Arising from many applications at the intersection of decision-making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) problems unify the two main classes of inference, namely maximization (optimization) and marginal inference (counting), and are believed to have higher complexity than both of them. We propose XOR MMAP provides a constant factor approximation to the Marginal MAP problem, by encoding it as a single optimization in a polynomial size of the original problem. We evaluate our approach in several machine learning and decision-making applications, and show that our approach outperforms several state-of-the-art Marginal MAP solvers.

Game theory provides a powerful framework for the design and analysis of multiagent systems that involve strategic interactions [see, e.g.,16].

Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are relatively robust to random noise. In this paper, we propose to study a semi-random noise regime that generalizes both the random and worst-case noise regimes. We propose the first quantitative analysis of the robustness of nonlinear classifiers in this general noise regime. We establish precise theoretical bounds on the robustness of classifiers in this general regime, which depend on the curvature of the classifier's decision boundary. Our bounds confirm and quantify the empirical observations that classifiers satisfying curvature constraints are robust to random noise. Moreover, we quantify the robustness of classifiers in terms of the subspace dimension in the semi-random noise regime, and show that our bounds remarkably interpolate between the worst-case and random noise regimes. We perform experiments and show that the derived bounds provide very accurate estimates when applied to various state-of-the-art deep neural networks and datasets. This result suggests bounds on the curvature of the classifiers' decision boundaries that we support experimentally, and more generally offers important insights onto the geometry of high dimensional classification problems.

Neural Information Processing Systems http://nips.cc/

Unfortunately, the notion is seriously flawed on two counts [8]. First, it doesn't ensure fairness.

We consider the problem of finding the best arm in a stochastic Mutli-armed Bandit (MAB) game and propose a general framework based on verification that applies to multiple well-motivated generalizations of the classic MAB problem. In these generalizations, additional structure is known in advance, causing the task of verifying the optimality of a candidate to be easier than discovering the best arm. Our results are focused on the scenario where the failure probability $\delta$ must be very low; we essentially show that in this high confidence regime, identifying the best arm is as easy as the task of verification. We demonstrate the effectiveness of our framework by applying it, and improving the state-of-the art results in the problems of: Linear bandits, Dueling bandits with the Condorcet assumption, Copeland dueling bandits, Unimodal bandits and Graphical bandits.

Neural Information Processing Systems http://nips.cc/

This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over the uncertainty in a latent path, like a state space model, we improve the state of the art results on the Blizzard and TIMIT speech modeling data sets by a large margin, while achieving comparable performances to competing methods on polyphonic music modeling.

Obtaining the human-like perception ability of abstracting visual concepts from concrete pixels has always been a fundamental and important target in machine learning research fields such as disentangled representation learning and scene decomposition. Towards this goal, we propose an unsupervised transformer-based Visual Concepts Tokenization framework, dubbed VCT, to perceive an image into a set of disentangled visual concept tokens, with each concept token responding to one type of independent visual concept. Particularly, to obtain these concept tokens, we only use cross-attention to extract visual information from the image tokens layer by layer without self-attention between concept tokens, preventing information leakage across concept tokens. We further propose a Concept Disentangling Loss to facilitate that different concept tokens represent independent visual concepts. The cross-attention and disentangling loss play the role of induction and mutual exclusion for the concept tokens, respectively. Extensive experiments on several popular datasets verify the effectiveness of VCT on the tasks of disentangled representation learning and scene decomposition. VCT achieves the state of the art results by a large margin.

In the context of lossy compression, Blau & Michaeli (2019) adopt a mathematical notion of perceptual quality and define the information rate-distortion-perception function, generalizing the classical rate-distortion tradeoff. We consider the notion of universal representations in which one may fix an encoder and vary the decoder to achieve any point within a collection of distortion and perception constraints. We prove that the corresponding information-theoretic universal rate-distortion-perception function is operationally achievable in an approximate sense. Under MSE distortion, we show that the entire distortion-perception tradeoff of a Gaussian source can be achieved by a single encoder of the same rate asymptotically. We then characterize the achievable distortion-perception region for a fixed representation in the case of arbitrary distributions, and identify conditions under which the aforementioned results continue to hold approximately. This motivates the study of practical constructions that are approximately universal across the RDP tradeoff, thereby alleviating the need to design a new encoder for each objective. We provide experimental results on MNIST and SVHN suggesting that on image compression tasks, the operational tradeoffs achieved by machine learning models with a fixed encoder suffer only a small penalty when compared to their variable encoder counterparts.