation of the data. However, manipulating such representation to perform meaningful and controllable transformations in the data space remains challenging without some form of supervision. While previous work has focused on exploiting statistical independence to disentangle latent factors, we argue that such requirement is too restrictive and propose instead a non-statistical framework that relies on counterfactual manipulations to uncover a modular structure of the network composed of disentangled groups of internal variables. Experiments with a variety of generative models trained on complex image datasets show the obtained modules can be used to design targeted interventions. This opens the way to applications such as computationally efficient style transfer and the automated assessment of robustness to contextual changes in pattern recognition systems., 26 pages, 17 figures

Long-TE gradient recalled-echo (GRE) scans are prone to phase artifacts due to B0 inhomogeneity. We propose a learning-based approach that does not rely on navigator readouts and allows to infer phase error offsets directly from corrupted data. Our method does not need to be pre-trained on a database of medical images that match a contrast/acquisition protocol of the input image. A sufficient input is a raw multi-coil spectrum of the image that needs to be corrected. We train a convolutional neural network to predict phase offsets for each k-space line of a 2D image. We synthesize training examples online by reconvolving the corrupted spectrum with point spread functions (PSFs) of the coil sensitivity profiles and superimposing artificial phase errors, which we attempt to predict. We evaluate our approach on “in vivo” data acquired with GRE sequence, and demonstrate an improvement in image quality after phase error correction.

Deep generative models such as Generative Ad- versarial Networks (GANs) and Variational Auto- Encoders (VAEs) are important tools to capture and investigate the properties of complex empiri- cal data. However, the complexity of their inner elements makes their functioning challenging to interpret and modify. In this respect, these archi- tectures behave as black box models. In order to better understand the function of such network, we analyze the modularity of these system by quantifying the disentanglement of their intrinsic parameters. This concept relates to a notion of invariance to transformations of internal variables of the generative model, recently introduced in the field of causality. Our experiments on generation of human faces with VAEs supports that modu- larity between weights distributed over layers of generator architecture is achieved to some degree, and can be used to understand better the function- ing of these architectures. Finally, we show that modularity can be enhanced during optimization.

Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the relationship between Ordinary Differential Equations and Structural Causal Models. We show how, under certain conditions, the asymptotic behaviour of an Ordinary Differential Equation under non-constant interventions can be modelled using Dynamic Structural Causal Models. In contrast to earlier work, we study not only the effect of interventions on equilibrium states; rather, we model asymptotic behaviour that is dynamic under interventions that vary in time, and include as a special case the study of static equilibria.

Purpose Phase artifacts due to B0 inhomogeneity can severely degrade the quality of MR images. The artifacts are particularly prominent in long-TE scans and usually appear as ghosting and blur. We propose a retrospective phase correction method based on autofocusing. The proposed method uses raw data acquired with standard imaging sequences, and does not rely on navigators or external measures of field inhomogeneity. Methods We formulate and solve the optimization problem, where we seek the latent phase offsets that are associated with an optimal value of the image quality measure that is evaluated in the spatial domain. As a quality measure we use entropy computed on spatial image gradients. We propose two types of objective function, both compatible with parallel imaging and accelerated image acquisition. Results We evaluate the method on both synthetic and real data. In real data case we evaluate the performance on a range of sequences and images acquired with different acceleration factors. The experimental results demonstrate that our method is capable of minimizing ghosting artifacts and that the quality of the output images is similar to navigator-based reconstructions. Conclusion The presented technique can be alternative to or complement navigator-based methods, and is able to improve images with severe phase artifacts from all standard imaging sequences.

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs., equal contribution between Rubenstein and Weichwald; accepted manuscript

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variables have been marginalised out; (b) micro-level models versus macro-level models in which the macro-variables are aggregate features of the micro-variables; (c) dynamical time series models versus models of their stationary behaviour. Our analysis stresses the importance of well specified interventions in the causal modelling process and sheds light on the interpretation of cyclic SEMs.

