The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do not readily extend to heterogeneous data that are a combination of numerical and categorical variables, e.g., arising from linked GPS and text data. In this paper, we are interested in learning probabilistic generative models from high-dimensional heterogeneous data in an unsupervised fashion. The learned generative model provides latent unified representations that capture the factors common to the multiple dimensions of the data, and thus enable fusing multimodal data for various machine learning tasks. Following a Bayesian approach, we propose a general framework that combines disparate data types through the natural parameterization of the exponential family of distributions. To scale the model inference to millions of instances with thousands of features, we use the Laplace-Bernstein approximation for posterior computations involving nonlinear link functions. The proposed algorithm is presented in detail for the commonly encountered heterogeneous datasets with real-valued (Gaussian) and categorical (multinomial) features. Experiments on two high-dimensional and heterogeneous datasets (NYC Taxi and MovieLens-10M) demonstrate the scalability and competitive performance of the proposed algorithm on different machine learning tasks such as anomaly detection, data imputation, and recommender systems.

We consider the problem of learning the behavioral preferences of an expert engaged in a task from noisy and partially-observable demonstrations. This is motivated by real-world applications such as a line robot learning from observing a human worker, where some observations are occluded by environmental objects that cannot be removed. Furthermore, robotic perception tends to be imperfect and noisy. Previous techniques for inverse reinforcement learning (IRL) take the approach of either omitting the missing portions or inferring it as part of expectation-maximization, which tends to be slow and prone to local optima. We present a new method that generalizes the well-known Bayesian maximum-a-posteriori (MAP) IRL method by marginalizing the occluded portions of the trajectory. This is additionally extended with an observation model to account for perception noise. We show that the marginal MAP (MMAP) approach significantly improves on the previous IRL technique under occlusion in both formative evaluations on a toy problem and in a summative evaluation on an onion sorting line task by a robot.

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function for regression uncertainty estimation based on the Bayesian Validation Metric (BVM) framework while using ensemble learning. A series of experiments on in-distribution data show that the proposed method is competitive with existing state-of-the-art methods. In addition, experiments on out-of-distribution data show that the proposed method is robust to statistical change and exhibits superior predictive capability.

The Wishart distribution is the standard conjugate prior for the precision of the multivariate Gaussian likelihood, when the mean is known -- while the normal-Wishart can be used when the mean is also unknown. It is however not so obvious how to assign values to the hyperparameters of these distributions. In particular, when forming non-informative limits of these distributions, the shape (or degrees of freedom) parameter of the Wishart must be handled with care. The intuitive solution of directly interpreting the shape as a pseudocount and letting it go to zero, as proposed by some authors, violates the restrictions on the shape parameter. We show how to use the scaled KL-divergence between multivariate Gaussians as an energy function to construct Wishart and normal-Wishart conjugate priors. When used as informative priors, the salient feature of these distributions is the mode, while the KL scaling factor serves as the pseudocount. The scale factor can be taken down to the limit at zero, to form non-informative priors that do not violate the restrictions on the Wishart shape parameter. This limit is non-informative in the sense that the posterior mode is identical to the maximum likelihood estimate of the parameters of the Gaussian.

We consider the problem of offline reinforcement learning with model-based control, whose goal is to learn a dynamics model from the experience replay and obtain a pessimism-oriented agent under the learned model. Current model-based constraint includes explicit uncertainty penalty and implicit conservative regularization that pushes Q-values of out-of-distribution state-action pairs down and the in-distribution up. While the uncertainty estimation, on which the former relies on, can be loosely calibrated for complex dynamics, the latter performs slightly better. To extend the basic idea of regularization without uncertainty quantification, we propose distributionally robust offline model-based policy optimization (DROMO), which leverages the ideas in distributionally robust optimization to penalize a broader range of out-of-distribution state-action pairs beyond the standard empirical out-of-distribution Q-value minimization. We theoretically show that our method optimizes a lower bound on the ground-truth policy evaluation, and it can be incorporated into any existing policy gradient algorithms. We also analyze the theoretical properties of DROMO's linear and non-linear instantiations.

