Seminar overview

More information: https://www.statistiktage.ch/en/call_made

More information: https://www.statistiktage.ch/en/call_made

More information: https://www.statistiktage.ch/en/call_made

Machine learning is now being deployed in safety- and security-critical systems such as autonomous vehicles, medical devices, and large recommender systems. If we want to use machine learning in these scenarios responsibly, we need to understand how reliable our current methodology is. One potential danger in the common ML workflow is the repeated use of the same test set for parameter tuning. To investigate this issue, I will present results of a reprodu-cibility study on the popular CIFAR-10 dataset. Surprisingly, we find no signs of overfitting despite multiple years of adaptive classifier tuning. Nevertheless, our results show that current classifiers are already susceptible to benign shifts in distribution. In the second part of the talk, I will then describe how robust optimization can address some of the challenges arising from distribution shifts in the form of adversarial examples. By exploring the loss landscape of min-max problems in deep neural networks, we can train classifiers with state-of-the art robustness to l_infinity perturbations and small spatial transformations. Based on joint works with Logan Engstrom, Aleksander Madry, Aleksandar Makelov, Benjamin Recht, Rebecca Roelofs, Vaishaal Shankar, Brandon Tran, Dimitris Tsipras, and Adrian Vladu.

In the first part of the talk, we will introduce spatial Gaussian processes. Spatial Gaussian processes are widely studied from a statistical point of view, and have found applications in many fields, including geostatistics, climate science and computer experiments. Exact inference can be conducted for Gaussian processes, thanks to the Gaussian conditioning theorem. Furthermore, covariance parameters can be estimated, for instance by Maximum Likelihood. In the second part of the talk, we will introduce a class of iterative sampling strategies for Gaussian processes, called 'stepwise uncertainty reduction' (SUR). We will give examples of SUR strategies which are widely applied to computer experiments, for instance for optimization or detection of failure domains. We will provide a general consistency result for SUR strategies, together with applications to the most standard examples.

Mendelian randomisation (MR) refers to situations where a genetic predisposition can be exploited as an instrumental variable (IV) to estimate the causal effect of a modifiable risk factor or exposure on an outcome of interest. For example, the ALDH2 gene is associated with alcohol consumption, and has therefore successfully been used as an IV to estimate the causal effect of alcohol on outcomes related to coronary heart disease. MR analyses have become very popular especially recently with the increased availa-bility of GWAS data. This gives rise to a number of challenges, especially around the theme of multiple IVs as it is common that several SNPs are found to be associated with an exposure of interest. However, the validity of such multiple IVs can often not been established in a convincing way and numerous methods that claim to allow for multiple but partially invalid IVs have been put forward in the last few years. In this talk I will propose and investigate a formal notion of „valid IV“ in the context of multiple and potentially invalid IVs - this has been neglected by all of the previous literature but turns out to be crucial to assess the plausbility of the various available methods.

Models specified by low-rank matrices are ubiquitous in contemporary applications. In many of these problem domains, the row/column space structure of a low-rank matrix carries information about some underlying phenomenon, and it is of interest in inferential settings to evaluate the extent to which the row/column spaces of an estimated low-rank matrix signify discoveries about the phenomenon. However, in contrast to variable selection, we lack a formal framework to assess true/false discoveries in low-rank estimation; in particular, the key source of difficulty is that the standard notion of a discovery is a discrete one that is ill-suited to the smooth structure underlying low-rank matrices. We address this challenge via a \emph{geometric} reformulation of the concept of a discovery, which then enables a natural definition in the low-rank case. We describe and analyze a generalization of the Stability Selection method of Meinshausen and B\"uhlmann to control for false discoveries in low-rank estimation, and we demonstrate its utility compared to previous approaches via numerical experiments.

