Joachim M. Buhmann

Simon Föll, Alina Dubatovka, Eugen Ernst et al. · oxford

The phenomenon of distribution shift (DS) occurs when a dataset at test time differs from the dataset at training time, which can significantly impair the performance of a machine learning model in practical settings due to a lack of knowledge about the data's distribution at test time. To address this problem, we postulate that real-world distributions are composed of latent Invariant Elementary Distributions (I.E.D) across different domains. This assumption implies an invariant structure in the solution space that enables knowledge transfer to unseen domains. To exploit this property for domain generalization, we introduce a modular neural network layer consisting of Gated Domain Units (GDUs) that learn a representation for each latent elementary distribution. During inference, a weighted ensemble of learning machines can be created by comparing new observations with the representations of each elementary distribution. Our flexible framework also accommodates scenarios where explicit domain information is not present. Extensive experiments on image, text, and graph data show consistent performance improvement on out-of-training target domains. These findings support the practicality of the I.E.D assumption and the effectiveness of GDUs for domain generalisation.

Zhongbin Fang, Xiangtai Li, Xia Li et al.

With the rise of large-scale models trained on broad data, in-context learning has become a new learning paradigm that has demonstrated significant potential in natural language processing and computer vision tasks. Meanwhile, in-context learning is still largely unexplored in the 3D point cloud domain. Although masked modeling has been successfully applied for in-context learning in 2D vision, directly extending it to 3D point clouds remains a formidable challenge. In the case of point clouds, the tokens themselves are the point cloud positions (coordinates) that are masked during inference. Moreover, position embedding in previous works may inadvertently introduce information leakage. To address these challenges, we introduce a novel framework, named Point-In-Context, designed especially for in-context learning in 3D point clouds, where both inputs and outputs are modeled as coordinates for each task. Additionally, we propose the Joint Sampling module, carefully designed to work in tandem with the general point sampling operator, effectively resolving the aforementioned technical issues. We conduct extensive experiments to validate the versatility and adaptability of our proposed methods in handling a wide range of tasks.

Lukas Klein, João B. S. Carvalho, Mennatallah El-Assady et al.

Explainable AI aims to render model behavior understandable by humans, which can be seen as an intermediate step in extracting causal relations from correlative patterns. Due to the high risk of possible fatal decisions in image-based clinical diagnostics, it is necessary to integrate explainable AI into these safety-critical systems. Current explanatory methods typically assign attribution scores to pixel regions in the input image, indicating their importance for a model's decision. However, they fall short when explaining why a visual feature is used. We propose a framework that utilizes interpretable disentangled representations for downstream-task prediction. Through visualizing the disentangled representations, we enable experts to investigate possible causation effects by leveraging their domain knowledge. Additionally, we deploy a multi-path attribution mapping for enriching and validating explanations. We demonstrate the effectiveness of our approach on a synthetic benchmark suite and two medical datasets. We show that the framework not only acts as a catalyst for causal relation extraction but also enhances model robustness by enabling shortcut detection without the need for testing under distribution shifts.

Đorđe Miladinović, Kumar Shridhar, Kushal Jain et al.

In principle, applying variational autoencoders (VAEs) to sequential data offers a method for controlled sequence generation, manipulation, and structured representation learning. However, training sequence VAEs is challenging: autoregressive decoders can often explain the data without utilizing the latent space, known as posterior collapse. To mitigate this, state-of-the-art models weaken the powerful decoder by applying uniformly random dropout to the decoder input. We show theoretically that this removes pointwise mutual information provided by the decoder input, which is compensated for by utilizing the latent space. We then propose an adversarial training strategy to achieve information-based stochastic dropout. Compared to uniform dropout on standard text benchmark datasets, our targeted approach increases both sequence modeling performance and the information captured in the latent space.

Eugene Bykovets, Yannick Metz, Mennatallah El-Assady et al.

