We propose a framework for Bayesian Likelihood-Free Inference (LFI) based on Generalized Bayesian Inference. To define the generalized posterior, we use Scoring Rules (SRs), which evaluate probabilistic models given an observation. As in LFI we can sample from the model (but not evaluate the likelihood), we employ SRs with easy empirical estimators. Our framework includes novel approaches and popular LFI techniques (such as Bayesian Synthetic Likelihood), which benefit from the generalized Bayesian interpretation. Our method enjoys posterior consistency in a well-specified setting when a strictly-proper SR is used (i.e., one whose expectation is uniquely minimized when the model corresponds to the data generating process). Further, we prove a finite sample generalization bound and outlier robustness for the Kernel and Energy Score posteriors, and propose a strategy suitable for the LFI setup for tuning the learning rate in the generalized posterior. We run simulations studies with pseudo-marginal Markov Chain Monte Carlo (MCMC) and compare with related approaches, which we show do not enjoy robustness and consistency.
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In this paper, we study the impact of combining profile and network data in a de-duplication setting. We also assess the influence of a range of prior distributions on the linkage structure. Furthermore, we explore stochastic gradient Hamiltonian Monte Carlo methods as a faster alternative to obtain samples from the posterior distribution for network parameters. Our methodology is evaluated using the RLdata500 data, which is a popular dataset in the record linkage literature.
The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This work explores the use of variational autoencoders (VAEs) for non-linear dimension reduction with the specific aim of {\em disentangling} the low-dimensional latent variables to identify independent physical parameters that generated the data. A disentangled decomposition is interpretable, and can be transferred to a variety of tasks including generative modeling, design optimization, and probabilistic reduced order modelling. A major emphasis of this work is to characterize disentanglement using VAEs while minimally modifying the classic VAE loss function (i.e. the Evidence Lower Bound) to maintain high reconstruction accuracy. The loss landscape is characterized by over-regularized local minima which surround desirable solutions. We illustrate comparisons between disentangled and entangled representations by juxtaposing learned latent distributions and the true generative factors in a model porous flow problem. Hierarchical priors are shown to facilitate the learning of disentangled representations. The regularization loss is unaffected by latent rotation when training with rotationally-invariant priors, and thus learning non-rotationally-invariant priors aids in capturing the properties of generative factors, improving disentanglement. Finally, it is shown that semi-supervised learning - accomplished by labeling a small number of samples ($O(1\%)$) - results in accurate disentangled latent representations that can be consistently learned.
This article proposes omnibus portmanteau tests for contrasting adequacy of time series models. The test statistics are based on combining the autocorrelation function of the conditional residuals, the autocorrelation function of the conditional squared residuals, and the cross-correlation function between these residuals and their squares. The maximum likelihood estimator is used to derive the asymptotic distribution of the proposed test statistics under a general class of time series models, including ARMA, GARCH, and other nonlinear structures. An extensive Monte Carlo simulation study shows that the proposed tests successfully control the type I error probability and tend to have more power than other competitor tests in many scenarios. Two applications to a set of weekly stock returns for 92 companies from the S&P 500 demonstrate the practical use of the proposed tests.
The improvement of pose estimation accuracy is currently the fundamental problem in mobile robots. This study aims to improve the use of observations to enhance accuracy. The selection of feature points affects the accuracy of pose estimation, leading to the question of how the contribution of observation influences the system. Accordingly, the contribution of information to the pose estimation process is analyzed. Moreover, the uncertainty model, sensitivity model, and contribution theory are formulated, providing a method for calculating the contribution of every residual term. The proposed selection method has been theoretically proven capable of achieving a global statistical optimum. The proposed method is tested on artificial data simulations and compared with the KITTI benchmark. The experiments revealed superior results in contrast to ALOAM and MLOAM. The proposed algorithm is implemented in LiDAR odometry and LiDAR Inertial odometry both indoors and outdoors using diverse LiDAR sensors with different scan modes, demonstrating its effectiveness in improving pose estimation accuracy. A new configuration of two laser scan sensors is subsequently inferred. The configuration is valid for three-dimensional pose localization in a prior map and yields results at the centimeter level.
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical framework, to compensate for model error. This work presents a new theoretical analysis of the statistical finite element method demonstrating that it has similar convergence properties to the finite element method on which it is based. Our results constitute a bound on the Wasserstein-2 distance between the ideal prior and posterior and the StatFEM approximation thereof, and show that this distance converges at the same mesh-dependent rate as finite element solutions converge to the true solution. Several numerical examples are presented to demonstrate our theory, including an example which test the robustness of StatFEM when extended to nonlinear quantities of interest.
Identifying harmful instances, whose absence in a training dataset improves model performance, is important for building better machine learning models. Although previous studies have succeeded in estimating harmful instances under supervised settings, they cannot be trivially extended to generative adversarial networks (GANs). This is because previous approaches require that (1) the absence of a training instance directly affects the loss value and that (2) the change in the loss directly measures the harmfulness of the instance for the performance of a model. In GAN training, however, neither of the requirements is satisfied. This is because, (1) the generator's loss is not directly affected by the training instances as they are not part of the generator's training steps, and (2) the values of GAN's losses normally do not capture the generative performance of a model. To this end, (1) we propose an influence estimation method that uses the Jacobian of the gradient of the generator's loss with respect to the discriminator's parameters (and vice versa) to trace how the absence of an instance in the discriminator's training affects the generator's parameters, and (2) we propose a novel evaluation scheme, in which we assess harmfulness of each training instance on the basis of how GAN evaluation metric (e.g., inception score) is expect to change due to the removal of the instance. We experimentally verified that our influence estimation method correctly inferred the changes in GAN evaluation metrics. Further, we demonstrated that the removal of the identified harmful instances effectively improved the model's generative performance with respect to various GAN evaluation metrics.
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is developed based on their mutual complementarity properties. The approximating objects are from the class of quadratic spline functions, constructed based both on interpolation conditions and on shape knowledge. It is proved that the approximant objects preserve the shape properties of the exact reliability polynomials. Numerical examples and simulations show the performance of the algorithm, both in terms of low complexity, small error and shape preserving. Possibilities of increasing the accuracy of approximation are discussed.
We present a generalization of the Cauchy/Lorentzian, Geman-McClure, Welsch/Leclerc, generalized Charbonnier, Charbonnier/pseudo-Huber/L1-L2, and L2 loss functions. By introducing robustness as a continous parameter, our loss function allows algorithms built around robust loss minimization to be generalized, which improves performance on basic vision tasks such as registration and clustering. Interpreting our loss as the negative log of a univariate density yields a general probability distribution that includes normal and Cauchy distributions as special cases. This probabilistic interpretation enables the training of neural networks in which the robustness of the loss automatically adapts itself during training, which improves performance on learning-based tasks such as generative image synthesis and unsupervised monocular depth estimation, without requiring any manual parameter tuning.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
Amortized inference has led to efficient approximate inference for large datasets. The quality of posterior inference is largely determined by two factors: a) the ability of the variational distribution to model the true posterior and b) the capacity of the recognition network to generalize inference over all datapoints. We analyze approximate inference in variational autoencoders in terms of these factors. We find that suboptimal inference is often due to amortizing inference rather than the limited complexity of the approximating distribution. We show that this is due partly to the generator learning to accommodate the choice of approximation. Furthermore, we show that the parameters used to increase the expressiveness of the approximation play a role in generalizing inference rather than simply improving the complexity of the approximation.
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