One key challenge in Machine Learning in Medicine is Association Mapping: to link genetic properties of patients to disease risk, progression and therapy success, in order to then exploit this knowledge for improved diagnosis, prognosis and treatment. Disappointingly, for most complex diseases, current feature selection methods have failed to discover strong associations. One possible explanation is that the vast majority of current methods ignores disease-related interactions between genetic properties - combinations of genome variants that jointly affect a disease. The difficulty in exploring these interactions through Combinatorial Association Mapping stems from the combinatorial explosion of the candidate space, which grows exponentially with the number of interacting loci. This leads both to an enormous computational efficiency problem and a severe multiple testing problem. Ignoring this multiple testing problem may lead to millions of false positive associations; accounting for it may lead to a complete loss of statistical power. For this reason, statistically sound and efficient Combinatorial Association Mapping was long deemed an unsolvable problem. In this talk, we will describe our recent progress in solving this problem of Combinatorial Association Mapping, and we will give an outlook on how our new association mapping algorithms will be applied in the “Personalized Swiss Sepsis Study”, as part of the Swiss Personalized Health Network (SPHN).

The lme4 package for R is widely used (google scholar claims more than 10,000 citations of our 2015 J. Stat. Soft. paper on it) but many of its users still encounter convergence problems or long delays in fitting complex models to large data sets. Several years ago I became interested in using the Julia programming language (julialang.org) to reimplement and improve the algorithms in lme4. The good news is that this project has been, I think, successful in that the MixedModels package provides fast and reliable fitting of both linear mixed-effects models and generalized linear mixed-effects models. However, not everyone is willing to switch to a new programming language to be able to take advantage of one package that may only be a small part of their usage. Julia does not yet have the scope and level of expertise for data analysis, manipulation and visualization that R does. It becomes important to provide the ability to communicate between the languages and, in particular, to exchange data between them. I will discuss some of the capabilities in Julia that make the development of the MixedModels package feasible and some of the mechanisms for communications between the languages.

Approximate Bayesian Computation (ABC) has become increasingly prominent as a method for conducting parameter inference in a range of challenging statistical problems, most notably those characterized by an intractable likelihood function. In this paper, we focus on the use of ABC not as a tool for parametric inference, but as a means of generating probabilistic forecasts; or for conducting what we refer to as ‘approximate Bayesian forecasting’. The four key issues explored are:
i) the link between the theoretical behavior of the ABC posterior and that of the ABC-based predictive;
ii) the use of proper scoring rules to measure the (potential) loss of forecast accuracy when using an approximate rather than an exact predictive;
iii) the performance ofapproximate Bayesian forecasting in state space models; and
iv) the use of forecasting criteria to inform the selection of ABC summaries in empirical settings. The primary finding of the paper is that ABC can provide a computationally efficient means of generating probabilistic forecasts that are nearly identical to those produced by the exact predictive, and in a fraction of the time required to produce predictions via an exact methods.

When modeling spatial data near the coast, we need to consider which assumptions to make on the Gaussian field with respect to the coastline, i.e. what kind of boundary effect to assume. One possibility is to have no boundary effect, modeling both water and land, but with observation and prediction locations only in water, leading to a model with a stationary correlation structure. However, a stationary field smooths over islands and peninsulas, inappropriately assuming that observations on two sides of land are highly correlated. Other approaches in the literature range from simple use of Dirichlet or Neumann boundary conditions, to being quite complex and costly. In this talk I showcase a new approach, the Barrier model, implemented in R-INLA, that is intuitive in the way correlation follows the coastline, and is as easy to set up and do inference with as a stationary field, with computational complexity O(n sqrt(n)). I compare this model to two others, showing significant improvement at reconstructing a test function. A real data application shows that the Barrier model smooths around peninsulas, and that inference is numerically stable. I also detail how the stochastic partial differential equations (SPDE) approach was used to construct the Barrier model.

We consider statistical inference for the explained variance $\beta^{\intercal}\Sigma \beta$ under the high-dimensional linear model $Y=X\beta+\epsilon$ in the semi-supervised setting, where $\beta$ is the regression vector and $\Sigma$ is the design covariance matrix. A calibrated estimator, which efficiently integrates both labelled and unlabelled data, is proposed. It is shown that the estimator achieves the minimax optimal rate of convergence in the general semi-supervised framework. The optimality result characterizes how the unlabelled data affects the minimax optimal rate. Moreover, the limiting distribution for the proposed estimator is established and data-driven confidence intervals for the explained variance are constructed. We further develop a randomized calibration technique for statistical inference in the presence of weak signals and apply the obtained inference results to a range of important statistical problems, including signal detection and global testing, prediction accuracy evaluation, and confidence ball construction. The numerical performance of the proposed methodology is demonstrated in simulation studies and an analysis of estimating heritability for a yeast segregant data set with multiple traits.

