Abstract: General robotic grippers are challenging to control because of their rich nonsmooth contact dynamics and the many sources of uncertainties due to the environment or sensor noise. In this work, we demonstrate how to compute 6-DoF grasp poses using simulation-based Bayesian inference through the full stochastic forward simulation of the robot in its environment while robustly accounting for many of the uncertainties in the system. A Riemannian manifold optimization procedure preserving the nonlinearity of the rotation space is used to compute the maximum a posteriori grasp pose. Abstract: Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning machines.

We present a new data analysis perspective to determine variable importance regardless of the underlying learning task. Traditionally, variable selection is considered an important step in supervised learning for both classification and regression problems. The variable selection also becomes critical when costs associated with the data collection and storage are considerably high for cases like remote sensing. Therefore, we propose a new methodology to select important variables from the data by first creating dependency networks among all variables and then ranking them (i.e. nodes) by graph centrality measures. Selecting Top-$n$ variables according to preferred centrality measure will yield a strong candidate subset of variables for further learning tasks e.g. clustering. We present our tool as a Shiny app which is a user-friendly interface development environment. We also extend the user interface for two well-known unsupervised variable selection methods from literature for comparison reasons.

Bayesian causal structure learning aims to learn a posterior distribution over directed acyclic graphs (DAGs), and the mechanisms that define the relationship between parent and child variables. By taking a Bayesian approach, it is possible to reason about the uncertainty of the causal model. The notion of modelling the uncertainty over models is particularly crucial for causal structure learning since the model could be unidentifiable when given only a finite amount of observational data. In this paper, we introduce a novel method to jointly learn the structure and mechanisms of the causal model using Variational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We extend the method of Bayesian causal structure learning using GFlowNets to learn not only the posterior distribution over the structure, but also the parameters of a linear-Gaussian model. Our results on simulated data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods, including the guarantee to sample acyclic graphs, and the flexibility to generalize to non-linear causal mechanisms.

Autonomous robots are required to reason about the behaviour of dynamic agents in their environment. The creation of models to describe these relationships is typically accomplished through the application of causal discovery techniques. However, as it stands observational causal discovery techniques struggle to adequately cope with conditions such as causal sparsity and non-stationarity typically seen during online usage in autonomous agent domains. Meanwhile, interventional techniques are not always feasible due to domain restrictions. In order to better explore the issues facing observational techniques and promote further discussion of these topics we carry out a benchmark across 10 contemporary observational temporal causal discovery methods in the domain of autonomous driving. By evaluating these methods upon causal scenes drawn from real world datasets in addition to those generated synthetically we highlight where improvements need to be made in order to facilitate the application of causal discovery techniques to the aforementioned use-cases. Finally, we discuss potential directions for future work that could help better tackle the difficulties currently experienced by state of the art techniques.

Machine learning models are often misspecified in the likelihood, which leads to a lack of robustness in the predictions. In this paper, we introduce a framework for correcting likelihood misspecifications in several paradigm agnostic noisy prior models and test the model's ability to remove the misspecification. The "ABC-GAN" framework introduced is a novel generative modeling paradigm, which combines Generative Adversarial Networks (GANs) and Approximate Bayesian Computation (ABC). This new paradigm assists the existing GANs by incorporating any subjective knowledge available about the modeling process via ABC, as a regularizer, resulting in a partially interpretable model that operates well under low data regimes. At the same time, unlike any Bayesian analysis, the explicit knowledge need not be perfect, since the generator in the GAN can be made arbitrarily complex. ABC-GAN eliminates the need for summary statistics and distance metrics as the discriminator implicitly learns them and enables simultaneous specification of multiple generative models. The model misspecification is simulated in our experiments by introducing noise of various biases and variances. The correction term is learnt via the ABC-GAN, with skip connections, referred to as skipGAN. The strength of the skip connection indicates the amount of correction needed or how misspecified the prior model is. Based on a simple experimental setup, we show that the ABC-GAN models not only correct the misspecification of the prior, but also perform as well as or better than the respective priors under noisier conditions. In this proposal, we show that ABC-GANs get the best of both worlds.

In this work we theoretically show that conservative objective models (COMs) for offline model-based optimisation (MBO) are a special kind of contrastive divergence-based energy model, one where the energy function represents both the unconditional probability of the input and the conditional probability of the reward variable. While the initial formulation only samples modes from its learned distribution, we propose a simple fix that replaces its gradient ascent sampler with a Langevin MCMC sampler. This gives rise to a special probabilistic model where the probability of sampling an input is proportional to its predicted reward. Lastly, we show that better samples can be obtained if the model is decoupled so that the unconditional and conditional probabilities are modelled separately.

Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of such SDEs typically requires a large number of time steps and hence a high computational cost. This is because of ill-conditioning properties of the score that we analyze mathematically. Previous approaches have relied on multiscale generation to considerably accelerate SGMs. We explain how this acceleration results from an implicit factorization of the data distribution into a product of conditional probabilities of wavelet coefficients across scales. The resulting Wavelet Score-based Generative Model (WSGM) synthesizes wavelet coefficients with the same number of time steps at all scales, and its time complexity therefore grows linearly with the image size. This is proved mathematically for Gaussian distributions, and shown numerically for physical processes at phase transition and natural image datasets.

A class of fast, supervised learning algorithms is presented. Inspired by Albus's CMAC model, the algorithms learn orders of magnitude more rapidly than typical imple(cid:173) mentations of back propagation, while often achieving comparable qualities of generalization. Furthermore, unlike most traditional function approximation methods, the algorithms are well suited for use in real time adaptive signal processing. Unlike simpler adaptive systems, such as linear predictive cod(cid:173) ing, the adaptive linear combiner, and the Kalman filter, the new algorithms are capable of efficiently capturing the structure of complicated non-linear systems. As an illustration, the algorithm is applied to the prediction of a chaotic timeseries.

One popular class of unsupervised algorithms are competitive algo(cid:173) rithms. In the traditional view of competition, only one competitor, the winner, adapts for any given case. I propose to view compet(cid:173) itive adaptation as attempting to fit a blend of simple probability generators (such as gaussians) to a set of data-points. The maxi(cid:173) mum likelihood fit of a model of this type suggests a "softer" form of competition, in which all competitors adapt in proportion to the relative probability that the input came from each competitor. I investigate one application of the soft competitive model, place(cid:173) ment of radial basis function centers for function interpolation, and show that the soft model can give better performance with little additional computational cost.

In this paper we develop a Bayes criterion which includes the Rissanen complexity, for inferring regular grammar models. We develop two methods for regular grammar Bayesian inference. The fIrst method is based on treating the regular grammar as a I-dimensional Markov source, and the second is based on the combinatoric characteristics of the regular grammar itself. We apply the resulting Bayes criteria to a particular example in order to show the efficiency of each method.