While deep reinforcement learning (RL) agents have showcased strong results across many domains, a major concern is their inherent opaqueness and the safety of such systems in real-world use cases. To overcome these issues, we need agents that can quantify their uncertainty and detect out-of-distribution (OOD) states. Existing uncertainty estimation techniques, like Monte-Carlo Dropout or Deep Ensembles, have not seen widespread adoption in on-policy deep RL. We posit that this is due to two reasons: concepts like uncertainty and OOD states are not well defined compared to supervised learning, especially for on-policy RL methods. Secondly, available implementations and comparative studies for uncertainty estimation methods in RL have been limited. To overcome the first gap, we propose definitions of uncertainty and OOD for Actor-Critic RL algorithms, namely, proximal policy optimization (PPO), and present possible applicable measures. In particular, we discuss the concepts of value and policy uncertainty. The second point is addressed by implementing different uncertainty estimation methods and comparing them across a number of environments. The OOD detection performance is evaluated via a custom evaluation benchmark of in-distribution (ID) and OOD states for various RL environments. We identify a trade-off between reward and OOD detection performance. To overcome this, we formulate a Pareto optimization problem in which we simultaneously optimize for reward and OOD detection performance. We show experimentally that the recently proposed method of Masksembles strikes a favourable balance among the survey methods, enabling high-quality uncertainty estimation and OOD detection while matching the performance of original RL agents.

Eugene Bykovets, Yannick Metz, Mennatallah El-Assady et al.

Robustness to adversarial perturbations has been explored in many areas of computer vision. This robustness is particularly relevant in vision-based reinforcement learning, as the actions of autonomous agents might be safety-critic or impactful in the real world. We investigate the susceptibility of vision-based reinforcement learning agents to gradient-based adversarial attacks and evaluate a potential defense. We observe that Bottleneck Attention Modules (BAM) included in CNN architectures can act as potential tools to increase robustness against adversarial attacks. We show how learned attention maps can be used to recover activations of a convolutional layer by restricting the spatial activations to salient regions. Across a number of RL environments, BAM-enhanced architectures show increased robustness during inference. Finally, we discuss potential future research directions.

João B. S. Carvalho, Mengtao Zhang, Robin Geyer et al.

Anomaly detection (AD) is the machine learning task of identifying highly discrepant abnormal samples by solely relying on the consistency of the normal training samples. Under the constraints of a distribution shift, the assumption that training samples and test samples are drawn from the same distribution breaks down. In this work, by leveraging tools from causal inference we attempt to increase the resilience of anomaly detection models to different kinds of distribution shifts. We begin by elucidating a simple yet necessary statistical property that ensures invariant representations, which is critical for robust AD under both domain and covariate shifts. From this property, we derive a regularization term which, when minimized, leads to partial distribution invariance across environments. Through extensive experimental evaluation on both synthetic and real-world tasks, covering a range of six different AD methods, we demonstrated significant improvements in out-of-distribution performance. Under both covariate and domain shift, models regularized with our proposed term showed marked increased robustness. Code is available at: https://github.com/JoaoCarv/invariant-anomaly-detection.

Robin C. Geyer, Alessandro Torcinovich, João B. Carvalho et al.

In unsupervised representation learning, models aim to distill essential features from high-dimensional data into lower-dimensional learned representations, guided by inductive biases. Understanding the characteristics that make a good representation remains a topic of ongoing research. Disentanglement of independent generative processes has long been credited with producing high-quality representations. However, focusing solely on representations that adhere to the stringent requirements of most disentanglement metrics, may result in overlooking many high-quality representations, well suited for various downstream tasks. These metrics often demand that generative factors be encoded in distinct, single dimensions aligned with the canonical basis of the representation space. Motivated by these observations, we propose two novel metrics: Importance-Weighted Orthogonality (IWO) and Importance-Weighted Rank (IWR). These metrics evaluate the mutual orthogonality and rank of generative factor subspaces. Throughout extensive experiments on common downstream tasks, over several benchmark datasets and models, IWO and IWR consistently show stronger correlations with downstream task performance than traditional disentanglement metrics. Our findings suggest that representation quality is closer related to the orthogonality of independent generative processes rather than their disentanglement, offering a new direction for evaluating and improving unsupervised learning models.

Đorđe Miladinović, Aleksandar Stanić, Stefan Bauer et al.

How to improve generative modeling by better exploiting spatial regularities and coherence in images? We introduce a novel neural network for building image generators (decoders) and apply it to variational autoencoders (VAEs). In our spatial dependency networks (SDNs), feature maps at each level of a deep neural net are computed in a spatially coherent way, using a sequential gating-based mechanism that distributes contextual information across 2-D space. We show that augmenting the decoder of a hierarchical VAE by spatial dependency layers considerably improves density estimation over baseline convolutional architectures and the state-of-the-art among the models within the same class. Furthermore, we demonstrate that SDN can be applied to large images by synthesizing samples of high quality and coherence. In a vanilla VAE setting, we find that a powerful SDN decoder also improves learning disentangled representations, indicating that neural architectures play an important role in this task. Our results suggest favoring spatial dependency over convolutional layers in various VAE settings. The accompanying source code is given at https://github.com/djordjemila/sdn.

