Kernel methods have achieved very good performance on large scale regression and classification problems, by using the Nystr\"om method and preconditioning techniques. The Nystr\"om approximation -- based on a subset of landmarks -- gives a low rank approximation of the kernel matrix, and is known to provide a form of implicit regularization. We further elaborate on the impact of sampling diverse landmarks for constructing the Nystr\"om approximation in supervised as well as unsupervised kernel methods. By using Determinantal Point Processes for sampling, we obtain additional theoretical results concerning the interplay between diversity and regularization. Empirically, we demonstrate the advantages of training kernel methods based on subsets made of diverse points. In particular, if the dataset has a dense bulk and a sparser tail, we show that Nystr\"om kernel regression with diverse landmarks increases the accuracy of the regression in sparser regions of the dataset, with respect to a uniform landmark sampling. A greedy heuristic is also proposed to select diverse samples of significant size within large datasets when exact DPP sampling is not practically feasible.

There is a need of ensuring machine learning models that are interpretable. Higher interpretability of the model means easier comprehension and explanation of future predictions for end-users. Further, interpretable machine learning models allow healthcare experts to make reasonable and data-driven decisions to provide personalized decisions that can ultimately lead to higher quality of service in healthcare. Generally, we can classify interpretability approaches in two groups where the first focuses on personalized interpretation (local interpretability) while the second summarizes prediction models on a population level (global interpretability). Alternatively, we can group interpretability methods into model-specific techniques, which are designed to interpret predictions generated by a specific model, such as a neural network, and model-agnostic approaches, which provide easy-to-understand explanations of predictions made by any machine learning model. Here, we give an overview of interpretability approaches and provide examples of practical interpretability of machine learning in different areas of healthcare, including prediction of health-related outcomes, optimizing treatments or improving the efficiency of screening for specific conditions. Further, we outline future directions for interpretable machine learning and highlight the importance of developing algorithmic solutions that can enable machine-learning driven decision making in high-stakes healthcare problems.

We consider the problem of stochastic $K$-armed dueling bandit in the contextual setting, where at each round the learner is presented with a context set of $K$ items, each represented by a $d$-dimensional feature vector, and the goal of the learner is to identify the best arm of each context sets. However, unlike the classical contextual bandit setup, our framework only allows the learner to receive item feedback in terms of their (noisy) pariwise preferences--famously studied as dueling bandits which is practical interests in various online decision making scenarios, e.g. recommender systems, information retrieval, tournament ranking, where it is easier to elicit the relative strength of the items instead of their absolute scores. However, to the best of our knowledge this work is the first to consider the problem of regret minimization of contextual dueling bandits for potentially infinite decision spaces and gives provably optimal algorithms along with a matching lower bound analysis. We present two algorithms for the setup with respective regret guarantees $\tilde O(d\sqrt{T})$ and $\tilde O(\sqrt{dT \log K})$. Subsequently we also show that $\Omega(\sqrt {dT})$ is actually the fundamental performance limit for this problem, implying the optimality of our second algorithm. However the analysis of our first algorithm is comparatively simpler, and it is often shown to outperform the former empirically. Finally, we corroborate all the theoretical results with suitable experiments.

In this paper, after observing that different training data instances affect the machine learning model to different extents, we attempt to improve the performance of differentially private empirical risk minimization (DP-ERM) from a new perspective. Specifically, we measure the contributions of various training data instances on the final machine learning model, and select some of them to add random noise. Considering that the key of our method is to measure each data instance separately, we propose a new `Data perturbation' based (DB) paradigm for DP-ERM: adding random noise to the original training data and achieving ($\epsilon,\delta$)-differential privacy on the final machine learning model, along with the preservation on the original data. By introducing the Influence Function (IF), we quantitatively measure the impact of the training data on the final model. Theoretical and experimental results show that our proposed DBDP-ERM paradigm enhances the model performance significantly.

Traditionally, there are two models on differential privacy: the central model and the local model. The central model focuses on the machine learning model and the local model focuses on the training data. In this paper, we study the \textit{input perturbation} method in differentially private empirical risk minimization (DP-ERM), preserving privacy of the central model. By adding noise to the original training data and training with the `perturbed data', we achieve ($\epsilon$,$\delta$)-differential privacy on the final model, along with some kind of privacy on the original data. We observe that there is an interesting connection between the local model and the central model: the perturbation on the original data causes the perturbation on the gradient, and finally the model parameters. This observation means that our method builds a bridge between local and central model, protecting the data, the gradient and the model simultaneously, which is more superior than previous central methods. Detailed theoretical analysis and experiments show that our method achieves almost the same (or even better) performance as some of the best previous central methods with more protections on privacy, which is an attractive result. Moreover, we extend our method to a more general case: the loss function satisfies the Polyak-Lojasiewicz condition, which is more general than strong convexity, the constraint on the loss function in most previous work.

