We develop a novel approach for supervised learning based on adaptively partitioning the feature space into different regions and learning local region-specific classifiers. We formulate an empirical risk minimization problem that incorporates both partitioning and classification in to a single global objective. We show that space partitioning can be equivalently reformulated as a supervised learning problem and consequently any discriminative learning method can be utilized in conjunction with our approach. Nevertheless, we consider locally linear schemes by learning linear partitions and linear region classifiers. Locally linear schemes can not only approximate complex decision boundaries and ensure low training error but also provide tight control on over-fitting and generalization error. We train locally linear classifiers by using LDA, logistic regression and perceptrons, and so our scheme is scalable to large data sizes and high-dimensions.

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing these probability distributions as mean embeddings in the reproducing kernel Hilbert space (RKHS), we are able to apply many standard kernel-based learning techniques in straightforward fashion. To accomplish this, we construct a generalization of the support vector machine (SVM) called a support measure machine (SMM). Our analyses of SMMs provides several insights into their relationship to traditional SVMs.

Both random Fourier features and the Nyström method have been successfully applied to efficient kernel learning. In this work, we investigate the fundamental difference between these two approaches, and how the difference could affect their generalization performances. Unlike approaches based on random Fourier features where the basis functions (i.e., cosine and sine functions) are sampled from a distribution {\it independent} from the training data, basis functions used by the Nyström method are randomly sampled from the training examples and are therefore {\it data dependent}. By exploring this difference, we show that when there is a large gap in the eigen-spectrum of the kernel matrix, approaches based the Nyström method can yield impressively better generalization error bound than random Fourier features based approach. We empirically verify our theoretical findings on a wide range of large data sets.

We consider estimation of multiple high-dimensional Gaussian graphical models corresponding to a single set of nodes under several distinct conditions. We assume that most aspects of the networks are shared, but that there are some structured differences between them. Specifically, the network differences are generated from node perturbations: a few nodes are perturbed across networks, and most or all edges stemming from such nodes differ between networks. This corresponds to a simple model for the mechanism underlying many cancers, in which the gene regulatory network is disrupted due to the aberrant activity of a few specific genes. We propose to solve this problem using the structured joint graphical lasso, a convex optimization problem that is based upon the use of a novel symmetric overlap norm penalty, which we solve using an alternating directions method of multipliers algorithm.

We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on binary/multiclass classification problems. We propose a model that is generic enough to handle any supervised learning task and also subsumes the model previously proposed for classification. We give a ''goodness'' criterion for similarity functions w.r.t. a given supervised learning task and then adapt a well-known landmarking technique to provide efficient algorithms for supervised learning using ''good'' similarity functions. We demonstrate the effectiveness of our model on three important supervised learning problems: a) real-valued regression, b) ordinal regression and c) ranking where we show that our method guarantees bounded generalization error.

This paper proposes a way of improving classification performance for classes which have very few training examples. The key idea is to discover classes which are similar and transfer knowledge among them. Our method organizes the classes into a tree hierarchy. The tree structure can be used to impose a generative prior over classification parameters. We show that these priors can be combined with discriminative models such as deep neural networks.

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. It has been shown that CCA regression can substantially reduce variance with a minimal increase in bias if the views contains accurate estimators. Recent theoretical and empirical work shows that regression with random features closely approximates kernel regression, implying that the accuracy requirement holds for random views.

Recent advancements in self-supervised learning have demonstrated that effective visual representations can be learned from unlabeled images. This has led to increased interest in applying self-supervised learning to the medical domain, where unlabeled images are abundant and labeled images are difficult to obtain. However, most self-supervised learning approaches are modeled as image level discriminative or generative proxy tasks, which may not capture the finer level representations necessary for dense prediction tasks like multi-organ segmentation. In this paper, we propose a novel contrastive learning framework that integrates Localized Region Contrast (LRC) to enhance existing self-supervised pre-training methods for medical image segmentation. Our approach involves identifying Super-pixels by Felzenszwalb's algorithm and performing local contrastive learning using a novel contrastive sampling loss. Through extensive experiments on three multi-organ segmentation datasets, we demonstrate that integrating LRC to an existing self-supervised method in a limited annotation setting significantly improves segmentation performance. Moreover, we show that LRC can also be applied to fully-supervised pre-training methods to further boost performance.

Companies that have an online presence-in particular, companies that are exclusively digital-often subscribe to this business model: collect data from the user base, then expose the data to advertisement agencies in order to turn a profit. Such companies routinely market a service as "free", while obfuscating the fact that they tend to "charge" users in the currency of personal information rather than money. However, online companies also gather user data for more principled purposes, such as improving the user experience and aggregating statistics. The problem is the sale of user data to third parties. In this work, we design an intelligent approach to online privacy protection that leverages supervised learning. By detecting and blocking data collection that might infringe on a user's privacy, we can restore a degree of digital privacy to the user. In our evaluation, we collect a dataset of network requests and measure the performance of several classifiers that adhere to the supervised learning paradigm. The results of our evaluation demonstrate the feasibility and potential of our approach.

Synthetic data are becoming a critical tool for building artificially intelligent systems. Simulators provide a way of generating data systematically and at scale. These data can then be used either exclusively, or in conjunction with real data, for training and testing systems. Synthetic data are particularly attractive in cases where the availability of ``real'' training examples might be a bottleneck. While the volume of data in healthcare is growing exponentially, creating datasets for novel tasks and/or that reflect a diverse set of conditions and causal relationships is not trivial. Furthermore, these data are highly sensitive and often patient specific. Recent research has begun to illustrate the potential for synthetic data in many areas of medicine, but no systematic review of the literature exists. In this paper, we present the cases for physical and statistical simulations for creating data and the proposed applications in healthcare and medicine. We discuss that while synthetics can promote privacy, equity, safety and continual and causal learning, they also run the risk of introducing flaws, blind spots and propagating or exaggerating biases.