Balancing Fit And Complexity In Learned Representations

This dissertation is about learning representations of functions while restricting complexity. In machine learning, maximizing the fit and minimizing the complexity are two conflicting objectives. Common approaches to this problem involve solving a regularized empirical minimization problem, with a complexity measure regularizer and a regularizing parameter that controls the trade-off between the two objectives. The regularizing parameter has to be tuned by repeatedly solving the problem and does not have a straightforward interpretation. This work formulates the problem as a minimization of the complexity measure subject to the fit constraints.The issue of complexity is tackled in reproducing kernel Hilbert spaces (RKHSs) by introducing a novel integral representation of a family of RKHSs that allows arbitrarily placed kernels of different widths. The functional estimation problem is then written as a sparse functional problem, which despite being non-convex and infinite-dimensional can be solved in the dual domain. This problem achieves representations of lower complexity than traditional methods because it searches over a family of RKHS rather than a subspace of a single RKHS. The integral representation is used in a federated classification setting, in which a global model is trained from a federation of agents. This is possible because the dual optimal variables give information about the samples that are fundamental to the classification. Each agent, therefore, learns a local model and sends only the fundamental samples over the network. This creates a federated learning method that requires only one network communication. Its solution is proven to asymptotically converges to that of traditional classification. Next, a theory for constraint specification is established. An optimization problem with a constraint for each sample point can easily become infeasible if the constraints are too tight. In contrast, relaxing all constraints can cause the solution to not fit the data well. The constrained specification method relaxes the constraints until the marginal cost of changing a constraint is equal to the marginal complexity measure. This problem is proven to be feasible and solvable and shown empirically to be resilient to outliers and corrupted training data

Selective Knowledge Sharing for Privacy-Preserving Federated Distillation without A Good Teacher

While federated learning is promising for privacy-preserving collaborative learning without revealing local data, it remains vulnerable to white-box attacks and struggles to adapt to heterogeneous clients. Federated distillation (FD), built upon knowledge distillation--an effective technique for transferring knowledge from a teacher model to student models--emerges as an alternative paradigm, which provides enhanced privacy guarantees and addresses model heterogeneity. Nevertheless, challenges arise due to variations in local data distributions and the absence of a well-trained teacher model, which leads to misleading and ambiguous knowledge sharing that significantly degrades model performance. To address these issues, this paper proposes a selective knowledge sharing mechanism for FD, termed Selective-FD. It includes client-side selectors and a server-side selector to accurately and precisely identify knowledge from local and ensemble predictions, respectively. Empirical studies, backed by theoretical insights, demonstrate that our approach enhances the generalization capabilities of the FD framework and consistently outperforms baseline methods. This study presents a promising direction for effective knowledge transfer in privacy-preserving collaborative learning

Client Selection for Federated Bayesian Learning

Distributed Stein Variational Gradient Descent (DSVGD) is a non-parametric distributed learning framework for federated Bayesian learning, where multiple clients jointly train a machine learning model by communicating a number of non-random and interacting particles with the server. Since communication resources are limited, selecting the clients with most informative local learning updates can improve the model convergence and communication efficiency. In this paper, we propose two selection schemes for DSVGD based on Kernelized Stein Discrepancy (KSD) and Hilbert Inner Product (HIP). We derive the upper bound on the decrease of the global free energy per iteration for both schemes, which is then minimized to speed up the model convergence. We evaluate and compare our schemes with conventional schemes in terms of model accuracy, convergence speed, and stability using various learning tasks and datasets

Black-Box Parallelization for Machine Learning

The landscape of machine learning applications is changing rapidly: large centralized datasets are replaced by high volume, high velocity data streams generated by a vast number of geographically distributed, loosely connected devices, such as mobile phones, smart sensors, autonomous vehicles or industrial machines. Current learning approaches centralize the data and process it in parallel in a cluster or computing center. This has three major disadvantages: (i) it does not scale well with the number of data-generating devices since their growth exceeds that of computing centers, (ii) the communication costs for centralizing the data are prohibitive in many applications, and (iii) it requires sharing potentially privacy-sensitive data. Pushing computation towards the data-generating devices alleviates these problems and allows to employ their otherwise unused computing power. However, current parallel learning approaches are designed for tightly integrated systems with low latency and high bandwidth, not for loosely connected distributed devices. Therefore, I propose a new paradigm for parallelization that treats the learning algorithm as a black box, training local models on distributed devices and aggregating them into a single strong one. Since this requires only exchanging models instead of actual data, the approach is highly scalable, communication-efficient, and privacy-preserving. Following this paradigm, this thesis develops black-box parallelizations for two broad classes of learning algorithms. One approach can be applied to incremental learning algorithms, i.e., those that improve a model in iterations. Based on the utility of aggregations it schedules communication dynamically, adapting it to the hardness of the learning problem. In practice, this leads to a reduction in communication by orders of magnitude. It is analyzed for (i) online learning, in particular in the context of in-stream learning, which allows to guarantee optimal regret and for (ii) batch learning based on empirical risk minimization where optimal convergence can be guaranteed. The other approach is applicable to non-incremental algorithms as well. It uses a novel aggregation method based on the Radon point that allows to achieve provably high model quality with only a single aggregation. This is achieved in polylogarithmic runtime on quasi-polynomially many processors. This relates parallel machine learning to Nick's class of parallel decision problems and is a step towards answering a fundamental open problem about the abilities and limitations of efficient parallel learning algorithms. An empirical study on real distributed systems confirms the potential of the approaches in realistic application scenarios

