We study the problem of efficient online multiclass linear classification with bandit feedback, where all examples belong to one of $K$ classes and lie in the $d$-dimensional Euclidean space. Previous works have left open the challenge of designing efficient algorithms with finite mistake bounds when the data is linearly separable by a margin $\gamma$. In this work, we take a first step towards this problem. We consider two notions of linear separability, \emph{strong} and \emph{weak}. 1. Under the strong linear separability condition, we design an efficient algorithm that achieves a near-optimal mistake bound of $O\left( K/\gamma^2 \right)$. 2. Under the more challenging weak linear separability condition, we design an efficient algorithm with a mistake bound of $\min (2^{\widetilde{O}(K \log^2 (1/\gamma))}, 2^{\widetilde{O}(\sqrt{1/\gamma} \log K)})$. Our algorithm is based on kernel Perceptron, which is inspired by the work of \citet{Klivans-Servedio-2008} on improperly learning intersection of halfspaces.

We study an online classification problem with partial feedback in which individuals arrive one at a time from a fixed but unknown distribution, and must be classified as positive or negative. Our algorithm only observes the true label of an individual if they are given a positive classification. This setting captures many classification problems for which fairness is a concern: for example, in criminal recidivism prediction, recidivism is only observed if the inmate is released; in lending applications, loan repayment is only observed if the loan is granted. We require that our algorithms satisfy common statistical fairness constraints (such as equalizing false positive or negative rates --- introduced as "equal opportunity" in Hardt et al. (2016)) at every round, with respect to the underlying distribution. We give upper and lower bounds characterizing the cost of this constraint in terms of the regret rate (and show that it is mild), and give an oracle efficient algorithm that achieves the upper bound.

The kernel null-space technique and its regression-based formulation (called one-class kernel spectral regression, a.k.a. OC-KSR) is known to be an effective and computationally attractive one-class classification framework. Despite its outstanding performance, the applicability of kernel null-space method is limited due to its susceptibility to possible training data corruptions and inability to rank training observations according to their conformity with the model. This work addresses these shortcomings by studying the effect of regularising the solution of the null-space kernel Fisher methodology in the context of its regression-based formulation (OC-KSR). In this respect, first, the effect of a Tikhonov regularisation in the Hilbert space is analysed where the one-class learning problem in presence of contaminations in the training set is posed as a sensitivity analysis problem. Next, driven by the success of the sparse representation methodology, the effect of a sparsity regularisation on the solution is studied. For both alternative regularisation schemes, iterative algorithms are proposed which recursively update label confidences and rank training observations based on their fit with the model. Through extensive experiments conducted on different data sets, the proposed methodology is found to enhance robustness against contamination in the training set as compared with the baseline kernel null-space technique as well as other existing approaches in a one-class classification paradigm while providing the functionality to rank training samples effectively.

The transfer of knowledge from one policy to another is an important tool in Deep Reinforcement Learning. This process, referred to as distillation, has been used to great success, for example, by enhancing the optimisation of agents, leading to stronger performance faster, on harder domains [26, 32, 5, 8]. Despite the widespread use and conceptual simplicity of distillation, many different formulations are used in practice, and the subtle variations between them can often drastically change the performance and the resulting objective that is being optimised. In this work, we rigorously explore the entire landscape of policy distillation, comparing the motivations and strengths of each variant through theoretical and empirical analysis. Our results point to three distillation techniques, that are preferred depending on specifics of the task. Specifically a newly proposed expected entropy regularised distillation allows for quicker learning in a wide range of situations, while still guaranteeing convergence.

Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous results on Riemannian metrics. We show how a class of heuristic measures gives more flexibility in finding meaningful, problem-specific distances, and how it can be applied to diverse generator types such as autoregressive generators commonly used in e.g. language and other sequence modeling. We further demonstrate how a diffusion-inspired transformation previously studied in cartography can be used to smooth out latent spaces, stretching them according to a chosen measure. In addition to providing more meaningful distances directly in latent space, this also provides a unique tool for novel kinds of data visualizations. We believe that the proposed methods can be a valuable tool for studying the structure of latent spaces and learned data distributions of generative models.