In the problem of variable selection in high-dimensional linear regression, the Lasso is known to require a strong condition on the design matrix and the true support of the regression coefficients in order to recover the true set of important variables. This difficulty being attributed to an excessive amount of shrinkage, multistage procedures and nonconcave penalties have been introduced to address this issue. We rather propose another approach called Lasso-Zero, based on the limit solution of Lasso as its tuning parameter tends to zero, in other words where Lasso's shrinkage effect is the weakest. Since this provides an overfitted model, Lasso-Zero relies on the generation of several random noise dictionaries concatenated to the design matrix. The obtained coefficients are thresholded by a parameter tuned by Quantile Universal Thresholding (QUT). We prove that under some beta-min condition, a simplified version of Lasso-Zero recovers the true model under a weaker condition on the design matrix than Lasso, and that it controls the FDR in the orthonormal case if it is tuned by QUT. Numerical experiments show that Lasso-Zero outperforms its competitors in terms of FDR/TPR tradeoff and exact model recovery.

In this paper, we derive a rate of convergence of the Lasso estimator when the penalty parameter λ for the estimator is chosen using K-fold cross-validation; in particular, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of λ, the prediction norm of the estimation error of the cross-validated Lasso estimator is with high probability bounded from above up to a constant by (slogp/n)1/2⋅log7/8(pn), where n is the sample size of available data, p is the number of covariates, and s is the number of non-zero coefficients in the model. Thus, the cross-validated Lasso estimator achieves the fastest possible rate of convergence up to a small logarithmic factor log7/8(pn). In addition, we derive a sparsity bound for the cross-validated Lasso estimator; in particular, we show that under the same conditions as above, the number of non-zero coefficients of the estimator is with high probability bounded from above up to a constant by slog5(pn). Finally, we show that our proof technique generates non-trivial bounds on the prediction norm of the estimation error of the cross-validated Lasso estimator even if the assumption of the Gaussian noise fails; in particular, the prediction norm of the estimation error is with high-probability bounded from above up to a constant by (slog2(pn)/n)1/4 under mild regularity conditions.

The first topic of this talk is to model the marginal distribution of rainfall data, extremes included. Precipitation amounts at daily or hourly scales are skewed to the right and heavy rainfall is poorly modeled by a simple gamma distribution. An important, yet challenging topic in hydrometeorology is to find a probability distribution that is able to model well low, moderate and heavy rainfall. In this context, another important aspect of your work is to completely bypass the threshold selection step, the latter being classically used to in Extreme Value Theory to deal with heavy rainfall. To address this issue, I will discuss different approaches and, in particular, I will emphasise a recent semiparametric distribution suitable for modeling the entire-range of rainfall amount. This joint work with P. Tencaliec, A.C. Favre and C. Prieur and it extends the article of Naveau P, Huser R, Ribereau P, Hannart A, (2016, WRR). In a second step, I will focus on how to couple different sources of data to accurately simulate the multivariate dependence structure among extremes rainfall. This is a joint with Marco Oesting. A convenient starting point to model the dependence among block maxima from environmental datasets is the class of max-stable processes. A typical max-stable can be represented by a max-linear combination that merge independent copies of a hidden stochastic process weighted by a Poisson point process. In practice, other levels of complexity emerge. For our example at hand, the spatial structure of heavy rainfall may neither be anisotropic nor stationary in space. By combining different data sources, we propose different types of data driven max-stables processes. They have the advantages to be parsimonious in parameters, easy to simulate and physically based (i.e. capable of incorporating nugget effects and reproducing spatial non-stationarity). We also compare our new method with classical approaches such as Brown-Resnick types. All our multivariate models are based on the recent work of Oesting (2017).