Domain Generalization for Medical Image Analysis: A Survey

Medical Image Analysis (MedIA) has become an essential tool in medicine and healthcare, aiding in disease diagnosis, prognosis, and treatment planning, and recent successes in deep learning (DL) have made significant contributions to its advances. However, DL models for MedIA remain challenging to deploy in real-world situations, failing for generalization under the distributional gap between training and testing samples, known as a distribution shift problem. Researchers have dedicated their efforts to developing various DL methods to adapt and perform robustly on unknown and out-of-distribution data distributions. This paper comprehensively reviews domain generalization studies specifically tailored for MedIA. We provide a holistic view of how domain generalization techniques interact within the broader MedIA system, going beyond methodologies to consider the operational implications on the entire MedIA workflow. Specifically, we categorize domain generalization methods into data-level, feature-level, model-level, and analysis-level methods. We show how those methods can be used in various stages of the MedIA workflow with DL equipped from data acquisition to model prediction and analysis. Furthermore, we include benchmark datasets and applications used to evaluate these approaches and analyze the strengths and weaknesses of various methods, unveiling future research opportunities

Federated Domain Generalization: A Survey

Machine learning typically relies on the assumption that training and testing distributions are identical and that data is centrally stored for training and testing. However, in real-world scenarios, distributions may differ significantly and data is often distributed across different devices, organizations, or edge nodes. Consequently, it is imperative to develop models that can effectively generalize to unseen distributions where data is distributed across different domains. In response to this challenge, there has been a surge of interest in federated domain generalization (FDG) in recent years. FDG combines the strengths of federated learning (FL) and domain generalization (DG) techniques to enable multiple source domains to collaboratively learn a model capable of directly generalizing to unseen domains while preserving data privacy. However, generalizing the federated model under domain shifts is a technically challenging problem that has received scant attention in the research area so far. This paper presents the first survey of recent advances in this area. Initially, we discuss the development process from traditional machine learning to domain adaptation and domain generalization, leading to FDG as well as provide the corresponding formal definition. Then, we categorize recent methodologies into four classes: federated domain alignment, data manipulation, learning strategies, and aggregation optimization, and present suitable algorithms in detail for each category. Next, we introduce commonly used datasets, applications, evaluations, and benchmarks. Finally, we conclude this survey by providing some potential research topics for the future

Provably Training Overparameterized Neural Network Classifiers with Non-convex Constraints

Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several recent works addressing non-convex constraints have only focused on simple models such as logistic regression or support vector machines. Neural networks, one of the most popular models for classification nowadays, are precluded and lack theoretical guarantees. In this work, we show that overparameterized neural networks could achieve a near-optimal and near-feasible solution of non-convex constrained optimization problems via the project stochastic gradient descent. Our key ingredient is the no-regret analysis of online learning for neural networks in the overparameterization regime, which may be of independent interest in online learning applications

Machine Learning for Informed Representation Learning

The way we view reality and reason about the processes surrounding us is intimately connected to our perception and the representations we form about our observations and experiences. The popularity of machine learning and deep learning techniques in that regard stems from their ability to form useful representations by learning from large sets of observations. Typical application examples include image recognition or language processing for which artificial neural networks are powerful tools to extract regularity patterns or relevant statistics. In this thesis, we leverage and further develop this representation learning capability to address relevant but challenging real-world problems in geoscience and chemistry, to learn representations in an informed manner relevant to the task at hand, and reason about representation learning in neural networks, in general. Firstly, we develop an approach for efficient and scalable semantic segmentation of degraded soil in alpine grasslands in remotely-sensed images based on convolutional neural networks. To this end, we consider different grassland erosion phenomena in several Swiss valleys. We find that we are able to monitor soil degradation consistent with state-of-the-art methods in geoscience and can improve detection of affected areas. Furthermore, our approach provides a scalable method for large-scale analysis which is infeasible with established methods. Secondly, we address the question of how to identify suitable latent representations to enable generation of novel objects with selected properties. For this, we introduce a new deep generative model in the context of manifold learning and disentanglement. Our model improves targeted generation of novel objects by making use of property cycle consistency in property-relevant and property-invariant latent subspaces. We demonstrate the improvements on the generation of molecules with desired physical or chemical properties. Furthermore, we show that our model facilitates interpretability and exploration of the latent representation. Thirdly, in the context of recent advances in deep learning theory and the neural tangent kernel, we empirically investigate the learning of feature representations in standard convolutional neural networks and corresponding random feature models given by the linearisation of the neural networks. We find that performance differences between standard and linearised networks generally increase with the difficulty of the task but decrease with the considered width or over-parametrisation of these networks. Our results indicate interesting implications for feature learning and random feature models as well as the generalisation performance of highly over-parametrised neural networks. In summary, we employ and study feature learning in neural networks and review how we may use informed representation learning for challenging tasks