Ivan Ovinnikov, Eugene Bykovets, Joachim M. Buhmann

Inverse reinforcement learning methods aim to retrieve the reward function of a Markov decision process based on a dataset of expert demonstrations. The commonplace scarcity and heterogeneous sources of such demonstrations can lead to the absorption of spurious correlations in the data by the learned reward function. Consequently, this adaptation often exhibits behavioural overfitting to the expert data set when a policy is trained on the obtained reward function under distribution shift of the environment dynamics. In this work, we explore a novel regularization approach for inverse reinforcement learning methods based on the causal invariance principle with the goal of improved reward function generalization. By applying this regularization to both exact and approximate formulations of the learning task, we demonstrate superior policy performance when trained using the recovered reward functions in a transfer setting

Ivan Ovinnikov, Joachim M. Buhmann

Imitation learning methods are used to infer a policy in a Markov decision process from a dataset of expert demonstrations by minimizing a divergence measure between the empirical state occupancy measures of the expert and the policy. The guiding signal to the policy is provided by the discriminator used as part of an versarial optimization procedure. We observe that this model is prone to absorbing spurious correlations present in the expert data. To alleviate this issue, we propose to use causal invariance as a regularization principle for adversarial training of these models. The regularization objective is applicable in a straightforward manner to existing adversarial imitation frameworks. We demonstrate the efficacy of the regularized formulation in an illustrative two-dimensional setting as well as a number of high-dimensional robot locomotion benchmark tasks.

Xia Li, Runzhao Yang, Muheng Li et al.

Deformable image registration (DIR) is a crucial tool in radiotherapy for analyzing anatomical changes and motion patterns. Current DIR implementations rely on discrete volumetric motion representation, which often leads to compromised accuracy and uncertainty when handling significant anatomical changes and sliding boundaries. This limitation affects the reliability of subsequent contour propagation and dose accumulation procedures, particularly in regions with complex anatomical interfaces such as the lung-chest wall boundary. Given that organ motion is inherently a continuous process in both space and time, we aimed to develop a model that preserves these fundamental properties. Drawing inspiration from fluid mechanics, we propose a novel approach using implicit neural representation (INR) for continuous modeling of patient anatomical motion. This approach ensures spatial and temporal continuity while effectively unifying Eulerian and Lagrangian specifications to enable natural continuous motion modeling and frame interpolation. The integration of these specifications provides a more comprehensive understanding of anatomical deformation patterns. By leveraging the continuous representations, the CPT-DIR method significantly enhances registration and interpolation accuracy, automation, and speed. The method demonstrates superior performance in landmark and contour precision, particularly in challenging anatomical regions, representing a substantial advancement over conventional approaches in deformable image registration. The improved efficiency and accuracy of CPT-DIR make it particularly suitable for real-time adaptive radiotherapy applications.

Mengyuan Liu, Zhongbin Fang, Xia Li et al.

With the emergence of large-scale models trained on diverse datasets, in-context learning has emerged as a promising paradigm for multitasking, notably in natural language processing and image processing. However, its application in 3D point cloud tasks remains largely unexplored. In this work, we introduce Point-In-Context (PIC), a novel framework for 3D point cloud understanding via in-context learning. We address the technical challenge of effectively extending masked point modeling to 3D point clouds by introducing a Joint Sampling module and proposing a vanilla version of PIC called Point-In-Context-Generalist (PIC-G). PIC-G is designed as a generalist model for various 3D point cloud tasks, with inputs and outputs modeled as coordinates. In this paradigm, the challenging segmentation task is achieved by assigning label points with XYZ coordinates for each category; the final prediction is then chosen based on the label point closest to the predictions. To break the limitation by the fixed label-coordinate assignment, which has poor generalization upon novel classes, we propose two novel training strategies, In-Context Labeling and In-Context Enhancing, forming an extended version of PIC named Point-In-Context-Segmenter (PIC-S), targeting improving dynamic context labeling and model training. By utilizing dynamic in-context labels and extra in-context pairs, PIC-S achieves enhanced performance and generalization capability in and across part segmentation datasets. PIC is a general framework so that other tasks or datasets can be seamlessly introduced into our PIC through a unified data format. We conduct extensive experiments to validate the versatility and adaptability of our proposed methods in handling a wide range of tasks and segmenting multi-datasets. Our PIC-S is capable of generalizing unseen datasets and performing novel part segmentation by customizing prompts.