This paper describes a computational model of multiagent multimodal categorization that realizes emergent communication. We clarify whether the computational model can reproduce the following functions in a symbol emergence system, comprising two agents with different sensory modalities playing a naming game. (1) Function for forming a shared lexical system that comprises perceptual categories and corresponding signs, formed by agents through individual learning and semiotic communication between agents. (2) Function to improve the categorization accuracy in an agent via semiotic communication with another agent, even when some sensory modalities of each agent are missing. (3) Function that an agent infers unobserved sensory information based on a sign sampled from another agent in the same manner as cross-modal inference. We propose an interpersonal multimodal Dirichlet mixture (Inter-MDM), which is derived by dividing an integrative probabilistic generative model, which is obtained by integrating two Dirichlet mixtures (DMs). The Markov chain Monte Carlo algorithm realizes emergent communication. The experimental results demonstrated that Inter-MDM enables agents to form multimodal categories and appropriately share signs between agents. It is shown that emergent communication improves categorization accuracy, even when some sensory modalities are missing. Inter-MDM enables an agent to predict unobserved information based on a shared sign.

This paper introduces V-SysId, a novel method that enables simultaneous keypoint discovery, 3D system identification, and extrinsic camera calibration from an unlabeled video taken from a static camera, using only the family of equations of motion of the object of interest as weak supervision. V-SysId takes keypoint trajectory proposals and alternates between maximum likelihood parameter estimation and extrinsic camera calibration, before applying a suitable selection criterion to identify the track of interest. This is then used to train a keypoint tracking model using supervised learning. Results on a range of settings (robotics, physics, physiology) highlight the utility of this approach.

In causal studies, systems of variables are described by causal models [18, 22], which are composed of two elements: (i) the graphical representation of relationships between variables in a model, encoded in a directed acyclic graph, and (ii) the mathematical description of conditional probability distribution of each variable given its causal parents. When a causal model involves hidden (i.e., unobserved) variables, any characterization of the model verifiable by observations should only include observed variables. Therefore, one of the objectives of causal inference is to eliminate all hidden variables from inequalities and equalities that describe the model. In principle, this can be achieved using the Tarski-Seidenberg quantifier elimination method [12]. However, its complexity is such that only models with few variables can be solved using this technique, hence the reason for the many attempts to simplify the problem.

Generative Adversarial Networks (GANs) have been impactful on many problems and applications but suffer from unstable training. The Wasserstein GAN (WGAN) leverages the Wasserstein distance to avoid the caveats in the minmax two-player training of GANs but has other defects such as mode collapse and lack of metric to detect the convergence. We introduce a novel inferential Wasserstein GAN (iWGAN) model, which is a principled framework to fuse auto-encoders and WGANs. The iWGAN model jointly learns an encoder network and a generator network motivated by the iterative primal dual optimization process. The encoder network maps the observed samples to the latent space and the generator network maps the samples from the latent space to the data space. We establish the generalization error bound of the iWGAN to theoretically justify its performance. We further provide a rigorous probabilistic interpretation of our model under the framework of maximum likelihood estimation. The iWGAN, with a clear stopping criteria, has many advantages over other autoencoder GANs. The empirical experiments show that the iWGAN greatly mitigates the symptom of mode collapse, speeds up the convergence, and is able to provide a measurement of quality check for each individual sample. We illustrate the ability of the iWGAN by obtaining competitive and stable performances for benchmark datasets.

We study the matrix completion problem that leverages hierarchical similarity graphs as side information in the context of recommender systems. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model, we characterize the exact information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) by proving sharp upper and lower bounds on the sample complexity. In the achievability proof, we demonstrate that probability of error of the maximum likelihood estimator vanishes for sufficiently large number of users and items, if all sufficient conditions are satisfied. On the other hand, the converse (impossibility) proof is based on the genie-aided maximum likelihood estimator. Under each necessary condition, we present examples of a genie-aided estimator to prove that the probability of error does not vanish for sufficiently large number of users and items. One important consequence of this result is that exploiting the hierarchical structure of social graphs yields a substantial gain in sample complexity relative to the one that simply identifies different groups without resorting to the relational structure across them. More specifically, we analyze the optimal sample complexity and identify different regimes whose characteristics rely on quality metrics of side information of the hierarchical similarity graph. Finally, we present simulation results to corroborate our theoretical findings and show that the characterized information-theoretic limit can be asymptotically achieved. N recent years, personalized recommender systems have emerged in an extensive range of Web applications to predict the preferences of its users and provide them with new and relevant items based on the scarce data about the users and/or items [2]. There are two major paradigms of recommender systems: (i) content-based filtering systems; (ii) collaborative filtering systems. Content-based filtering approach exploits a profile of users' preferences and/or properties of the items to carry out the recommendation task.