This note explores probabilistic sampling weighted by uncertainty in active learning. This method has been previously used and authors have tangentially remarked on its efficacy. The scheme has several benefits: (1) it is computationally cheap, (2) it can be implemented in a single-pass streaming fashion which is a benefit when deployed in real-world systems where different subsystems perform the suggestion scoring and extraction of user feedback, and (3) it is easily parameterizable. In this paper, we show on publicly available datasets that using probabilistic weighting is often beneficial and strikes a good compromise between exploration and representation especially when the starting set of labelled points is biased.

We introduce a framework using Generative Adversarial Networks (GANs) for likelihood--free inference (LFI) and Approximate Bayesian Computation (ABC). Our approach addresses both the key problems in likelihood--free inference, namely how to compare distributions and how to efficiently explore the parameter space. Our framework allows one to use the simulator model as a black box and leverage the power of deep networks to generate a rich set of features in a data driven fashion (as opposed to previous ad hoc approaches). Thereby it is a step towards a powerful alternative approach to LFI and ABC. On benchmark data sets, our approach improves on others with respect to scalability, ability to handle high dimensional data and complex probability distributions.

The Lovasz $\theta$ function of a graph, is a fundamental tool in combinatorial optimization and approximation algorithms. Computing $\theta$ involves solving a SDP and is extremely expensive even for moderately sized graphs. In this paper we establish that the Lovasz $\theta$ function is equivalent to a kernel learning problem related to one class SVM. This interesting connection opens up many opportunities bridging graph theoretic algorithms and machine learning. We show that there exist graphs, which we call $SVM-\theta$ graphs, on which the Lovasz $\theta$ function can be approximated well by a one-class SVM. This leads to a novel use of SVM techniques to solve algorithmic problems in large graphs e.g. identifying a planted clique of size $\Theta({\sqrt{n}})$ in a random graph $G(n,\frac{1}{2})$. A classic approach for this problem involves computing the $\theta$ function, however it is not scalable due to SDP computation. We show that the random graph with a planted clique is an example of $SVM-\theta$ graph, and as a consequence a SVM based approach easily identifies the clique in large graphs and is competitive with the state-of-the-art. Further, we introduce the notion of a ''common orthogonal labeling'' which extends the notion of a ''orthogonal labelling of a single graph (used in defining the $\theta$ function) to multiple graphs. The problem of finding the optimal common orthogonal labelling is cast as a Multiple Kernel Learning problem and is used to identify a large common dense region in multiple graphs. The proposed algorithm achieves an order of magnitude scalability compared to the state of the art.