Marc Bartholet, Taehyeon Kim, Ami Beuret et al.

Federated Learning (FL) faces significant challenges with domain shifts in heterogeneous data, degrading performance. Traditional domain generalization aims to learn domain-invariant features, but the federated nature of model averaging often limits this due to its linear aggregation of local learning. To address this, we propose a robust framework, coined as hypernetwork-based Federated Fusion (hFedF), using hypernetworks for non-linear aggregation, facilitating generalization to unseen domains. Our method employs client-specific embeddings and gradient alignment techniques to manage domain generalization effectively. Evaluated in both zero-shot and few-shot settings, hFedF demonstrates superior performance in handling domain shifts. Comprehensive comparisons on PACS, Office-Home, and VLCS datasets show that hFedF consistently achieves the highest in-domain and out-of-domain accuracy with reliable predictions. Our study contributes significantly to the under-explored field of Federated Domain Generalization (FDG), setting a new benchmark for performance in this area.

João Borges S. Carvalho, Victor Jimenez Rodriguez, Alessandro Torcinovich et al.

The robustness of algorithms against covariate shifts is a fundamental problem with critical implications for the deployment of machine learning algorithms in the real world. Current evaluation methods predominantly measure robustness through the lens of standard generalization, relying on task performance measures like accuracy. This approach lacks a theoretical justification and underscores the need for a principled foundation of robustness assessment under distribution shifts. In this work, we set the desiderata for a robustness measure, and we propose a novel principled framework for the robustness assessment problem that directly follows the Posterior Agreement (PA) theory of model validation. Specifically, we extend the PA framework to the covariate shift setting and propose a measure for robustness evaluation. We assess the soundness of our measure in controlled environments and through an empirical robustness analysis in two different covariate shift scenarios: adversarial learning and domain generalization. We illustrate the suitability of PA by evaluating several models under different nature and magnitudes of shift, and proportion of affected observations. The results show that PA offers a reliable analysis of the vulnerabilities in learning algorithms across different shift conditions and provides higher discriminability than accuracy-based measures, while requiring no supervision.

Omar G. Younis, Luca Corinzia, Ioannis N. Athanasiadis et al.

Crop breeding is crucial in improving agricultural productivity while potentially decreasing land usage, greenhouse gas emissions, and water consumption. However, breeding programs are challenging due to long turnover times, high-dimensional decision spaces, long-term objectives, and the need to adapt to rapid climate change. This paper introduces the use of Reinforcement Learning (RL) to optimize simulated crop breeding programs. RL agents are trained to make optimal crop selection and cross-breeding decisions based on genetic information. To benchmark RL-based breeding algorithms, we introduce a suite of Gym environments. The study demonstrates the superiority of RL techniques over standard practices in terms of genetic gain when simulated in silico using real-world genomic maize data.

João B. S. Carvalho, João A. Santinha, Đorđe Miladinović et al.

In clinical practice, regions of interest in medical imaging often need to be identified through a process of precise image segmentation. The quality of this image segmentation step critically affects the subsequent clinical assessment of the patient status. To enable high accuracy, automatic image segmentation, we introduce a novel deep neural network architecture that exploits the inherent spatial coherence of anatomical structures and is well equipped to capture long-range spatial dependencies in the segmented pixel/voxel space. In contrast to the state-of-the-art solutions based on convolutional layers, our approach leverages on recently introduced spatial dependency layers that have an unbounded receptive field and explicitly model the inductive bias of spatial coherence. Our method performs favourably to commonly used U-Net and U-Net++ architectures as demonstrated by improved Dice and Jaccardscore in three different medical segmentation tasks: nuclei segmentation in microscopy images, polyp segmentation in colonoscopy videos, and liver segmentation in abdominal CT scans.

Luca Corinzia, Paolo Penna, Wojciech Szpankowski et al.

