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1. Masked Prediction: A Parameter Identifiability View

   Liu, Bingbin; Hsu, Daniel J.; Ravikumar, Pradeep; Risteski, Andrej (January 2022, Advances in neural information processing systems)

   The vast majority of work in self-supervised learning have focused on assessing recovered features by a chosen set of downstream tasks. While there are several commonly used benchmark datasets, this lens of feature learning requires assumptions on the downstream tasks which are not inherent to the data distribution itself. In this paper, we present an alternative lens, one of parameter identifiability: assuming data comes from a parametric probabilistic model, we train a self-supervised learning predictor with a suitable parametric form, and ask whether the parameters of the optimal predictor can be used to extract the parameters of the ground truth generative model. Specifically, we focus on latent-variable models capturing sequential structures, namely Hidden Markov Models with both discrete and conditionally Gaussian observations. We focus on masked prediction as the self-supervised learning task and study the optimal masked predictor. We show that parameter identifiability is governed by the task difficulty, which is determined by the choice of data model and the amount of tokens to predict. Technique-wise, we uncover close connections with the uniqueness of tensor rank decompositions, a widely used tool in studying identifiability through the lens of the method of moments. 

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2. D-VAE: A Variational Autoencoder for Directed Acyclic Graphs

   Zhang, Muhan; Jiang, Shali; Cui, Zhicheng; Garnett, Roman; Chen, Yixin (January 2019, Advances in neural information processing systems)

   Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization. 

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3. Adaptive Bayesian Estimation of Discrete‐Continuous Distributions Under Smoothness and Sparsity

   https://doi.org/10.3982/ECTA17884  

   Norets, Andriy; Pelenis, Justinas (January 2022, Econometrica)

   We consider nonparametric estimation of a mixed discrete‐continuous distribution under anisotropic smoothness conditions and a possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates. Next, we consider a nonparametric mixture of normals model that uses continuous latent variables for the discrete part of the observations. We show that the posterior in this model contracts at rates that are equal to the derived lower bounds up to a log factor. Thus, Bayesian mixture of normals models can be used for (up to a log factor) optimal adaptive estimation of mixed discrete‐continuous distributions. The proposed model demonstrates excellent performance in simulations mimicking the first stage in the estimation of structural discrete choice models. 

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4. Identification of Nonlinear Latent Hierarchical Models

   Kong, Lingjing; Huang, Biwei; Xie, Feng; Xing, Eric; Chi, Yuejie; Zhang, Kun (December 2023, Advances in neural information processing systems)

   Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of causal structures and latent variables (up to invertible transformations) can be achieved under mild assumptions: on causal structures, we allow for multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we permit general nonlinearity and multi-dimensional continuous variables, alleviating existing work's parametric assumptions. Specifically, we first develop an identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models. 

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5. Anomaly detection in aeronautics data with quantum-compatible discrete deep generative model

   https://doi.org/10.1088/2632-2153/ace756  

   Templin, Thomas; Memarzadeh, Milad; Vinci, Walter; Lott, P. Aaron; Akbari Asanjan, Ata; Alexiades Armenakas, Anthony; Rieffel, Eleanor (August 2023, Machine Learning: Science and Technology)

   Abstract Deep generative learning cannot only be used for generating new data with statistical characteristics derived from input data but also for anomaly detection, by separating nominal and anomalous instances based on their reconstruction quality. In this paper, we explore the performance of three unsupervised deep generative models—variational autoencoders (VAEs) with Gaussian, Bernoulli, and Boltzmann priors—in detecting anomalies in multivariate time series of commercial-flight operations. We created two VAE models with discrete latent variables (DVAEs), one with a factorized Bernoulli prior and one with a restricted Boltzmann machine (RBM) with novel positive-phase architecture as prior, because of the demand for discrete-variable models in machine-learning applications and because the integration of quantum devices based on two-level quantum systems requires such models. To the best of our knowledge, our work is the first that applies DVAE models to anomaly-detection tasks in the aerospace field. The DVAE with RBM prior, using a relatively simple—and classically or quantum-mechanically enhanceable—sampling technique for the evolution of the RBM’s negative phase, performed better in detecting anomalies than the Bernoulli DVAE and on par with the Gaussian model, which has a continuous latent space. The transfer of a model to an unseen dataset with the same anomaly but without re-tuning of hyperparameters or re-training noticeably impaired anomaly-detection performance, but performance could be improved by post-training on the new dataset. The RBM model was robust to change of anomaly type and phase of flight during which the anomaly occurred. Our studies demonstrate the competitiveness of a discrete deep generative model with its Gaussian counterpart on anomaly-detection problems. Moreover, the DVAE model with RBM prior can be easily integrated with quantum sampling by outsourcing its generative process to measurements of quantum states obtained from a quantum annealer or gate-model device. 

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