The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize these approaches. In our setting, the cause-mechanism relationship is assessed by comparing it against a null hypothesis through the application of random generic group transformations. We show that the group theoretic view provides a very general tool to study the structure of data generating mechanisms with direct applications to machine learning., Comment: 16 pages, 6 figures

We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show that if the observational distribution follows a structural equation model with an additive noise structure, the directed acyclic graph becomes identifiable from the distribution under mild conditions. This constitutes an interesting alternative to traditional methods that assume faithfulness and identify only the Markov equivalence class of the graph, thus leaving some edges undirected. We provide practical algorithms for finitely many samples, RESIT (Regression with Subsequent Independence Test) and two methods based on an independence score. We prove that RESIT is correct in the population setting and provide an empirical evaluation.

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable $X$ lead to consistent estimators of the mean embedding of $f(X)$. For Mat\'ern kernels and sufficiently smooth functions we also provide rates of convergence. Our results extend to functions of multiple random variables. If the variables are dependent, we require an estimator of the mean embedding of their joint distribution as a starting point; if they are independent, it is sufficient to have separate estimators of the mean embeddings of their marginal distributions. In either case, our results cover both mean embeddings based on i.i.d. samples as well as "reduced set" expansions in terms of dependent expansion points. The latter serves as a justification for using such expansions to limit memory resources when applying the approach as a basis for probabilistic programming., Comment: 17 pages including appendix

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i \times Y_i$, and $l_i$ is a binary label indicating whether "$X_i \to Y_i$" or "$X_i \leftarrow Y_i$". Given these data, we build a causal inference rule in two steps. First, we featurize each $S_i$ using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.

We describe a method for removing the effect of confounders in order to reconstruct a latent quantity of interest. The method, referred to as half-sibling regression, is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification and illustrate the potential of the method in a challenging astronomy application., Comment: Extended version of a paper appearing in the Proceedings of the 32nd International Conference on Machine Learning, Lille, France, 2015

We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models., Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013)

We propose one-class support measure machines (OCSMMs) for group anomaly detection which aims at recognizing anomalous aggregate behaviors of data points. The OCSMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish an interesting connection to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications., Comment: Conference on Uncertainty in Artificial Intelligence (UAI2013)

Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures from these observed cascades? What kind of cascades and how many cascades do we need? Are there some network structures which are more difficult than others to recover? Can we design efficient inference algorithms with provable guarantees? Despite the increasing availability of cascade data and methods for inferring networks from these data, a thorough theoretical understanding of the above questions remains largely unexplored in the literature. In this paper, we investigate the network structure inference problem for a general family of continuous-time diffusion models using an $l_1$-regularized likelihood maximization framework. We show that, as long as the cascade sampling process satisfies a natural incoherence condition, our framework can recover the correct network structure with high probability if we observe $O(d^3 \log N)$ cascades, where $d$ is the maximum number of parents of a node and $N$ is the total number of nodes. Moreover, we develop a simple and efficient soft-thresholding inference algorithm, which we use to illustrate the consequences of our theoretical results, and show that our framework outperforms other alternatives in practice., To appear in the 31st International Conference on Machine Learning (ICML), 2014

Many applications require the analysis of complex interactions between time series. These interactions can be non-linear and involve vector valued as well as complex data structures such as graphs or strings. Here we provide a general framework for the statistical analysis of these interactions when random variables are sampled from stationary time-series of arbitrary objects. To achieve this goal we analyze the properties of the kernel cross-spectral density operator induced by positive definite kernels on arbitrary input domains. This framework enables us to develop an independence test between time series as well as a similarity measure to compare different types of coupling. The performance of our test is compared to the HSIC test using i.i.d. assumptions, showing improvement in terms of detection errors as well as the suitability of this approach for testing dependency in complex dynamical systems. Finally, we use this approach to characterize complex interactions in electrophysiological neural time series.