We study the problem of estimating a rank-1 additive deformation of a Gaussian tensor according to the \emph{maximum-likelihood estimator} (MLE). The analysis is carried out in the sparse setting, where the underlying signal has a support that scales sublinearly with the total number of dimensions. We show that for Bernoulli distributed signals, the MLE undergoes an \emph{all-or-nothing} (AoN) phase transition, already established for the minimum mean-square-error estimator (MMSE) in the same problem. The result follows from two main technical points: (i) the connection established between the MLE and the MMSE, using the first and second-moment methods in the constrained signal space, (ii) a recovery regime for the MMSE stricter than the simple error vanishing characterization given in the standard AoN, that is here proved as a general result.

Luca Corinzia, Paolo Penna, Wojciech Szpankowski et al.

In this work, we consider the problem of recovery a planted $k$-densest sub-hypergraph on $d$-uniform hypergraphs. This fundamental problem appears in different contexts, e.g., community detection, average-case complexity, and neuroscience applications as a structural variant of tensor-PCA problem. We provide tight \emph{information-theoretic} upper and lower bounds for the exact recovery threshold by the maximum-likelihood estimator, as well as \emph{algorithmic} bounds based on approximate message passing algorithms. The problem exhibits a typical statistical-to-computational gap observed in analogous sparse settings that widen with increasing sparsity of the problem. The bounds show that the signal structure impacts the location of the statistical and computational phase transition that the known existing bounds for the tensor-PCA model do not capture. This effect is due to the generic planted signal prior that this latter model addresses.

Luca Corinzia, Fabian Laumer, Alessandro Candreva et al.

The segmentation of the mitral valve annulus and leaflets specifies a crucial first step to establish a machine learning pipeline that can support physicians in performing multiple tasks, e.g.\ diagnosis of mitral valve diseases, surgical planning, and intraoperative procedures. Current methods for mitral valve segmentation on 2D echocardiography videos require extensive interaction with annotators and perform poorly on low-quality and noisy videos. We propose an automated and unsupervised method for the mitral valve segmentation based on a low dimensional embedding of the echocardiography videos using neural network collaborative filtering. The method is evaluated in a collection of echocardiography videos of patients with a variety of mitral valve diseases, and additionally on an independent test cohort. It outperforms state-of-the-art \emph{unsupervised} and \emph{supervised} methods on low-quality videos or in the case of sparse annotation.

Yatao Bian, Joachim M. Buhmann, Andreas Krause

Continuous submodular functions are a category of generally non-convex/non-concave functions with a wide spectrum of applications. The celebrated property of this class of functions - continuous submodularity - enables both exact minimization and approximate maximization in poly. time. Continuous submodularity is obtained by generalizing the notion of submodularity from discrete domains to continuous domains. It intuitively captures a repulsive effect amongst different dimensions of the defined multivariate function. In this paper, we systematically study continuous submodularity and a class of non-convex optimization problems: continuous submodular function maximization. We start by a thorough characterization of the class of continuous submodular functions, and show that continuous submodularity is equivalent to a weak version of the diminishing returns (DR) property. Thus we also derive a subclass of continuous submodular functions, termed continuous DR-submodular functions, which enjoys the full DR property. Then we present operations that preserve continuous (DR-)submodularity, thus yielding general rules for composing new submodular functions. We establish intriguing properties for the problem of constrained DR-submodular maximization, such as the local-global relation. We identify several applications of continuous submodular optimization, ranging from influence maximization, MAP inference for DPPs to provable mean field inference. For these applications, continuous submodularity formalizes valuable domain knowledge relevant for optimizing this class of objectives. We present inapproximability results and provable algorithms for two problem settings: constrained monotone DR-submodular maximization and constrained non-monotone DR-submodular maximization. Finally, we extensively evaluate the effectiveness of the proposed algorithms.

Aytunc Sahin, Yatao Bian, Joachim M. Buhmann et al.

Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest, because this domain relates naturally to many practical problem settings, such as multilabel graph cut, budget allocation and revenue maximization with discrete assignments. In contrast, the use of these functions for probabilistic modeling has received surprisingly little attention so far. In this work, we firstly propose the Generalized Multilinear Extension, a continuous DR-submodular extension for integer submodular functions. We study central properties of this extension and formulate a new probabilistic model which is defined through integer submodular functions. Then, we introduce a block-coordinate ascent algorithm to perform approximate inference for those class of models. Finally, we demonstrate its effectiveness and viability on several real-world social connection graph datasets with integer submodular objectives.

