Deep learning models are full of hyperparameters, which are set manually before the learning process can start. To find the best configuration for these hyperparameters in such a high dimensional space, with time-consuming and expensive model training / validation, is not a trivial challenge. Bayesian optimization is a powerful tool for the joint optimization of hyperparameters, efficiently trading off exploration and exploitation of the hyperparameter space. In this paper, we discuss Bayesian hyperparameter optimization, including hyperparameter optimization, Bayesian optimization, and Gaussian processes. We also review BoTorch, GPyTorch and Ax, the new open-source frameworks that we use for Bayesian optimization, Gaussian process inference and adaptive experimentation, respectively. For experimentation, we apply Bayesian hyperparameter optimization, for optimizing group weights, to weighted group pooling, which couples unsupervised tiered graph autoencoders learning and supervised graph classification learning for molecular graphs. We find that Ax, BoTorch and GPyTorch together provide a simple-to-use but powerful framework for Bayesian hyperparameter optimization, using Ax's high-level API that constructs and runs a full optimization loop and returns the best hyperparameter configuration.
We introduce a new approach to learning in hierarchical latent-variable generative models called the "distributed distributional code Helmholtz machine", which emphasises flexibility and accuracy in the inferential process. In common with the original Helmholtz machine and later variational autoencoder algorithms (but unlike adverserial methods) our approach learns an explicit inference or "recognition" model to approximate the posterior distribution over the latent variables. Unlike in these earlier methods, the posterior representation is not limited to a narrow tractable parameterised form (nor is it represented by samples). To train the generative and recognition models we develop an extended wake-sleep algorithm inspired by the original Helmholtz Machine. This makes it possible to learn hierarchical latent models with both discrete and continuous variables, where an accurate posterior representation is essential. We demonstrate that the new algorithm outperforms current state-of-the-art methods on synthetic, natural image patch and the MNIST data sets.
One of the goals of the ICML workshop on representation and learning is to establish benchmark scores for a new data set of labeled facial expressions. This paper presents the performance of a "Null" model consisting of convolutions with random weights, PCA, pooling, normalization, and a linear readout. Our approach focused on hyperparameter optimization rather than novel model components. On the Facial Expression Recognition Challenge held by the Kaggle website, our hyperparameter optimization approach achieved a score of 60% accuracy on the test data. This paper also introduces a new ensemble construction variant that combines hyperparameter optimization with the construction of ensembles. This algorithm constructed an ensemble of four models that scored 65.5% accuracy. These scores rank 12th and 5th respectively among the 56 challenge participants. It is worth noting that our approach was developed prior to the release of the data set, and applied without modification; our strong competition performance suggests that the TPE hyperparameter optimization algorithm and domain expertise encoded in our Null model can generalize to new image classification data sets.
While off-policy temporal difference (TD) methods have widely been used in reinforcement learning due to their efficiency and simple implementation, their Bayesian counterparts have not been utilized as frequently. One reason is that the non-linear max operation in the Bellman optimality equation makes it difficult to define conjugate distributions over the value functions. In this paper, we introduce a novel Bayesian approach to off-policy TD methods using Assumed Density Filtering (ADFQ), which updates beliefs on state-action values (Q) through an online Bayesian inference method. Uncertainty measures in the beliefs provide a natural regularization for learning, and we show how ADFQ reduces in a limiting case to the traditional Q-learning algorithm. Our empirical results demonstrate that the proposed ADFQ algorithms outperform comparable algorithms on several task domains. Moreover, our algorithms are computationally more efficient than other existing approaches to Bayesian reinforcement learning.
Variational methods that rely on a recognition network to approximate the posterior of directed graphical models offer better inference and learning than previous methods. Recent advances that exploit the capacity and flexibility in this approach have expanded what kinds of models can be trained. However, as a proposal for the posterior, the capacity of the recognition network is limited, which can constrain the representational power of the generative model and increase the variance of Monte Carlo estimates. To address these issues, we introduce an iterative refinement procedure for improving the approximate posterior of the recognition network and show that training with the refined posterior is competitive with state-of-the-art methods. The advantages of refinement are further evident in an increased effective sample size, which implies a lower variance of gradient estimates.