We introduce a method for inferring and predicting latent states in the important and difficult case of state-space models where observations can only be simulated, and transition dynamics are unknown. In this setting, the likelihood of observations is not available and only synthetic observations can be generated from a black-box simulator. We propose a way of doing likelihood-free inference (LFI) of states and state prediction with a limited number of simulations. Our approach uses a multi-output Gaussian process for state inference, and a Bayesian Neural Network as a model of the transition dynamics for state prediction. We improve upon existing LFI methods for the inference task, while also accurately learning transition dynamics. The proposed method is necessary for modelling inverse problems in dynamical systems with computationally expensive simulations, as demonstrated in experiments with non-stationary user models.

Variational Bayes (VB) applied to latent Dirichlet allocation (LDA) is the original inference mechanism for LDA. Many variants of VB for LDA, as well as for VB in general, have been developed since LDA's inception in 2013, but standard VB is still widely applied to LDA. Variational message passing (VMP) is the message passing equivalent of VB and is a useful tool for constructing a variational inference solution for a large variety of conjugate exponential graphical models (there is also a non conjugate variant available for other models). In this article we present the VMP equations for LDA and also provide a brief discussion of the equations. We hope that this will assist others when deriving variational inference solutions to other similar graphical models.

Crowdsourcing systems enable us to collect noisy labels from crowd workers. A graphical model representing local dependencies between workers and tasks provides a principled way of reasoning over the true labels from the noisy answers. However, one needs a predictive model working on unseen data directly from crowdsourced datasets instead of the true labels in many cases. To infer true labels and learn a predictive model simultaneously, we propose a new data-generating process, where a neural network generates the true labels from task features. We devise an EM framework alternating variational inference and deep learning to infer the true labels and to update the neural network, respectively. Experimental results with synthetic and real datasets show a belief-propagation-based EM algorithm is robust to i) corruption in task features, ii) multi-modal or mismatched worker prior, and iii) few spammers submitting noises to many tasks.

Fast, highly accurate, and reliable inference of the sky origin of gravitational waves would enable real-time multi-messenger astronomy. Current Bayesian inference methodologies, although highly accurate and reliable, are slow. Deep learning models have shown themselves to be accurate and extremely fast for inference tasks on gravitational waves, but their output is inherently questionable due to the blackbox nature of neural networks. In this work, we join Bayesian inference and deep learning by applying importance sampling on an approximate posterior generated by a multi-headed convolutional neural network. The neural network parametrizes Von Mises-Fisher and Gaussian distributions for the sky coordinates and two masses for given simulated gravitational wave injections in the LIGO and Virgo detectors. We generate skymaps for unseen gravitational-wave events that highly resemble predictions generated using Bayesian inference in a few minutes. Furthermore, we can detect poor predictions from the neural network, and quickly flag them.

This paper is to consider the problems of estimation and recognition from the perspective of sigma-max inference (probability-possibility inference), with a focus on discovering whether some of the unknown quantities involved could be more faithfully modeled as fuzzy uncertainty. Two related key issues are addressed: 1) the random-fuzzy dual interpretation of unknown quantity being estimated; 2) the principle of selecting sigma-max operator for practical problems, such as estimation and recognition. Our perspective, conceived from definitions of randomness and fuzziness, is that continuous unknown quantity involved in estimation with inaccurate prior should be more appropriately modeled as randomness and handled by sigma inference; whereas discrete unknown quantity involved in recognition with insufficient (and inaccurate) prior could be better modeled as fuzziness and handled by max inference. The philosophy was demonstrated by an updated version of the well-known interacting multiple model (IMM) filter, for which the jump Markovian System is reformulated as a hybrid uncertainty system, with continuous state evolution modeled as usual as model-conditioned stochastic system and discrete mode transitions modeled as fuzzy system by a possibility (instead of probability) transition matrix, and hypotheses mixing is conducted by using the operation of "max" instead of "sigma". For our example of maneuvering target tracking using simulated data from both a short-range fire control radar and a long-range surveillance radar, the updated IMM filter shows significant improvement over the classic IMM filter, due to its peculiarity of hard decision of system model and a faster response to the transition of discrete mode.