With the introduction of the variational autoencoder (VAE), probabilistic latent variable models have received renewed attention as powerful generative models. However, their performance in terms of test likelihood and quality of generated samples has been surpassed by autoregressive models without stochastic units. Furthermore, flow-based models have recently been shown to be an attractive alternative that scales well to high-dimensional data. In this paper we close the performance gap by constructing VAE models that can effectively utilize a deep hierarchy of stochastic variables and model complex covariance structures. We introduce the Bidirectional-Inference Variational Autoencoder (BIVA), characterized by a skip-connected generative model and an inference network formed by a bidirectional stochastic inference path. We show that BIVA reaches state-of-the-art test likelihoods, generates sharp and coherent natural images, and uses the hierarchy of latent variables to capture different aspects of the data distribution. We observe that BIVA, in contrast to recent results, can be used for anomaly detection. We attribute this to the hierarchy of latent variables which is able to extract high-level semantic features. Finally, we extend BIVA to semi-supervised classification tasks and show that it performs comparably to state-of-the-art results by generative adversarial networks.

ABSTRACT In this work we propose a method for reducing the dimensionality of tensor objects in a binary classification framework. The proposed Common Mode Patterns method takes into consideration the labels' information, and ensures that tensor objects that belong to different classes do not share common features after the reduction of their dimensionality. We experimentally validate the proposed supervised subspace learning technique and compared it against Multilinear Principal Component Analysis using a publicly available hyper-spectral imaging dataset. Experimental results indicate that the proposed CMP method can efficiently reduce the dimensionality of tensor objects, while, at the same time, increasing the inter-class separability. Index Terms -- Tensor dimensionality reduction, supervised tensor subspace learning, common mode patterns 1. INTRODUCTION Advances in sensing technologies have led to the continuous generation of massive multidimensional data, used in a wide range of applications.

Generative modeling is a fundamental problem in machine learning with many potential applications. Efficient learning of generative models requires available prior knowledge to be exploited as much as possible. In this paper, we propose a method to exploit prior knowledge of relative dependence between features for learning generative models. Such knowledge is available, for example, when side-information on features is present. We incorporate the prior knowledge by forcing marginals of the learned generative model to follow a prescribed relative feature dependence. To this end, we formulate a regularization term using a kernel-based dependence criterion. The proposed method can be incorporated straightforwardly into many optimization-based learning schemes of generative models, including variational autoencoders and generative adversarial networks. We show the effectiveness of the proposed method in experiments with multiple types of datasets and models.

Efficient training of deep neural networks (DNNs) is a challenge due to the associated highly nonconvex optimization. The alternating direction method of multipliers (ADMM) has attracted rising attention in deep learning for its potential of distributed computing. However, it remains an open problem to establish the convergence of ADMM in DNN training due to the nonlinear constraints involved. In this paper, we provide an answer to this problem by establishing the convergence of some nonlinearly constrained ADMM for DNNs with smooth activations. To be specific, we establish the global convergence to a Karush-Kuhn-Tucker (KKT) point at a ${\cal O}(1/k)$ rate. To achieve this goal, the key development lies in a new local linear approximation technique which enables us to overcome the hurdle of nonlinear constraints in ADMM for DNNs.

We ask whether the neural network interpretation methods can be fooled via adversarial model manipulation, which is defined as a model fine-tuning step that aims to radically alter the explanations without hurting the accuracy of the original model. By incorporating the interpretation results directly in the regularization term of the objective function for fine-tuning, we show that the state-of-the-art interpreters, e.g., LRP and Grad-CAM, can be easily fooled with our model manipulation. We propose two types of fooling, passive and active, and demonstrate such foolings generalize well to the entire validation set as well as transfer to other interpretation methods. Our results are validated by both visually showing the fooled explanations and reporting quantitative metrics that measure the deviations from the original explanations. We claim that the stability of neural network interpretation method with respect to our adversarial model manipulation is an important criterion to check for developing robust and reliable neural network interpretation method.