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Register a new userScalable Variational Inference in Log-supermodular Models
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We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing approximate inference techniques such as belief propagation, mean field, and variants. We show that a recently proposed variational approach to inference in log-supermodular models -L-FIELD- reduces to the widely-studied minimum norm problem for submodular minimization. This insight allows to leverage powerful existing tools, and hence to solve the variational problem orders of magnitude more efficiently than previously possible. We then provide another natural interpretation of L-FIELD, demonstrating that it exactly minimizes a specific type of Renyi divergence measure. This insight sheds light on the nature of the variational approximations produced by L-FIELD. Furthermore, we show how to perform parallel inference as message passing in a suitable factor graph at a linear convergence rate, without having to sum up over all the configurations of the factor. Finally, we apply our approach to a challenging image segmentation task. Our experiments confirm scalability of our approach, high quality of the marginals, and the benefit of incorporating higher-order potentials.
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Inference in log-linear models scales linearly in the size of output space in the worst-case. This is often a bottleneck in natural language processing and computer vision tasks when the output space is feasibly enumerable but very large. We propose a method to perform inference in log-linear models with sublinear amortized cost. Our idea hinges on using Gumbel random variable perturbations and a pre-computed Maximum Inner Product Search data structure to access the most-likely elements in sublinear amortized time. Our method yields provable runtime and accuracy guarantees. Further, we present empirical experiments on ImageNet and Word Embeddings showing significant speedups for sampling, inference, and learning in log-linear models.
Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest, because this domain relates naturally to many practical problem settings, such as multilabel graph cut, budget allocation and revenue maximization with discrete assignments. In contrast, the use of these functions for probabilistic modeling has received surprisingly little attention so far. In this work, we firstly propose the Generalized Multilinear Extension, a continuous DR-submodular extension for integer submodular functions. We study central properties of this extension and formulate a new probabilistic model which is defined through integer submodular functions. Then, we introduce a block-coordinate ascent algorithm to perform approximate inference for those class of models. Finally, we demonstrate its effectiveness and viability on several real-world social connection graph datasets with integer submodular objectives.
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the expectation of interested functions w.r.t. a target distribution. When it comes to high dimensional probability models and large datasets, efficient approximate inference becomes critically important. In this thesis, we propose a new framework for approximate inference, which combines the advantages of these three frameworks and overcomes their limitations. Our proposed four algorithms are motivated by the recent computational progress of Steins method. Our proposed algorithms are applied to continuous and discrete distributions under the setting when the gradient information of the target distribution is available or unavailable. Theoretical analysis is provided to prove the convergence of our proposed algorithms. Our adaptive IS algorithm iteratively improves the importance proposal by functionally decreasing the KL divergence between the updated proposal and the target. When the gradient of the target is unavailable, our proposed sampling algorithm leverages the gradient of a surrogate model and corrects induced bias with importance weights, which significantly outperforms other gradient-free sampling algorithms. In addition, our theoretical results enable us to perform the goodness-of-fit test on discrete distributions. At the end of the thesis, we propose an importance-weighted method to efficiently aggregate local models in distributed learning with one-shot communication. Results on simulated and real datasets indicate the statistical efficiency and wide applicability of our algorithm.
Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable when each likelihood evaluation is computationally expensive. New approaches combining variational inference with normalizing flow are characterized by a computational cost that grows only linearly with the dimensionality of the latent variable space, and rely on gradient-based optimization instead of sampling, providing a more efficient approach for Bayesian inference about the model parameters. Moreover, the cost of frequently evaluating an expensive likelihood can be mitigated by replacing the true model with an offline trained surrogate model, such as neural networks. However, this approach might generate significant bias when the surrogate is insufficiently accurate around the posterior modes. To reduce the computational cost without sacrificing inferential accuracy, we propose Normalizing Flow with Adaptive Surrogate (NoFAS), an optimization strategy that alternatively updates the normalizing flow parameters and the weights of a neural network surrogate model. We also propose an efficient sample weighting scheme for surrogate model training that ensures some global accuracy of the surrogate while capturing the likely regions of the parameters that yield the observed data. We demonstrate the inferential and computational superiority of NoFAS against various benchmarks, including cases where the underlying model lacks identifiability. The source code and numerical experiments used for this study are available at https://github.com/cedricwangyu/NoFAS.
Deep clustering (DC) has become the state-of-the-art for unsupervised clustering. In principle, DC represents a variety of unsupervised methods that jointly learn the underlying clusters and the latent representation directly from unstructured datasets. However, DC methods are generally poorly applied due to high operational costs, low scalability, and unstable results. In this paper, we first evaluate several popular DC variants in the context of industrial applicability using eight empirical criteria. We then choose to focus on variational deep clustering (VDC) methods, since they mostly meet those criteria except for simplicity, scalability, and stability. To address these three unmet criteria, we introduce four generic algorithmic improvements: initial $gamma$-training, periodic $beta$-annealing, mini-batch GMM (Gaussian mixture model) initialization, and inverse min-max transform. We also propose a novel clustering algorithm S3VDC (simple, scalable, and stable VDC) that incorporates all those improvements. Our experiments show that S3VDC outperforms the state-of-the-art on both benchmark tasks and a large unstructured industrial dataset without any ground truth label. In addition, we analytically evaluate the usability and interpretability of S3VDC.
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