Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been developed which do not require explicit computation of the normalization constant, such as noise contrastive estimation (NCE) and score matching. However, model selection methods for general non-normalized models have not been proposed so far. In this study, we develop information criteria for non-normalized models estimated by NCE or score matching. They are derived as approximately unbiased estimators of discrepancy measures for non-normalized models. Experimental results demonstrate that the proposed criteria enable selection of the appropriate non-normalized model in a data-driven manner. Extension to a finite mixture of non-normalized models is also discussed.

We present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the Bayesian evidential learning approach and exploits learning the direct relation between seismic data and reservoir properties to efficiently estimate reservoir properties. The theoretical framework we develop allows incorporation of non-linear statistical models for seismic estimation problems. Uncertainty quantification is performed with Approximate Bayesian Computation. With the help of a synthetic example of estimation of reservoir net-to-gross and average fluid saturations in sub-resolution thin-sand reservoir, several nuances are foregrounded regarding the applicability of unsupervised and supervised learning methods for seismic estimation problems. Finally, we demonstrate the efficacy of our approach by estimating posterior uncertainty of reservoir net-to-gross in sub-resolution thin-sand reservoir from an offshore delta dataset using 3D pre-stack seismic data.

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence between the approximate and the exact posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to parameter inference and demonstrate the method on several examples.

Events in the world may be caused by other, unobserved events. We consider sequences of events in continuous time. Given a probability model of complete sequences, we propose particle smoothing---a form of sequential importance sampling---to impute the missing events in an incomplete sequence. We develop a trainable family of proposal distributions based on a type of bidirectional continuous-time LSTM: Bidirectionality lets the proposals condition on future observations, not just on the past as in particle filtering. Our method can sample an ensemble of possible complete sequences (particles), from which we form a single consensus prediction that has low Bayes risk under our chosen loss metric. We experiment in multiple synthetic and real domains, using different missingness mechanisms, and modeling the complete sequences in each domain with a neural Hawkes process (Mei & Eisner 2017). On held-out incomplete sequences, our method is effective at inferring the ground-truth unobserved events, with particle smoothing consistently improving upon particle filtering.

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a quasi-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. In recent years, a number of data discrepancy measures bypassing the construction of summary statistics have been proposed, including the Kullback--Leibler divergence, the Wasserstein distance and maximum mean discrepancies. Here we propose a novel importance-sampling (IS) ABC algorithm relying on the so-called \textit{two-sample energy statistic}. We establish a new asymptotic result for the case where both the observed sample size and the simulated data sample size increase to infinity, which highlights to what extent the data discrepancy measure impacts the asymptotic pseudo-posterior. The result holds in the broad setting of IS-ABC methodologies, thus generalizing previous results that have been established only for rejection ABC algorithms. Furthermore, we propose a consistent V-statistic estimator of the energy statistic, under which we show that the large sample result holds. Our proposed energy statistic based ABC algorithm is demonstrated on a variety of models, including a Gaussian mixture, a moving-average model of order two, a bivariate beta and a multivariate $g$-and-$k$ distribution. We find that our proposed method compares well with alternative discrepancy measures.

This paper deals with estimating model parameters in graphical models. We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We show that our approach is a strong alternative to the celebrated EM approach for learning in graphical models. Actually, our natural gradient based strategy leads to learning optimal parameters for the final objective function without artificially trying to fit a distribution that may not correspond to the real one. We support our theoretical findings with the question of trend detection in financial markets and show that the learned model performs better than traditional practitioner methods and is less prone to overfitting.

Recent studies have explored the use of deep generative models of speech spectra based of variational autoencoders (VAEs), combined with unsupervised noise models, to perform speech enhancement. These studies developed iterative algorithms involving either Gibbs sampling or gradient descent at each step, making them computationally expensive. This paper proposes a variational inference method to iteratively estimate the power spectrogram of the clean speech. Our main contribution is the analytical derivation of the variational steps in which the en-coder of the pre-learned VAE can be used to estimate the varia-tional approximation of the true posterior distribution, using the very same assumption made to train VAEs. Experiments show that the proposed method produces results on par with the afore-mentioned iterative methods using sampling, while decreasing the computational cost by a factor 36 to reach a given performance .

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte Carlo, but these can be expensive when the data set is large and/or the model is complex, so more efficient variational approximations have recently received considerable attention. The traditional variational methods, that seek to minimize the Kullback--Leibler divergence between the posterior and a relatively simple parametric family, provide accurate and efficient estimation of the posterior mean, but often does not capture other moments, and have limitations in terms of the models to which they can be applied. Here we propose the construction of variational approximations based on minimizing the Fisher divergence, and develop an efficient computational algorithm that can be applied to a wide range of models without conjugacy or potentially unrealistic mean-field assumptions. We demonstrate the superior performance of the proposed method for the benchmark case of logistic regression.

We argue that pushing is an essential motion primitive in a robot's manipulative repertoire. Consider, for instance, a household robot reaching for a bottle of milk located in the back of the fridge. Instead of picking up every yoghurt, egg carton, or jam jar obstructing the path to create space, the robot can use gentle pushes to create a corridor to its lactic target. Moving larger obstacles out of the way is even more important to mobile robots in environments as extreme as abandoned mines (Ferguson et al., 2004), the moon (King, 2016), or for rescue missions as for the Fukushima Daiichi Nuclear Power Plant. In order to save cost, space, or reduce payload, such robots are often not equipped with grippers, meaning that prehensile manipulation is not an option. Even in the presence of grippers, objects may be too large or too heavy to grasp. In addition to the considered scenarios, pushing has numerous beneficial applications that come to mind less easily. For instance, pushing is effective at manipulating objects under uncertainty (Brost, 1988; Dogar and Srinivasa, 2010), and for pre-grasp manipulation, allowing robots to bring objects into configurations where they can be easily grasped (King et al., 2013). Less existential, yet highly interesting and entertaining, dexterous pushing skills are also widely applied and applauded in robot soccer (Emery and Balch, 2001).

Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local structure/consistency of GM have been investigated as popular choices in practice. However, due to their local/iterative nature, they often output poor approximations or even do not converge, e.g., in low-temperature regimes (hard instances of large parameters). To overcome the limitation, we propose a novel approach utilizing the global spectral feature of GM. Our contribution is two-fold: (a) we first propose a fully polynomial-time approximation scheme (FPTAS) for approximating the partition function of GM associating with a low-rank coupling matrix; (b) for general high-rank GMs, we design a spectral mean-field scheme utilizing (a) as a subroutine, where it approximates a high-rank GM into a product of rank-1 GMs for an efficient approximation of the partition function. The proposed algorithm is more robust in its running time and accuracy than prior methods, i.e., neither suffers from the convergence issue nor depends on hard local structures, as demonstrated in our experiments.