Seminar overview

Contextual bandit problems are the primary way to model the inherent tradeoff between exploration and exploitation in dynamic personalized decision making in healthcare, marketing, revenue management, and beyond. Naturally, the tradeoff (that is, the optimal rate of regret) depends on how complex the underlying learning problem is -- how much can observing reward in one context tell us about mean rewards in another -- but this obvious-seeming relationship is not supported by the current theory. To characterize it more precisely we study a nonparametric contextual bandit problem where the expected reward functions belong to a Hölder class with smoothness parameter β (roughly meaning they are β-times differentiable). We show how this interpolates between two extremes that were previously studied in isolation: non-differentiable bandits (β ≤ 1), where rate-optimal regret is achieved by running separate non-contextual bandits in different context regions, and parametric-response bandits (β = ∞), where rate-optimal regret can be achieved with minimal or no exploration due to infinite extrapolatability from one context to another. We develop a novel algorithm that carefully adjusts to any smoothness setting in between and we prove its regret is rate-optimal by establishing matching upper and lower bounds, recovering the existing results at the two extremes. In this sense, our work bridges the gap between the existing literature on parametric and nondifferentiable contextual bandit problems and between bandit algorithms that exclusively use global or local information, shedding light on the crucial interplay of complexity and regret in dynamic decision making. Paper: https://arxiv.org/abs/1909.02553

Joint work with: Nicolai Meinshausen, Erich Fischer, Eniko Székely, Flavio Lehner, Angeline Pendergrass, Reto Knutti Internal climate variability fundamentally limits short- and medium-term climate predictability, and the separation of forced changes from internal variability is a key goal in climate change detection and attribution (D&A). In this talk, we discuss the identification of forced climate signals and internal variability in observations and models from spatial patterns of climate variables by using statistical learning techniques. We first introduce a detection approach using climate model simulations and a statistical learning algorithm to encapsulate the relationship between spatial patterns of daily temperature and humidity, and key climate change metrics such as annual global mean temperature. Observations are then projected onto this relationship to detect climatic changes, and it is shown that externally forced climate change can be assessed and detected in the observed global climate record at time steps such as months or days. Second, we discuss how these approaches can be extended to address key remaining uncertainties related to the role of decadal-scale internal variability (DIV). DIV is difficult to quantify accurately from observations, and D&A requires that models simulate internal climate variability sufficiently accurately. We show that a recently developed statistical learning technique, anchor regression, allows to identify the externally forced global temperature response, while increasing the robustness towards different representations of DIV (via an explicit `anchor’ on decadal-scale variability). The fraction of warming due to external factors, based on these optimized patterns, is more robust across different climate models even if DIV would be larger than current best estimates. These findings increase the confidence that warming over past decades is dominated by external forcing, irrespective of remaining uncertainties in the magnitude of climate variability

We show that the learning trajectory of a wide neural network in a lazy training regime can be described by an explicit asymptotic formula at large training times. Specifically, the leading term in the asymptotic expansion of the loss behaves as a power law $L(t) \sim C t^{-\xi}$ with exponent $\xi$ expressed only through the data dimension, the smoothness of the activation function, and the class of function being approximated. The constant C can also be found analytically. Our results are based on spectral analysis of the integral NTK operator. Importantly, the techniques we employ do not require a specific form of the data distribution, for example Gaussian, thus making our findings sufficiently universal. This is joint work with M. Velikanov.

Replicability of research findings is crucial to the credibility of all empirical domains of science. Large-scale replication projects are increasingly conducted in order to assess to what extent claims of new discoveries can be confirmed in independent replication studies. However, there is no established standard how to assess replication success and in practice many different approaches are used. We argue that Reverse-Bayes methods have a key role to play in the assessment of replication success. The main idea is to reverse Bayes' Theorem to determine a sceptical prior that would make the original finding no longer convincing. Sufficient incompatability of the sceptical prior and the replication study result is then used to quantify the degree of replication success. We show how this approach is directly related to the relative effect size, the ratio of the replication to the original effect estimate. This perspective leads to a new proposal to recalibrate the assessment of replication success.

