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Several applications, like malicious URL detection and web spam detection, require classification on very high-dimensional data. In such cases anomalous data is hard to find but normal data is easily available. As such it is increasingly common to use a one-class classifier (OCC). Unfortunately, most OCC algorithms cannot scale to datasets with extremely high dimensions. In this paper, we present Fast Random projection-based One-Class Classification (FROCC), an extremely efficient, scalable and easily parallelizable method for one-class classification with provable theoretical guarantees. Our method is based on the simple idea of transforming the training data by projecting it onto a set of random unit vectors that are chosen uniformly and independently from the unit sphere, and bounding the regions based on separation of the data. FROCC can be naturally extended with kernels. We provide a new theoretical framework to prove that that FROCC generalizes well in the sense that it is stable and has low bias for some parameter settings. We then develop a fast scalable approximation of FROCC using vectorization, exploiting data sparsity and parallelism to develop a new implementation called ParDFROCC. ParDFROCC achieves up to 2 percent points better ROC than the next best baseline, with up to 12× speedup in training and test times over a range of state-of-the-art benchmarks for the OCC task.

Generalization of machine learning models trained on a set of source domains on unseen target domains with different statistics, is a challenging problem. While many approaches have been proposed to solve this problem, they only utilize source data during training but do not take advantage of the fact that a single target example is available at the time of inference. Motivated by this, we propose a method that effectively uses the target sample during inference beyond mere classification. Our method has three components - (i) A label-preserving feature or metric transformation on source data such that the source samples are clustered in accordance with their class irrespective of their domain (ii) A generative model trained on the these features (iii) A label-preserving projection of the target point on the source-feature manifold during inference via solving an optimization problem on the input space of the generative model using the learned metric. Finally, the projected target is used in the classifier. Since the projected target feature comes from the source manifold and has the same label as the real target by design, the classifier is expected to perform better on it than the true target. We demonstrate that our method outperforms the state-of-the-art Domain Generalization methods on multiple datasets and tasks.