Luca Corinzia, Ami Beuret, Joachim M. Buhmann

In federated learning, a central server coordinates the training of a single model on a massively distributed network of devices. This setting can be naturally extended to a multi-task learning framework, to handle real-world federated datasets that typically show strong statistical heterogeneity among devices. Despite federated multi-task learning being shown to be an effective paradigm for real-world datasets, it has been applied only on convex models. In this work, we introduce VIRTUAL, an algorithm for federated multi-task learning for general non-convex models. In VIRTUAL the federated network of the server and the clients is treated as a star-shaped Bayesian network, and learning is performed on the network using approximated variational inference. We show that this method is effective on real-world federated datasets, outperforming the current state-of-the-art for federated learning, and concurrently allowing sparser gradient updates.

Đorđe Miladinović, Muhammad Waleed Gondal, Bernhard Schölkopf et al.

Sequential data often originates from diverse domains across which statistical regularities and domain specifics exist. To specifically learn cross-domain sequence representations, we introduce disentangled state space models (DSSM) -- a class of SSM in which domain-invariant state dynamics is explicitly disentangled from domain-specific information governing that dynamics. We analyze how such separation can improve knowledge transfer to new domains, and enable robust prediction, sequence manipulation and domain characterization. We furthermore propose an unsupervised VAE-based training procedure to implement DSSM in form of Bayesian filters. In our experiments, we applied VAE-DSSM framework to achieve competitive performance in online ODE system identification and regression across experimental settings, and controlled generation and prediction of bouncing ball video sequences across varying gravitational influences.

Patrick Schwab, Lorenz Linhardt, Stefan Bauer et al.

Estimating what would be an individual's potential response to varying levels of exposure to a treatment is of high practical relevance for several important fields, such as healthcare, economics and public policy. However, existing methods for learning to estimate counterfactual outcomes from observational data are either focused on estimating average dose-response curves, or limited to settings with only two treatments that do not have an associated dosage parameter. Here, we present a novel machine-learning approach towards learning counterfactual representations for estimating individual dose-response curves for any number of treatments with continuous dosage parameters with neural networks. Building on the established potential outcomes framework, we introduce performance metrics, model selection criteria, model architectures, and open benchmarks for estimating individual dose-response curves. Our experiments show that the methods developed in this work set a new state-of-the-art in estimating individual dose-response.

An Bian, Joachim M. Buhmann, Andreas Krause

Mean field inference in probabilistic models is generally a highly nonconvex problem. Existing optimization methods, e.g., coordinate ascent algorithms, can only generate local optima. In this work we propose provable mean filed methods for probabilistic log-submodular models and its posterior agreement (PA) with strong approximation guarantees. The main algorithmic technique is a new Double Greedy scheme, termed DR-DoubleGreedy, for continuous DR-submodular maximization with box-constraints. It is a one-pass algorithm with linear time complexity, reaching the optimal 1/2 approximation ratio, which may be of independent interest. We validate the superior performance of our algorithms against baseline algorithms on both synthetic and real-world datasets.

Philippe Wenk, Alkis Gotovos, Stefan Bauer et al.

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computational cost are well established, a rigorous mathematical framework has been missing. We offer a novel interpretation which leads to a better understanding and improvements in state-of-the-art performance in terms of accuracy for nonlinear dynamical systems.

An Bian, Kfir Y. Levy, Andreas Krause et al.

DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others. DR-submodularity captures a subclass of non-convex functions that enables both exact minimization and approximate maximization in polynomial time. In this work we study the problem of maximizing non-monotone DR-submodular continuous functions under general down-closed convex constraints. We start by investigating geometric properties that underlie such objectives, e.g., a strong relation between (approximately) stationary points and global optimum is proved. These properties are then used to devise two optimization algorithms with provable guarantees. Concretely, we first devise a "two-phase" algorithm with $1/4$ approximation guarantee. This algorithm allows the use of existing methods for finding (approximately) stationary points as a subroutine, thus, harnessing recent progress in non-convex optimization. Then we present a non-monotone Frank-Wolfe variant with $1/e$ approximation guarantee and sublinear convergence rate. Finally, we extend our approach to a broader class of generalized DR-submodular continuous functions, which captures a wider spectrum of applications. Our theoretical findings are validated on synthetic and real-world problem instances.

