In the problem of learning a mixture of linear classifiers, the aim is to learn a collection of hyperplanes from a sequence of binary responses. Each response is a result of querying with a vector and indicates the side of a randomly chosen hyperplane from the collection the query vector belong to. This model provides a rich representation of heterogeneous data with categorical labels and has only been studied in some special settings. We look at a hitherto unstudied problem of query complexity upper bound of recovering all the hyperplanes, especially for the case when the hyperplanes are sparse. This setting is a natural generalization of the extreme quantization problem known as 1-bit compressed sensing.

We also apply our method to recent GAN variants and improve state-of-the-art FID for conditional generation from 9.21 to 8.57 on CIFAR-10.

The proposed deterministic codes are proven to perfectly tolerate arbitrary Byzantine attacks.

The implementations of the experiments on ABC and FTDC datasets are similar. For the stability analysis, we are interested in the norm of term 1. In Section E.1, we briefly discuss the motivation behind studying age prediction and PCA-based statistical analysis in this context. In Section E.2, we provide additional details on cortical thickness data acquisition. In Section E.3, we report the results for stability analysis of VNNs and PCA-regression models for FTDC100 ( In Section E.4, we study the stability of VNNs on two simulated In Section E.5, we include additional figures A promising application of brain age prediction is early detection of neurodegenerative diseases (such as Alzheimer's, Huntingson's disease) which may manifest themselves as error in age prediction in pathological contexts by machine learning models trained E.4 Stability of VNNs on Synthetic Data We consider two settings for synthetic data.

Graph neural networks (GNN) are an effective framework that exploit interrelationships within graph-structured data for learning.