During rest, brain activity is intrinsically synchronized between different brain regions, forming networks of coherent activity. These functional networks (FNs), consisting of multiple regions widely distributed across lobes and hemispheres, appear to be a fundamental theme of neural organization in mammalian brains. Despite hundreds of studies detailing this phenomenon, the genetic and molecular mechanisms supporting these functional networks remain undefined. Previous work has mostly focused on polymorphisms in candidate genes, or used a twin study approach to demonstrate heritability of aspects of resting-state connectivity. The recent availability of high spatial resolution post-mortem brain gene expression datasets, together with several large-scale imaging genetics datasets, which contain joint in-vivo functional brain imaging data and genotype data for several hundred subjects, opens intriguing data analysis avenues. Using novel cross-modal graph-based statistics, we show that functional brain networks defined with resting-state fMRI can be recapitulated using measures of correlated gene expression, and that the relationship is not driven by gross tissue types. The set of genes we identify is significantly enriched for certain types of ion channels and synapse-related genes. We validate results by showing that polymorphisms in this set significantly correlate with alterations of in-vivo resting-state functional connectivity in a group of 259 adolescents. We further validate results on another species by showing that our list of genes is significantly associated with neuronal connectivity in the mouse brain. These results provide convergent, multimodal evidence that resting-state functional networks emerge from the orchestrated activity of dozens of genes linked to ion channel activity and synaptic function. Functional brain networks are also known to be perturbed in a variety of neurological and neuropsychological disorders, including Alzheimer's and schizophrenia. Given this link between disease and networks, and the fact that many brain disorders have genetic contributions, it seems that functional brain networks may be an interesting endophenotype for clinical use. We discuss the translational potential of the imaging genomics techniques we developed.
Organizers: Moritz Grosse-Wentrup
Human diseases show considerable heterogeneity at the molecular level. Such heterogeneity is central to personalized medicine efforts that seek to exploit molecular data to better understand disease biology and inform clinical decision making. An emerging notion is that diseases and disease subgroups may differ not only at the level of mean molecular abundance, but also with respect to patterns of molecular interplay. I will discuss our ongoing efforts to develop methods to investigate such heterogeneity, with an emphasis on some high-dimensional aspects.
In machine learning, the standard explanation of Ockham's razor is to minimize predictive risk. But prediction is interpreted passively---one may not rely on predictions to change the probability distribution used for training. That limitation may be overcome by studying alternatively manipulated systems in randomized experimental trials, but experiments on multivariate systems or on human subjects are often infeasible or immoral. Happily, the past three decades have witnessed the development of a range of statistical techniques for discovering causal relations from non-experimental data. One characteristic of such methods is a strong Ockham bias toward simpler causal theories---i.e., theories with fewer causal connections among the variables of interest. Our question is what Ockham's razor has to do with finding true (rather than merely plausible) causal theories from non-experimental data. The traditional story of minimizing predictive risk does not apply, because uniform consistency is often infeasible in non-experimental causal discovery: without strong and implausible assumptions, the probability of erroneous causal orientation may be arbitrarily high at any sample size. The standard justification for causal discovery methods is point-wise consistency, or convergence in probability to the true causes. But Ockham's razor is not necessary for point-wise convergence: a Bayesian with a strong prior bias toward a complex model would also be point-wise consistent. Either way, the crucial Ockham bias remains disconnected from learning performance. A method reverses its opinion in probability when it probably says A at some sample size and probably says B incompatible with A at a higher sample size. A method cycles in probability when it probably says A, then probably says B incompatible with A, and then probably says A again. Uniform consistency allows for no reversals or cycles in probability. Point-wise consistency allows for arbitrarily many. Lying plausibly between those two extremes is straightest possible convergence to the truth, which allows for only as many cycles and reversals in probability as are necessary to solve the learning problem at hand. We show that Ockham's razor is necessary for cycle-minimal convergence and that patience, or waiting for nature to choose among simplest theories, is necessary for reversal-minimal convergence. The idea yields very tight constraints on inductive statistical methods, both classical and Bayesian, with causal discovery methods as an important special case. It also provides a valid interpretation of significance and power when tests are used to fish inductively for models. The talk is self-contained for a general scientific audience. Novel concepts are illustrated amply with figures and simulations.