In this talk, I will present an overview of Sequential Monte Carlo (SMC) methods, their original motivation (filtering), their current applications in many areas of science (robotics, epidemiology, social sciences, to name a few), and the challenges that remain to be addressed to make them fully usable in certain areas. I will make a distinction between particle filters, which are SMC algorithms used to perform sequential inference in hidden Markov models, and SMC samplers, a more recent class of algorithms which may be used to approximate one, or several arbitrary distributions.

The goal of statistical inference is to draw conclusions about properties of a population given a finite observed sample. This typically proceeds by first specifying a parametric statistical model (that identifies a likelihood function) for the data generating process which is indexed by parameters that need to be calibrated (estimated). There is always a trade-off between model simplicity / inferencial effort / prediction power. When we want to work with a realistic model, the likelihood function may not be analytically available, for example because it involves complex integrals besides the ones needed to compute normalizing constants. Still we can retain the ability to simulate pseudo samples from the model once a set or parameter values has been specified. These simulator-based models are very natural in several contexts such as Astrophysics, Neuroscience, Econometrics, Epidemiology, Ecology, Genetics and so on. When a simulator-based model is available we can rely on Approximate Bayesian Computation (ABC) to calibrate it. Indeed, ABC is a class of algorithms which has been developed to perform statistical inference (from point estimation all the way to hypothesis testing, model selection and prediction) in the absence of a likelihood function but in a setting where there exists a data generating mechanism able to return pseudo-samples. In this talk I will introduce the basic idea behind ABC and explain some of the algorithms useful for statistical inference including the simulated annealing approach by C. Albert, HR Künsch and A Scheidegger (2014). I will conclude with an example related to epidemiological models for Covid-19 data.

Machine learning is ubiquitous in daily decisions and producing fair and non-discriminatory predictions is a major societal concern. Various criteria of fairness have been proposed in the literature, and we will start with a short (biased!) tour on fairness concepts in machine learning. Many decision problems are of a sequential nature, and efforts are needed to better handle such settings. We consider a general setting of fair online learning with stochastic sensitive and non-sensitive contexts. We propose a unified approach for fair learning in this adversarial setting, by interpreting this problem as an approachability problem. This point of view offers a generic way to produce algorithms and theoretical results. Adapting Blackwell’s approachability theory, we exhibit a general necessary and sufficient condition for some learning objectives to be compatible with some fairness constraints, and we characterize the optimal trade-off between the two, when they are not compatible. joint work with E. Chzhen and G. Stoltz

Biomedical image data offers quantitative information about health, disease, and disease progression under treatment - both at the patient and at the population level. Computational routines are instrumental in extracting these information in a structured fashion, typically following a succession of image segmenation, 'radiomic' feature extraction, and predictive modeling with respect to a given image marker or disease-related outcome. This pipeline can also be complemented by a functional and patient-specific modeling of the features or processses underlying the given image observations, for example, the tumor-growth underlying a set of magnetic resonance scans acquired prior to and after treatment. I will talk about this image processing pipeline, together open problems that we continue to work in Zurich, focusing on two aspects: a) the development and benchmarking of image segmenation routines in the 'Multi-modal Brain Tumor Image Segmentation Benchmark' (BRATS), one of the largest benchmark challenges in biomedical image computing, and b) the image-based modeling of tumor growth using partial differential equations, and a fast personalization and inversion of those models via neural networks.

Our work is to analyze human bodies under the change of shape, pose and motion. This problem is challenging since 3D human shapes vary significantly across subjects and body postures. We analyze human poses and motion by introducing three sequences of easily calculated surface descriptors that are invariant under reparametrizations and Euclidean transformations. These descriptors are obtained by associating to each finitely triangulated surface two functions on the unit sphere: for each unit vector u we compute the weighted area of the projection of the surface onto the plane orthogonal to u and the length of its projection onto the line spanned by u. The L2 norms and inner products of the projections of these functions onto the space of spherical harmonics of order k provide us with three sequences of Euclidean and reparametrization invariants of the surface. The use of these invariants reduces the comparison of 3D+time surface representations to the comparison of polygonal curves in Rn. Moreover, a slight modification of our method yields good results on noisy human data. The experimental results on the FAUST and CVSSP3D datasets are promising.