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Register a new userDiBS: Differentiable Bayesian Structure Learning
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Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes DiBS directly applicable to posterior inference of nonstandard Bayesian network models, e.g., with nonlinear dependencies encoded by neural networks. Building on recent advances in variational inference, we use DiBS to devise an efficient general purpose method for approximating posteriors over structural models. In evaluations on simulated and real-world data, our method significantly outperforms related approaches to joint posterior inference.
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Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually over-parameterized space. This paper investigates a new line of Bayesian deep learning by performing Bayesian inference on network structure. Instead of building structure from scratch inefficiently, we draw inspirations from neural architecture search to represent the network structure. We then develop an efficient stochastic variational inference approach which unifies the learning of both network structure and weights. Empirically, our method exhibits competitive predictive performance while preserving the benefits of Bayesian principles across challenging scenarios. We also provide convincing experimental justification for our modeling choice.
The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The NKN architecture is based on the composition rules for kernels, so that each unit of the network corresponds to a valid kernel. It can compactly approximate compositional kernel structures such as those used by the Automatic Statistician (Lloyd et al., 2014), but because the architecture is differentiable, it is end-to-end trainable with gradient-based optimization. We show that the NKN is universal for the class of stationary kernels. Empirically we demonstrate pattern discovery and extrapolation abilities of NKN on several tasks that depend crucially on identifying the underlying structure, including time series and texture extrapolation, as well as Bayesian optimization.
We study the power of learning via mini-batch stochastic gradient descent (SGD) on the population loss, and batch Gradient Descent (GD) on the empirical loss, of a differentiable model or neural network, and ask what learning problems can be learnt using these paradigms. We show that SGD and GD can always simulate learning with statistical queries (SQ), but their ability to go beyond that depends on the precision $rho$ of the gradient calculations relative to the minibatch size $b$ (for SGD) and sample size $m$ (for GD). With fine enough precision relative to minibatch size, namely when $b rho$ is small enough, SGD can go beyond SQ learning and simulate any sample-based learning algorithm and thus its learning power is equivalent to that of PAC learning; this extends prior work that achieved this result for $b=1$. Similarly, with fine enough precision relative to the sample size $m$, GD can also simulate any sample-based learning algorithm based on $m$ samples. In particular, with polynomially many bits of precision (i.e. when $rho$ is exponentially small), SGD and GD can both simulate PAC learning regardless of the mini-batch size. On the other hand, when $b rho^2$ is large enough, the power of SGD is equivalent to that of SQ learning.
Deep learning models have demonstrated outstanding performance in several problems, but their training process tends to require immense amounts of computational and human resources for training and labeling, constraining the types of problems that can be tackled. Therefore, the design of effective training methods that require small labeled training sets is an important research direction that will allow a more effective use of resources.Among current approaches designed to address this issue, two are particularly interesting: data augmentation and active learning. Data augmentation achieves this goal by artificially generating new training points, while active learning relies on the selection of the most informative subset of unlabeled training samples to be labelled by an oracle. Although successful in practice, data augmentation can waste computational resources because it indiscriminately generates samples that are not guaranteed to be informative, and active learning selects a small subset of informative samples (from a large un-annotated set) that may be insufficient for the training process. In this paper, we propose a Bayesian generative active deep learning approach that combines active learning with data augmentation -- we provide theoretical and empirical evidence (MNIST, CIFAR-${10,100}$, and SVHN) that our approach has more efficient training and better classification results than data augmentation and active learning.
Classical Machine Learning (ML) pipelines often comprise of multiple ML models where models, within a pipeline, are trained in isolation. Conversely, when training neural network models, layers composing the neural models are simultaneously trained using backpropagation. We argue that the isolated training scheme of ML pipelines is sub-optimal, since it cannot jointly optimize multiple components. To this end, we propose a framework that translates a pre-trained ML pipeline into a neural network and fine-tunes the ML models within the pipeline jointly using backpropagation. Our experiments show that fine-tuning of the translated pipelines is a promising technique able to increase the final accuracy.
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