As a popular meta-learning approach, the model-agnostic meta-learning (MAML) algorithm has been widely used due to its simplicity and effectiveness. However, the convergence of the general multi-step MAML still remains unexplored. In this paper, we develop a new theoretical framework, under which we characterize the convergence rate and the computational complexity of multi-step MAML. Our results indicate that $N$-step MAML attains the convergence with linearly increasing complexity with $N$ under a properly chosen inner stepsize. We then take a further step to develop a more efficient Hessian-free MAML. We first show that the existing zeroth-order Hessian estimator contains a constant-level estimation error so that the MAML algorithm can perform unstably. To address this issue, we propose a novel Hessian estimator via a gradient-based Gaussian smoothing method, and show that it achieves a much smaller estimation bias and variance, and the resulting algorithm achieves the same performance guarantee as the original MAML under mild conditions. Our experiments validate our theory and demonstrate the effectiveness of the proposed Hessian estimator.

Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they are not equally suitable for visualisation purposes. In this work, we merge Mapper, an algorithm from the field of Topological Data Analysis (TDA), with the expressive power of Graph Neural Networks (GNNs) to produce hierarchical, topologically-grounded visualisations of graphs. These visualisations do not only help discern the structure of complex graphs but also provide a means of understanding the models applied to them for solving various tasks. We further demonstrate the suitability of Mapper as a topological framework for graph pooling by mathematically proving an equivalence with Min-Cut and Diff Pool. Building upon this framework, we introduce a novel pooling algorithm based on PageRank, which obtains competitive results with state of the art methods on graph classification benchmarks.

Analysis of histopathology slides is a critical step for many diagnoses, and in particular in oncology where it defines the gold standard. In the case of digital histopathological analysis, highly trained pathologists must review vast whole-slide-images of extreme digital resolution ($100,000^2$ pixels) across multiple zoom levels in order to locate abnormal regions of cells, or in some cases single cells, out of millions. The application of deep learning to this problem is hampered not only by small sample sizes, as typical datasets contain only a few hundred samples, but also by the generation of ground-truth localized annotations for training interpretable classification and segmentation models. We propose a method for disease localization in the context of weakly supervised learning, where only image-level labels are available during training. Even without pixel-level annotations, we are able to demonstrate performance comparable with models trained with strong annotations on the Camelyon-16 lymph node metastases detection challenge. We accomplish this through the use of pre-trained deep convolutional networks, feature embedding, as well as learning via top instances and negative evidence, a multiple instance learning technique from the field of semantic segmentation and object detection.

Generative Adversarial Network (GAN) is a current focal point of research. The body of knowledge is fragmented, leading to a trial-error method while selecting an appropriate GAN for a given scenario. We provide a comprehensive summary of the evolution of GANs starting from its inception addressing issues like mode collapse, vanishing gradient, unstable training and non-convergence. We also provide a comparison of various GANs from the application point of view, its behaviour and implementation details. We propose a novel framework to identify candidate GANs for a specific use case based on architecture, loss, regularization and divergence. We also discuss application of the framework using an example, and we demonstrate a significant reduction in search space. This efficient way to determine potential GANs lowers unit economics of AI development for organizations.

Federated learning enables training a global machine learning model from data distributed across multiple sites, without having to move the data. This is particularly relevant in healthcare applications, where data is rife with personal, highly-sensitive information, and data analysis methods must provably comply with regulatory guidelines. Although federated learning prevents sharing raw data, it is still possible to launch privacy attacks on the model parameters that are exposed during the training process, or on the generated machine learning model. In this paper, we propose the first syntactic approach for offering privacy in the context of federated learning. Unlike the state-of-the-art differential privacy-based frameworks, our approach aims to maximize utility or model performance, while supporting a defensible level of privacy, as demanded by GDPR and HIPAA. We perform a comprehensive empirical evaluation on two important problems in the healthcare domain, using real-world electronic health data of 1 million patients. The results demonstrate the effectiveness of our approach in achieving high model performance, while offering the desired level of privacy. Through comparative studies, we also show that, for varying datasets, experimental setups, and privacy budgets, our approach offers higher model performance than differential privacy-based techniques in federated learning.