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Register a new userVariational Adaptive-Newton Method for Explorative Learning
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We present the Variational Adaptive Newton (VAN) method which is a black-box optimization method especially suitable for explorative-learning tasks such as active learning and reinforcement learning. Similar to Bayesian methods, VAN estimates a distribution that can be used for exploration, but requires computations that are similar to continuous optimization methods. Our theoretical contribution reveals that VAN is a second-order method that unifies existing methods in distinct fields of continuous optimization, variational inference, and evolution strategies. Our experimental results show that VAN performs well on a wide-variety of learning tasks. This work presents a general-purpose explorative-learning method that has the potential to improve learning in areas such as active learning and reinforcement learning.
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We introduce Pathfinder, a variational method for approximately sampling from differentiable log densities. Starting from a random initialization, Pathfinder locates normal approximations to the target density along a quasi-Newton optimization path, with local covariance estimated using the inverse Hessian estimates produced by the optimizer. Pathfinder returns draws from the approximation with the lowest estimated Kullback-Leibler (KL) divergence to the true posterior. We evaluate Pathfinder on a wide range of posterior distributions, demonstrating that its approximate draws are better than those from automatic differentiation variational inference (ADVI) and comparable to those produced by short chains of dynamic Hamiltonian Monte Carlo (HMC), as measured by 1-Wasserstein distance. Compared to ADVI and short dynamic HMC runs, Pathfinder requires one to two orders of magnitude fewer log density and gradient evaluations, with greater reductions for more challenging posteriors. Importance resampling over multiple runs of Pathfinder improves the diversity of approximate draws, reducing 1-Wasserstein distance further and providing a measure of robustness to optimization failures on plateaus, saddle points, or in minor modes. The Monte Carlo KL-divergence estimates are embarrassingly parallelizable in the core Pathfinder algorithm, as are multiple runs in the resampling version, further increasing Pathfinders speed advantage with multiple cores.
We develop a data driven approach to perform clustering and end-to-end feature learning simultaneously for streaming data that can adaptively detect novel clusters in emerging data. Our approach, Adaptive Nonparametric Variational Autoencoder (AdapVAE), learns the cluster membership through a Bayesian Nonparametric (BNP) modeling framework with Deep Neural Networks (DNNs) for feature learning. We develop a joint online variational inference algorithm to learn feature representations and clustering assignments simultaneously via iteratively optimizing the Evidence Lower Bound (ELBO). We resolve the catastrophic forgetting citep{kirkpatrick2017overcoming} challenges with streaming data by adopting generative samples from the trained AdapVAE using previous data, which avoids the need of storing and reusing past data. We demonstrate the advantages of our model including adaptive novel cluster detection without discarding useful information learned from past data, high quality sample generation and comparable clustering performance as end-to-end batch mode clustering methods on both image and text corpora benchmark datasets.
Variational Monte Carlo (VMC) is an approach for computing ground-state wavefunctions that has recently become more powerful due to the introduction of neural network-based wavefunction parametrizations. However, efficiently training neural wavefunctions to converge to an energy minimum remains a difficult problem. In this work, we analyze optimization and sampling methods used in VMC and introduce alterations to improve their performance. First, based on theoretical convergence analysis in a noiseless setting, we motivate a new optimizer that we call the Rayleigh-Gauss-Newton method, which can improve upon gradient descent and natural gradient descent to achieve superlinear convergence with little added computational cost. Second, in order to realize this favorable comparison in the presence of stochastic noise, we analyze the effect of sampling error on VMC parameter updates and experimentally demonstrate that it can be reduced by the parallel tempering method. In particular, we demonstrate that RGN can be made robust to energy spikes that occur when new regions of configuration space become available to the sampler over the course of optimization. Finally, putting theory into practice, we apply our enhanced optimization and sampling methods to the transverse-field Ising and XXZ models on large lattices, yielding ground-state energy estimates with remarkably high accuracy after just 200-500 parameter updates.
Class imbalanced datasets are common in real-world applications that range from credit card fraud detection to rare disease diagnostics. Several popular classification algorithms assume that classes are approximately balanced, and hence build the accompanying objective function to maximize an overall accuracy rate. In these situations, optimizing the overall accuracy will lead to highly skewed predictions towards the majority class. Moreover, the negative business impact resulting from false positives (positive samples incorrectly classified as negative) can be detrimental. Many methods have been proposed to address the class imbalance problem, including methods such as over-sampling, under-sampling and cost-sensitive methods. In this paper, we consider the over-sampling method, where the aim is to augment the original dataset with synthetically created observations of the minority classes. In particular, inspired by the recent advances in generative modelling techniques (e.g., Variational Inference and Generative Adversarial Networks), we introduce a new oversampling technique based on variational autoencoders. Our experiments show that the new method is superior in augmenting datasets for downstream classification tasks when compared to traditional oversampling methods.
We consider the problem of online learning in the presence of sudden distribution shifts as frequently encountered in applications such as autonomous navigation. Distribution shifts require constant performance monitoring and re-training. They may also be hard to detect and can lead to a slow but steady degradation in model performance. To address this problem we propose a new Bayesian meta-algorithm that can both (i) make inferences about subtle distribution shifts based on minimal sequential observations and (ii) accordingly adapt a model in an online fashion. The approach uses beam search over multiple change point hypotheses to perform inference on a hierarchical sequential latent variable modeling framework. Our proposed approach is model-agnostic, applicable to both supervised and unsupervised learning, and yields significant improvements over state-of-the-art Bayesian online learning approaches.
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