Nico S. Gorbach, Stefan Bauer, Joachim M. Buhmann

Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical integration. However, for many real-world applications, only sparse observations are available or even unobserved variables are included in the model description. In these cases most gradient matching methods are difficult to apply or simply do not provide satisfactory results. That is why, despite the high computational cost, numerical integration is still the gold standard in many applications. Using an existing gradient matching approach, we propose a scalable variational inference framework which can infer states and parameters simultaneously, offers computational speedups, improved accuracy and works well even under model misspecifications in a partially observable system.

Andrew An Bian, Joachim M. Buhmann, Andreas Krause et al.

We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for maximizing submodular functions, there are few guarantees for non-submodular ones. However, Greedy enjoys strong empirical performance for many important non-submodular functions, e.g., the Bayesian A-optimality objective in experimental design. We prove theoretical guarantees supporting the empirical performance. Our guarantees are characterized by a combination of the (generalized) curvature $α$ and the submodularity ratio $γ$. In particular, we prove that Greedy enjoys a tight approximation guarantee of $\frac{1}α(1- e^{-γα})$ for cardinality constrained maximization. In addition, we bound the submodularity ratio and curvature for several important real-world objectives, including the Bayesian A-optimality objective, the determinantal function of a square submatrix and certain linear programs with combinatorial constraints. We experimentally validate our theoretical findings for both synthetic and real-world applications.

Gabriel Krummenacher, Brian McWilliams, Yannic Kilcher et al.

Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by accumulating past gradients which are used to tune the step size adaptively. In certain situations the full-matrix variant of AdaGrad is expected to attain better performance, however in high dimensions it is computationally impractical. We present Ada-LR and RadaGrad two computationally efficient approximations to full-matrix AdaGrad based on randomized dimensionality reduction. They are able to capture dependencies between features and achieve similar performance to full-matrix AdaGrad but at a much smaller computational cost. We show that the regret of Ada-LR is close to the regret of full-matrix AdaGrad which can have an up-to exponentially smaller dependence on the dimension than the diagonal variant. Empirically, we show that Ada-LR and RadaGrad perform similarly to full-matrix AdaGrad. On the task of training convolutional neural networks as well as recurrent neural networks, RadaGrad achieves faster convergence than diagonal AdaGrad.

Nico S. Gorbach, Stefan Bauer, Joachim M. Buhmann

Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which implies that the joint distribution given the ODE's and GP kernels is also Gaussian distributed. The state-derivatives are integrated out analytically since they are modelled as latent variables. However, the state variables themselves are also latent variables because they are contaminated by noise. Previous work sampled the state variables since integrating them out is \textit{not} analytically tractable. In this paper we use mean-field approximation to establish tight variational lower bounds that decouple state variables and are therefore, in contrast to the integral over state variables, analytically tractable and even concave for a restricted family of ODE's, including nonlinear and periodic ODE's. Such variational lower bounds facilitate "hill climbing" to determine the maximum a posteriori estimate of ODE parameters. An additional advantage of our approach over sampling methods is the determination of a proxy to the intractable posterior distribution over state variables given observations and the ODE's.

Benjamin Fischer, Nico Gorbach, Stefan Bauer et al.

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in their fundamental structure. It is often not clear which function structure to choose, for instance to decide between a squared exponential and a rational quadratic kernel. Based on the principle of approximation set coding, we develop a framework for model selection to rank kernels for Gaussian process regression. In our experiments approximation set coding shows promise to become a model selection criterion competitive with maximum evidence (also called marginal likelihood) and leave-one-out cross-validation.

Andrew An Bian, Baharan Mirzasoleiman, Joachim M. Buhmann et al.

Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation guarantees. Specifically, i) We introduce the weak DR property that gives a unified characterization of submodularity for all set, integer-lattice and continuous functions; ii) for maximizing monotone DR-submodular continuous functions under general down-closed convex constraints, we propose a Frank-Wolfe variant with $(1-1/e)$ approximation guarantee, and sub-linear convergence rate; iii) for maximizing general non-monotone submodular continuous functions subject to box constraints, we propose a DoubleGreedy algorithm with $1/3$ approximation guarantee. Submodular continuous functions naturally find applications in various real-world settings, including influence and revenue maximization with continuous assignments, sensor energy management, multi-resolution data summarization, facility location, etc. Experimental results show that the proposed algorithms efficiently generate superior solutions compared to baseline algorithms.

Stefan Bauer, Nicolas Carion, Peter Schüffler et al.

