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1. Excess Risk Bounds for the Bayes Risk using Variational Inference in Latent Gaussian Models

   Sheth, Rishit; Khardon, Roni (January 2017, Advances in neural information processing systems)

   Bayesian models are established as one of the main successful paradigms for complex problems in machine learning. To handle intractable inference, research in this area has developed new approximation methods that are fast and effective. However, theoretical analysis of the performance of such approximations is not well developed. The paper furthers such analysis by providing bounds on the excess risk of variational inference algorithms and related regularized loss minimization algorithms for a large class of latent variable models with Gaussian latent variables. We strengthen previous results for variational algorithms by showing they are competitive with any point-estimate predictor. Unlike previous work, we also provide bounds on the risk of the \emph{Bayesian} predictor and not just the risk of the Gibbs predictor for the same approximate posterior. The bounds are applied in complex models including sparse Gaussian processes and correlated topic models. Theoretical results are complemented by identifying novel approximations to the Bayesian objective that attempt to minimize the risk directly. An empirical evaluation compares the variational and new algorithms shedding further light on their performance. 

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2. Meta Learning with Relational Information for Short Sequences

   Xie, Y; Jiang, H; Liu, F; Zhao, T; Zha, H (January 2019, Advances in neural information processing systems)

   This paper proposes a new meta-learning method – named HARMLESS (HAwkes Relational Meta LEarning method for Short Sequences) for learning heterogeneous point process models from short event sequence data along with a relational network. Specifically, we propose a hierarchical Bayesian mixture Hawkes process model, which naturally incorporates the relational information among sequences into point process modeling. Compared with existing methods, our model can capture the underlying mixed-community patterns of the relational network, which simultaneously encourages knowledge sharing among sequences and facilitates adaptive learning for each individual sequence. We further propose an efficient stochastic variational meta expectation maximization algorithm that can scale to large problems. Numerical experiments on both synthetic and real data show that HARMLESS outperforms existing methods in terms of predicting the future events. 

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3. Meta Learning with Relational Information for Short Sequences

   Xie, Yujia; Jiang, Haoming; Liu, Feng; Zhao, Tuo; Zha, Hongyuan Zha. (December 2019, Advances in neural information processing systems)

   This paper proposes a new meta-learning method – named HARMLESS (HAwkes Relational Meta LEarning method for Short Sequences) for learning heterogeneous point process models from short event sequence data along with a relational net- work. Specifically, we propose a hierarchical Bayesian mixture Hawkes process model, which naturally incorporates the relational information among sequences into point process modeling. Compared with existing methods, our model can capture the underlying mixed-community patterns of the relational network, which simultaneously encourages knowledge sharing among sequences and facilitates adaptive learning for each individual sequence. We further propose an efficient stochastic variational meta expectation maximization algorithm that can scale to large problems. Numerical experiments on both synthetic and real data show that HARMLESS outperforms existing methods in terms of predicting the future events. 

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4. Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlo

   Gürbüzbalaban, M.; Gao, X.; Hu, Y.; Zhu, L. (January 2021, Journal of machine learning research)

   Stochastic gradient Langevin dynamics (SGLD) and stochastic gradient Hamiltonian Monte Carlo (SGHMC) are two popular Markov Chain Monte Carlo (MCMC) algorithms for Bayesian inference that can scale to large datasets, allowing to sample from the posterior distribution of the parameters of a statistical model given the input data and the prior distribution over the model parameters. However, these algorithms do not apply to the decentralized learning setting, when a network of agents are working collaboratively to learn the parameters of a statistical model without sharing their individual data due to privacy reasons or communication constraints. We study two algorithms: Decentralized SGLD (DE-SGLD) and Decentralized SGHMC (DE-SGHMC) which are adaptations of SGLD and SGHMC methods that allow scaleable Bayesian inference in the decentralized setting for large datasets. We show that when the posterior distribution is strongly log-concave and smooth, the iterates of these algorithms converge linearly to a neighborhood of the target distribution in the 2-Wasserstein distance if their parameters are selected appropriately. We illustrate the efficiency of our algorithms on decentralized Bayesian linear regression and Bayesian logistic regression problems 

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5. Robust Learning via Ensemble Density Propagation in Deep Neural Networks

   https://doi.org/10.1109/MLSP49062.2020.9231635  

   Carannante, Giuseppina; Dera, Dimah; Rasool, Ghulam; Bouaynaya, Nidhal C.; Mihaylova, Lyudmila (September 2020, IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP))

   null (Ed.)

   Learning in uncertain, noisy, or adversarial environments is a challenging task for deep neural networks (DNNs). We propose a new theoretically grounded and efficient approach for robust learning that builds upon Bayesian estimation and Variational Inference. We formulate the problem of density propagation through layers of a DNN and solve it using an Ensemble Density Propagation (EnDP) scheme. The EnDP approach allows us to propagate moments of the variational probability distribution across the layers of a Bayesian DNN, enabling the estimation of the mean and covariance of the predictive distribution at the output of the model. Our experiments using MNIST and CIFAR-10 datasets show a significant improvement in the robustness of the trained models to random noise and adversarial attacks. 

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