For this reason, existing methods for inferring context-specific Bayesian networks have favored breaking datasets into subsamples, limiting statistical power and resolution, and preventing the use of multidimensional and latent contexts. To overcome this challenge, we propose NOTEARS-optimized Mixtures of Archetypal DAGs (NOTMAD). NOTMAD models context-specific Bayesian networks as the output of a function which learns to mix archetypal networks according to sample context. The archetypal networks are estimated jointly with the context-specific networks and do not require any prior knowledge. We encode the acyclicity constraint as a smooth regularization loss which is back-propagated to the mixing function; in this way, NOTMAD shares information between context-specific acyclic graphs, enabling the estimation of Bayesian network structures and parameters at even single-sample resolution. We demonstrate the utility of NOTMAD and sample-specific network inference through analysis and experiments, including patient-specific gene expression networks which correspond to morphological variation in cancer.

After the user provides a few examples of desired outcomes, MURAL automatically infers a reward function that takes into account these examples and the agent's uncertainty for each state. Although reinforcement learning has shown success in domains such as robotics, chip placement and playing video games, it is usually intractable in its most general form. In particular, deciding when and how to visit new states in the hopes of learning more about the environment can be challenging, especially when the reward signal is uninformative. These questions of reward specification and exploration are closely connected -- the more directed and "well shaped" a reward function is, the easier the problem of exploration becomes. The answer to the question of how to explore most effectively is likely to be closely informed by the particular choice of how we specify rewards.

Modelling dependencies between climate extremes is important for climate risk assessment, for instance when allocating emergency management funds. In statistics, multivariate extreme value theory is often used to model spatial extremes. However, most commonly used approaches require strong assumptions and are either too simplistic or over-parametrised. From a machine learning perspective, Generative Adversarial Networks (GANs) are a powerful tool to model dependencies in high-dimensional spaces. Yet in the standard setting, GANs do not well represent dependencies in the extremes. Here we combine GANs with extreme value theory (evtGAN) to model spatial dependencies in summer maxima of temperature and winter maxima in precipitation over a large part of western Europe. We use data from a stationary 2000-year climate model simulation to validate the approach and explore its sensitivity to small sample sizes. Our results show that evtGAN outperforms classical GANs and standard statistical approaches to model spatial extremes. Already with about 50 years of data, which corresponds to commonly available climate records, we obtain reasonably good performance. In general, dependencies between temperature extremes are better captured than dependencies between precipitation extremes due to the high spatial coherence in temperature fields. Our approach can be applied to other climate variables and can be used to emulate climate models when running very long simulations to determine dependencies in the extremes is deemed infeasible.

Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in correlation estimation will result in poor predictive performance and uncertainty quantification. We introduce a method that automatically accounts for temporal misalignment in a unified generative model that improves predictive performance. Our method uses Gaussian processes (GPs) to model the correlations both within and between the tasks. Building on the previous work by Kazlauskaiteet al. [2019], we include a separate monotonic warp of the input data to model temporal misalignment. In contrast to previous work, we formulate a lower bound that accounts for uncertainty in both the estimates of the warping process and the underlying functions. Also, our new take on a monotonic stochastic process, with efficient path-wise sampling for the warp functions, allows us to perform full Bayesian inference in the model rather than MAP estimates. Missing data experiments, on synthetic and real time-series, demonstrate the advantages of accounting for misalignments (vs standard unaligned method) as well as modelling the uncertainty in the warping process(vs baseline MAP alignment approach).

From the previous article, we know that Bayesian Neural Network would treat the model weights and outputs as variables. Instead of finding a set of optimal estimates, we are fitting the probability distributions for them. But the problem is "How can we know what their distributions look like?" To answer this, you have to learn what prior, posterior, and Bayes' theorem are. In the following, we will use an example for illustration.