Learning from positive ( P) and unlabeled ( U) data has a rich history as it finds use in multiple applications. In this paper, we provide a novel framework to tackle this problem in a model agnostic fashion. We say model agnostic since, our solution involves identifying and weighting positive as well as negative examples in an unsupervised manner which could then be passed as input to any standard classification algorithm. Moreover, based on our framework we provide approximation guarantees for our algorithm in terms of how well the identified positive examples from U along with their weights match the distribution of P. Such a principled approach has been missing for other methods that belong to the model agnostic category, not to mention that the current state-of-the-art are model dependent strategies that involve modifying the training algorithm. For Kernel Support Vector Machines, trained on a (non-negative) weighted dataset that as such is the output of our method, we derive generalization bounds. Given the advantages of having model agnostic methods (viz. use with (almost) any classifier, one time running cost), we show that our algorithm which possesses these benefits, is competitive with the best methods based on experiments on three real datasets. In fact, in a couple of cases we observe that our approach has better test performance than even standard supervised learning which has access to all positive as well as negative labels.

Prototypical examples that best summarize and compactly represent an underlying complex data distribution, communicate meaningful insights to humans in domains where simple explanations are hard to extract. In this paper, we present algorithms with strong theoretical guarantees to mine these data sets and select prototypes, a.k.a. representatives that optimally describes them. Our work notably generalizes the recent work by Kim et al. (2016) where in addition to selecting prototypes, we also associate non-negative weights which are indicative of their importance. This extension provides a single coherent framework under which both prototypes and criticisms (i.e. outliers) can be found. Furthermore, our framework works for any symmetric positive definite kernel thus addressing one of the key open questions laid out in Kim et al. (2016). By establishing that our objective function enjoys a key property of that of weak submodularity, we present a fast ProtoDash algorithm and also derive approximation guarantees for the same. We demonstrate the efficacy of our method on diverse domains such as retail, digit recognition (MNIST) and on publicly available 40 health questionnaires obtained from the Center for Disease Control (CDC) website maintained by the US Dept. of Health. We validate the results quantitatively as well as qualitatively based on expert feedback and recently published scientific studies on public health, thus showcasing the power of our technique in providing actionability (for retail), utility (for MNIST), and insight (on CDC datasets), which arguably are the hallmarks of an effective interpretable machine learning method.

Summary form only given. We present efficient machine learning methods for color image compression which simultaneously learn bases for compact image representation as well as the color space. We show the benefits of representing color image patches as 2D matrices of size n × 3n rather than as 3D patches of size n × n × 3. We also present a method to leverage greater representational power from a learned dictionary without increasing its size.