Accurate and robust cell nuclei classification is the cornerstone for a wider range of tasks in digital and Computational Pathology. However, most machine learning systems require extensive labeling from expert pathologists for each individual problem at hand, with no or limited abilities for knowledge transfer between datasets and organ sites. In this paper we implement and evaluate a variety of deep neural network models and model ensembles for nuclei classification in renal cell cancer (RCC) and prostate cancer (PCa). We propose a convolutional neural network system based on residual learning which significantly improves over the state-of-the-art in cell nuclei classification. Finally, we show that the combination of tissue types during training increases not only classification accuracy but also overall survival analysis.

Dmitry Laptev, Nikolay Savinov, Joachim M. Buhmann et al.

In this paper we present a deep neural network topology that incorporates a simple to implement transformation invariant pooling operator (TI-POOLING). This operator is able to efficiently handle prior knowledge on nuisance variations in the data, such as rotation or scale changes. Most current methods usually make use of dataset augmentation to address this issue, but this requires larger number of model parameters and more training data, and results in significantly increased training time and larger chance of under- or overfitting. The main reason for these drawbacks is that the learned model needs to capture adequate features for all the possible transformations of the input. On the other hand, we formulate features in convolutional neural networks to be transformation-invariant. We achieve that using parallel siamese architectures for the considered transformation set and applying the TI-POOLING operator on their outputs before the fully-connected layers. We show that this topology internally finds the most optimal "canonical" instance of the input image for training and therefore limits the redundancy in learned features. This more efficient use of training data results in better performance on popular benchmark datasets with smaller number of parameters when comparing to standard convolutional neural networks with dataset augmentation and to other baselines.

Thomas J. Fuchs, Joachim M. Buhmann

The histological assessment of human tissue has emerged as the key challenge for detection and treatment of cancer. A plethora of different data sources ranging from tissue microarray data to gene expression, proteomics or metabolomics data provide a detailed overview of the health status of a patient. Medical doctors need to assess these information sources and they rely on data driven automatic analysis tools. Methods for classification, grouping and segmentation of heterogeneous data sources as well as regression of noisy dependencies and estimation of survival probabilities enter the processing workflow of a pathology diagnosis system at various stages. This paper reports on state-of-the-art of the design and effectiveness of computational pathology workflows and it discusses future research directions in this emergent field of medical informatics and diagnostic machine learning.

Brian McWilliams, Gabriel Krummenacher, Mario Lucic et al.

Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence that was developed for regression diagnostics can be used to detect such corrupted observations as shown in this paper. This property of influence -- for which we also develop a randomized approximation -- motivates our proposed subsampling algorithm for large scale corrupted linear regression which limits the influence of data points since highly influential points contribute most to the residual error. Under a general model of corrupted observations, we show theoretically and empirically on a variety of simulated and real datasets that our algorithm improves over the current state-of-the-art approximation schemes for ordinary least squares.

Brian McWilliams, David Balduzzi, Joachim M. Buhmann

This paper presents Correlated Nystrom Views (XNV), a fast semi-supervised algorithm for regression and classification. The algorithm draws on two main ideas. First, it generates two views consisting of computationally inexpensive random features. Second, XNV applies multiview regression using Canonical Correlation Analysis (CCA) on unlabeled data to bias the regression towards useful features. It has been shown that, if the views contains accurate estimators, CCA regression can substantially reduce variance with a minimal increase in bias. Random views are justified by recent theoretical and empirical work showing that regression with random features closely approximates kernel regression, implying that random views can be expected to contain accurate estimators. We show that XNV consistently outperforms a state-of-the-art algorithm for semi-supervised learning: substantially improving predictive performance and reducing the variability of performance on a wide variety of real-world datasets, whilst also reducing runtime by orders of magnitude.

Christian D. Sigg, Tomas Dikk, Joachim M. Buhmann

Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training data matrix into a dictionary and a sparse coding matrix. The learned dictionary is characterized by two properties: the coherence of the dictionary to observations of the signal class, and the self-coherence of the dictionary atoms. A high coherence to the signal class enables the sparse coding of signal observations with a small approximation error, while a low self-coherence of the atoms guarantees atom recovery and a more rapid residual error decay rate for the sparse coding algorithm. The two goals of high signal coherence and low self-coherence are typically in conflict, therefore one seeks a trade-off between them, depending on the application. We present a dictionary learning method with an effective control over the self-coherence of the trained dictionary, enabling a trade-off between maximizing the sparsity of codings and approximating an equiangular tight frame.