A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference step of modern kernel methods that rely on embedding probability distributions in RKHSs. Given a finite sample, an empirical average has been used commonly as a standard estimator of the true kernel mean. Despite a widespread use of this estimator, we show that it can be improved thanks to the well-known Stein phenomenon. We propose a new family of estimators called kernel mean shrinkage estimators (KMSEs), which benefit from both theoretical justifications and good empirical performance. The results demonstrate that the proposed estimators outperform the standard one, especially in a "large d, small n" paradigm., Comment: 41 pages

Purpose: Subject motion can severely degrade MR images. A retrospective motion correction algorithm, Gradient-based motion correction, which significantly reduces ghosting and blurring artifacts due to subject motion was proposed. The technique uses the raw data of standard imaging sequences; no sequence modifications or additional equipment such as tracking devices are required. Rigid motion is assumed. Methods: The approach iteratively searches for the motion trajectory yielding the sharpest image as measured by the entropy of spatial gradients. The vast space of motion parameters is efficiently explored by gradient-based optimization with a convergence guarantee. Results: The method has been evaluated on both synthetic and real data in two and three dimentions using standard imaging techniques. MR images are consistently improved over different kinds of motion trajectories. Using a graphics processing unit implementation, computation times are in the order of a few minutes for a full three-dimentional volume. Conclusion: The presented technique can be an alternative or a complement to prospective motion correction methods and is able to improve images with strong motion artifacts from standard imaging sequences without requiring additional data.

We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structural Causal Models, especially for cyclic models.

Networks provide a skeleton for the spread of contagions, like, information, ideas, behaviors and diseases. Many times networks over which contagions diffuse are unobserved and need to be inferred. Here we apply survival theory to develop general additive and multiplicative risk models under which the network inference problems can be solved efficiently by exploiting their convexity. Our additive risk model generalizes several existing network inference models. We show all these models are particular cases of our more general model. Our multiplicative model allows for modeling scenarios in which a node can either increase or decrease the risk of activation of another node, in contrast with previous approaches, which consider only positive risk increments. We evaluate the performance of our network inference algorithms on large synthetic and real cascade datasets, and show that our models are able to predict the length and duration of cascades in real data., Comment: To appear at ICML '13

© 2013 Massachusetts Institute of Technology.Inference of human intention may be an essential step towards understanding human actions and is hence important for realizing efficient human-robot interaction. In this paper, we propose the Intention-Driven Dynamics Model (IDDM), a latent variable model for inferring unknown human intentions. We train the model based on observed human movements/actions. We introduce an efficient approximate inference algorithm to infer the humans intention from an ongoing movement. We verify the feasibility of the IDDM in two scenarios, i.e., target inference in robot table tennis and action recognition for interactive humanoid robots. In both tasks, the IDDM achieves substantial improvements over state-of-The-Art regression and classification.

Subjects operating a brain-computer interface (BCI) based on sensorimotor rhythms exhibit large variations in performance over the course of an experimental session. Here, we show that high-frequency gamma-oscillations, originating in fronto-parietal networks, predict such variations on a trial-to-trial basis. We interpret this finding as empirical support for an in uence of attentional networks on BCI-performance via modulation of the sensorimotor rhythm.

The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the network. However, this still remains largely unexplored to date. To this end, given a network and its temporal dynamics, we first describe how continuous time Markov chains allow us to analytically compute the average total number of nodes reached by a diffusion process starting in a set of source nodes. We then show that selecting the set of most influential source nodes in the continuous time influence maximization problem is NP-hard and develop an efficient approximation algorithm with provable near-optimal performance. Experiments on synthetic and real diffusion networks show that our algorithm outperforms other state of the art algorithms by at least ~20% and is robust across different network topologies., Comment: To appear in the 29th International Conference on Machine Learning (ICML), 2012. Website: http://www.stanford.edu/~manuelgr/influmax/