We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical …

Deep learning algorithms are well-known to have a propensity for fitting the training data very well and often fit even outliers and mislabeled data points. Such fitting requires memorization of training data labels, a phenomenon that has attracted significant research interest but has not been given a compelling explanation so far. A recent work of Feldman (2019) proposes a theoretical …

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal …

Data augmentation methods are indispensable heuristics to boost the performance of deep neural networks, especially in image recognition tasks. Recently, several studies have shown that augmentation strategies found by search algorithms outperform hand-made strategies. Such methods employ black-box search algorithms over image transformations with continuous or discrete parameters and require a …

In the "Corona Summer" of 2020, Prof. Dr. Philipp Hennig remotely taught the course on Probabilistic Machine Learning within the Tübingen International Master Programme on Machine Learning. The course consists of two ~90min lectures per week (26 lectures in total) plus a weekly practical / tutorial. Videos of all lectures are available on the youtube channel of the Tübingen Machine Learning …

Within the Copernicus Climate Change Service (C3S), ECMWF is producing the ERA5 reanalysis which, once completed, will embody a detailed record of the global atmosphere, land surface and ocean waves from 1950 onwards. This new reanalysis replaces the ERA-Interim reanalysis (spanning 1979 onwards) which was started in 2006. ERA5 is based on the Integrated Forecasting System (IFS) Cy41r2 which was …

Detecting out-of-distribution (OOD) data is crucial for robust machine learning systems. Normalizing flows are flexible deep generative models that often surprisingly fail to distinguish between in- and out-of-distribution data: a flow trained on pictures of clothing assigns higher likelihood to handwritten digits. We investigate why normalizing flows perform poorly for OOD detection. We …

Miscalibration -- a mismatch between a model's confidence and its correctness -- of Deep Neural Networks (DNNs) makes their predictions hard to rely on. Ideally, we want networks to be accurate, calibrated and confident. We show that, as opposed to the standard cross-entropy loss, focal loss (Lin et al., 2017) allows us to learn models that are already very well calibrated. When combined with …

We study how robust current ImageNet models are to distribution shifts arising from natural variations in datasets. Most research on robustness focuses on synthetic image perturbations (noise, simulated weather artifacts, adversarial examples, etc.), which leaves open how robustness on synthetic distribution shift relates to distribution shift arising in real data. Informed by an evaluation of 204 …

A novel approach to processing graph-structured data by neural networks, leveraging attention over a node's neighborhood. Achieves state-of-the-art results on transductive citation network tasks...

Offline reinforcement learning (RL), also known as batch RL, offers the prospect of policy optimization from large pre-recorded datasets without online environment interaction. It addresses challenges with regard to the cost of data collection and safety, both of which are particularly pertinent to real-world applications of RL. Unfortunately, most off-policy algorithms perform poorly when …

Federated learning (FL) is a popular technique to train machine learning (ML) models on decentralized data sources. In order to sustain long-term participation of data owners, it is important to fairly appraise each data source and compensate data owners for their contribution to the training process. The Shapley value (SV) defines a unique payoff scheme that satisfies many desiderata for a data …

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which are typically underspecified by the data, and can represent many compelling but different solutions. We show that deep ensembles provide an effective mechanism …

Today, machine learning is being applied to a growing variety of problems in a bewildering variety of domains. When doing machine learning, a fundamental challenge is connecting the abstract mathematics of a particular machine learning technique to a concrete, real-world problem. This book tackles this challenge through model-based machine learning. Model-based machine learning is an approach …

Quantifying the value of data is a fundamental problem in machine learning and has multiple important use cases: (1) building insights about the dataset and task, (2) domain adaptation, (3) corrupted sample discovery, and (4) robust learning. We propose Data Valuation using Reinforcement Learning (DVRL), to adaptively learn data values jointly with the predictor model. DVRL uses a data value …

Causal inference is a complex scientific task that relies on combining evidence from multiple sources, and on the application of a variety of methodological approaches. Causal Inference: What If is an introduction to causal inference when data are collected on each individual in a population. The book is divided into three parts of increasing difficulty: causal inference without models, causal …

Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach …

Deep learning frameworks have often focused on either usability or speed, but not both. PyTorch is a machine learning library that shows that these two goals are in fact compatible: it provides an imperative and Pythonic programming style that supports code as a model, makes debugging easy and is consistent with other popular scientific computing libraries, while remaining efficient and supporting …

We present a sampling-free approach for computing the epistemic uncertainty of a neural network. Epistemic uncertainty is an important quantity for the deployment of deep neural networks in safety-critical applications, since it represents how much one can trust predictions on new data. Recently promising works were proposed using noise injection combined with Monte-Carlo sampling at inference …

Physics-informed neural networks (PINNs) use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a Petrov-Galerkin version of PINNs based on the nonlinear approximation of deep neural networks (DNNs) by selecting the *trial space* to be the space of neural networks …

In reinforcement learning (RL) research, it is common to assume access to direct online interactions with the environment. However in many real-world applications, access to the environment is limited to a fixed offline dataset of logged experience. In such settings, standard RL algorithms have been shown to diverge or otherwise yield poor performance. Accordingly, recent work has suggested a …

Off-policy reinforcement learning aims to leverage experience collected from prior policies for sample-efficient learning. However, in practice, commonly used off-policy approximate dynamic programming methods based on Q-learning and actor-critic methods are highly sensitive to the data distribution, and can make only limited progress without collecting additional on-policy data. As a step towards …

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation approximation. We demonstrate that the ResNet block can be considered as a one-step method that is exact in temporal integration. We then present two multi-step …

In this paper, we aim to develop a simple and scalable reinforcement learning algorithm that uses standard supervised learning methods as subroutines. Our goal is an algorithm that utilizes only simple and convergent maximum likelihood loss functions, while also being able to leverage off-policy data. Our proposed approach, which we refer to as advantage-weighted regression (AWR), consists of two …

Despite the widespread usage of machine learning throughout organizations, there are some key principles that are commonly missed. In particular: 1) There are at least four main families for supervised learning: logical modeling methods, linear combination methods, case-based reasoning methods, and iterative summarization methods. 2) For many application domains, almost all machine learning …

A number of techniques have been proposed to explain a machine learning model's prediction by attributing it to the corresponding input features. Popular among these are techniques that apply the Shapley value method from cooperative game theory. While existing papers focus on the axiomatic motivation of Shapley values, and efficient techniques for computing them, they offer little justification …

When fitting black box supervised learning models (e.g., complex trees, neural networks, boosted trees, random forests, nearest neighbors, local kernel-weighted methods, etc.), visualizing the main effects of the individual predictor variables and their low-order interaction effects is often important, and partial dependence (PD) plots are the most popular approach for accomplishing this. However, …

Probabilistic time series forecasting involves estimating the distribution of future based on its history, which is essential for risk management in downstream decision-making. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks and the dependency is modeled by recurrent neural nets. …