Facebook serves close to a billion people every day, who are only able to consume a small subset of the information available to them. In this talk I will give some examples of how machine learning is used to personalize people’s Facebook experience. I will also present some data science experiments with fairly counter-intuitive results.
Stochastic differential equations (SDEs) arise naturally as descriptions of continuous time dynamical systems. My talk addresses the problem of inferring the dynamical state and parameters of such systems from observations taken at discrete times. I will discuss the application of approximate inference methods such as the variational method and expectation propagation and show how higher dimensional systems can be treated by a mean field approximation. In the second part of my talk I will discuss the nonparametric estimation of the drift (i.e. the deterministic part of the ‘force’ which governs the dynamics) as a function of the state using Gaussian process approaches.
The recent theory of compressive sensing predicts that (approximately) sparse vectors can be recovered from vastly incomplete linear measurements using efficient algorithms. This principle has a large number of potential applications in signal and image processing, machine learning and more. Optimal measurement matrices in this context known so far are based on randomness. Recovery algorithms include convex optimization approaches (l1-minimization) as well as greedy methods. Gaussian and Bernoulli random matrices are provably optimal in the sense that the smallest possible number of samples is required. Such matrices, however, are of limited practical interest because of the lack of any structure. In fact, applications demand for certain structure so that there is only limited freedom to inject randomness. We present recovery results for various structured random matrices including random partial Fourier matrices and partial random circulant matrices. We will also review recent extensions of compressive sensing for recovering matrices of low rank from incomplete information via efficient algorithms such as nuclear norm minimization. This principle has recently found applications for phaseless estimation, i.e., in situations where only the magnitude of measurements is available. Another extension considers the recovery of low rank tensors (multi-dimensional arrays) from incomplete linear information. Several obstacles arise when passing from matrices and tensors such as the lack of a singular value decomposition which shares all the nice properties of the matrix singular value decomposition. Although only partial theoretical results are available, we discuss algorithmic approaches for this problem.
Organizers: Michel Besserve
This talk reviews differential equations on manifolds of matrices or tensors of low rank. They serve to approximate, in a low-rank format, large time-dependent matrices and tensors that are either given explicitly via their increments or are unknown solutions of differential equations. Furthermore, low-rank differential equations are used in novel algorithms for eigenvalue optimisation, for instance in robust-stability problems.
Organizers: Philipp Hennig
Gaussian process regression is a non-parametric Bayesian machine learning paradigm, where instead of estimating parameters of fixed-form functions, we model the whole unknown functions as Gaussian processes. Gaussian processes are also commonly used for representing uncertainties in models of dynamic systems in many applications such as tracking, navigation, and automatic control systems. The latter models are often formulated as state-space models, where the use of non-linear Kalman filter type of methods is common. The aim of this talk is to discuss connections of Kalman filtering methods and Gaussian process regression. In particular, I discuss representations of Gaussian processes as state-space models, which enable the use of computationally efficient Kalman-filter-based (or more general Bayesian-filter-based) solutions to Gaussian process regression problems. This also allows for computationally efficient inference in latent force models (LFM), which are models combining first-principles mechanical models with non-parametric Gaussian process regression models.
Organizers: Philipp Hennig
(joint work with Jan. C. Neddermeyer) A technique for online estimation of spot volatility for high-frequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction. Furthermore, a nonlinear market microstructure noise model is proposed that reproduces several stylized facts of high frequency data. A computationally efficient particle filter is used that allows for the approximation of the unknown efficient prices and, in combination with a recursive EM algorithm, for the estimation of the volatility curve. We neither assume that the transaction times are equidistant nor do we use interpolated prices. We also make a distinction between volatility per time unit and volatility per transaction and provide estimators for both. More precisely we use a model with random time change where spot volatility is decomposed into spot volatility per transaction times the trading intensity - thus highlighting the influence of trading intensity on volatility.
Organizers: Michel Besserve