**Excessive Gap Technique**

In compressed sensing, the sensing matrix is assumed perfectly known. However, there exists perturbation in the sensing matrix in reality due to sensor offsets or noise disturbance. Directions-of-arrival (DoA) estimation with off-grid effect satisfies this situation, and can be formulated into a (non)convex optimization problem with linear inequalities constraints, which can be solved by the interior point method (using the CVX tools), but at a large computational cost. In this work, in order to design efficient algorithms, we consider various alternative formulations, such as unconstrained formulation, primal-dual formulation, or conic formulation to develop group-sparsity promoted solvers. First, the consensus alternating direction method of multipliers (C-ADMM) is applied. Then, iterative algorithms for the BPDN formulation is proposed by combining the Nesterov smoothing technique with accelerated proximal gradient method, and the convergence analysis of the method is conducted as well. We also developed a variant of EGT (Excessive Gap Technique)-based primal-dual method to systematically reduce the smoothing parameter sequentially. Finally, we propose algorithms for quadratically constrained L2-L1 mixed norm minimization problem by using the smoothed dual conic optimization (SDCO) and continuation technique. The performance of accuracy and convergence for all the proposed methods are demonstrated in the numerical simulations. … **pair2vec**

Reasoning about implied relationships (e.g. paraphrastic, common sense, encyclopedic) between pairs of words is crucial for many cross-sentence inference problems. This paper proposes new methods for learning and using embeddings of word pairs that implicitly represent background knowledge about such relationships. Our pairwise embeddings are computed as a compositional function of each word’s representation, which is learned by maximizing the pointwise mutual information (PMI) with the contexts in which the the two words co-occur. We add these representations to the cross-sentence attention layer of existing inference models (e.g. BiDAF for QA, ESIM for NLI), instead of extending or replacing existing word embeddings. Experiments show a gain of 2.72% on the recently released SQuAD 2.0 and 1.3% on MultiNLI. Our representations also aid in better generalization with gains of around 6-7% on adversarial SQuAD datasets, and 8.8% on the adversarial entailment test set by Glockner et al. … **PlaNet**

Research into how artificial agents can improve their decisions over time is progressing rapidly via reinforcement learning (RL). For this technique, an agent observes a stream of sensory inputs (e.g. camera images) while choosing actions (e.g. motor commands), and sometimes receives a reward for achieving a specified goal. Model-free approaches to RL aim to directly predict good actions from the sensory observations, enabling DeepMind’s DQN to play Atari and other agents to control robots. However, this blackbox approach often requires several weeks of simulated interaction to learn through trial and error, limiting its usefulness in practice. Model-based RL, in contrast, attempts to have agents learn how the world behaves in general. Instead of directly mapping observations to actions, this allows an agent to explicitly plan ahead, to more carefully select actions by ‘imagining’ their long-term outcomes. Model-based approaches have achieved substantial successes, including AlphaGo, which imagines taking sequences of moves on a fictitious board with the known rules of the game. However, to leverage planning in unknown environments (such as controlling a robot given only pixels as input), the agent must learn the rules or dynamics from experience. Because such dynamics models in principle allow for higher efficiency and natural multi-task learning, creating models that are accurate enough for successful planning is a long-standing goal of RL. … **Differentially Private Markov Chain Monte Carlo (DPMCMC)**

Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP Bayesian learning by presenting the first general DP Markov chain Monte Carlo (MCMC) algorithm whose privacy-guarantees are not subject to unrealistic assumptions on Markov chain convergence and that is applicable to posterior inference in arbitrary models. Our algorithm is based on a decomposition of the Barker acceptance test that allows evaluating the R\’enyi DP privacy cost of the accept-reject choice. We further show how to improve the DP guarantee through data subsampling and approximate acceptance tests. …

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Jul 2021

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