Machine learning has achieved an important role in the automatic classification of variable stars, and several classifiers have been proposed over the last decade. These classifiers have achieved impressive performance in several astronomical catalogues. However, some scientific articles have also shown that the training data therein contain multiple sources of bias. Hence, the performance of those classifiers on objects not belonging to the training data is uncertain, potentially resulting in the selection of incorrect models. Besides, it gives rise to the deployment of misleading classifiers. An example of the latter is the creation of open-source labelled catalogues with biased predictions. In this paper, we develop a method based on an informative marginal likelihood to evaluate variable star classifiers. We collect deterministic rules that are based on physical descriptors of RR Lyrae stars, and then, to mitigate the biases, we introduce those rules into the marginal likelihood estimation. We perform experiments with a set of Bayesian Logistic Regressions, which are trained to classify RR Lyraes, and we found that our method outperforms traditional non-informative cross-validation strategies, even when penalized models are assessed. Our methodology provides a more rigorous alternative to assess machine learning models using astronomical knowledge. From this approach, applications to other classes of variable stars and algorithmic improvements can be developed.

In some cases we will need an array with more than two axes. In the general case, an array of numbers arranged on a regular grid with a variable number of axes is known as a tensor. Tensors and Multidimensional arrays are different types of object, the first is a type of function, the second is a data structure suitable for representing a tensor in a coordinate system. A scalar is just a single number, in contrast to most of the other objects studied in linear algebra, which are usually arrays of multiple numbers. In terms of tensor -- A tensor that contains only one number is called a Scalar(or scalar tensor, or 0-dimensional tensor, or 0D tensor).

Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the weight matrices in neural networks have been shown to empirically correlate with test set accuracy in several works (e.g. arXiv:1901.08276), but a formal relationship between heavy-tail distributed parameters and generalization bounds was yet to be demonstrated. In this work, the compression framework of arXiv:1802.05296 is utilized to show that matrices with heavy-tail distributed matrix elements can be compressed, resulting in networks with sparse weight matrices. Since the parameter count has been reduced to a sum of the non-zero elements of sparse matrices, the compression framework allows us to bound the generalization gap of the resulting compressed network with a non-vacuous generalization bound. Further, the action of these matrices on a vector is discussed, and how they may relate to compression and resilient classification is analyzed.

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused on formally evaluating the predictive uncertainties of these models. Furthermore, existing works point out the difficulties of encoding domain knowledge in models like NLMs, making them unsuitable for applications where interpretability is required. In this work, we show that traditional training procedures for NLMs can drastically underestimate uncertainty in data-scarce regions. We identify the underlying reasons for this behavior and propose a novel training method that can both capture useful predictive uncertainties as well as allow for incorporation of domain knowledge.

Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This work aims to fill this gap and proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. It is used to construct a coordinate transformation that relates the Riemannian manifold associated with the metric to Euclidean space. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation by a normal distribution. Furthermore, the algorithmic structure allows for an efficient implementation of geoVI which is demonstrated on multiple examples, ranging from low-dimensional illustrative ones to non-linear, hierarchical Bayesian inverse problems in thousands of dimensions.

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. However, the most popular inference algorithms for SBL become too expensive for high-dimensional problems due to the need to maintain a large covariance matrix. To resolve this issue, we introduce a new SBL inference algorithm that avoids explicit computation of the covariance matrix, thereby saving significant time and space. Instead of performing costly matrix inversions, our covariance-free method solves multiple linear systems to obtain provably unbiased estimates of the posterior statistics needed by SBL. These systems can be solved in parallel, enabling further acceleration of the algorithm via graphics processing units. In practice, our method can be up to thousands of times faster than existing baselines, reducing hours of computation time to seconds. We showcase how our new algorithm enables SBL to tractably tackle high-dimensional signal recovery problems, such as deconvolution of calcium imaging data and multi-contrast reconstruction of magnetic resonance images. Finally, we open-source a toolbox containing all of our implementations to drive future research in SBL.

The computational cost of usual Monte Carlo methods for sampling a posteriori laws in Bayesian inference scales linearly with the number of data points. One option to reduce it to a fraction of this cost is to resort to mini-batching in conjunction with unadjusted discretizations of Langevin dynamics, in which case only a random fraction of the data is used to estimate the gradient. However, this leads to an additional noise in the dynamics and hence a bias on the invariant measure which is sampled by the Markov chain. We advocate using the so-called Adaptive Langevin dynamics, which is a modification of standard inertial Langevin dynamics with a dynamical friction which automatically corrects for the increased noise arising from mini-batching. We investigate the practical relevance of the assumptions underpinning Adaptive Langevin (constant covariance for the estimation of the gradient), which are not satisfied in typical models of Bayesian inference; and show how to extend the approach to more general situations.

Reinforcement learning (RL) can be used to create a decision-making agent for autonomous driving. However, previous approaches provide only black-box solutions, which do not offer information on how confident the agent is about its decisions. An estimate of both the aleatoric and epistemic uncertainty of the agent's decisions is fundamental for real-world applications of autonomous driving. Therefore, this paper introduces the Ensemble Quantile Networks (EQN) method, which combines distributional RL with an ensemble approach, to obtain a complete uncertainty estimate. The distribution over returns is estimated by learning its quantile function implicitly, which gives the aleatoric uncertainty, whereas an ensemble of agents is trained on bootstrapped data to provide a Bayesian estimation of the epistemic uncertainty. A criterion for classifying which decisions that have an unacceptable uncertainty is also introduced. The results show that the EQN method can balance risk and time efficiency in different occluded intersection scenarios, by considering the estimated aleatoric uncertainty. Furthermore, it is shown that the trained agent can use the epistemic uncertainty information to identify situations that the agent has not been trained for and thereby avoid making unfounded, potentially dangerous, decisions outside of the training distribution.

Neuronal ensemble inference is a significant problem in the study of biological neural networks. Various methods have been proposed for ensemble inference from experimental data of neuronal activity. Among them, Bayesian inference approach with generative model was proposed recently. However, this method requires large computational cost for appropriate inference. In this work, we give an improved Bayesian inference algorithm by modifying update rule in Markov chain Monte Carlo method and introducing the idea of simulated annealing for hyperparameter control. We compare the performance of ensemble inference between our algorithm and the original one, and discuss the advantage of our method.

Research in Cognitive Science suggests that humans understand and represent knowledge of the world through causal relationships. In addition to observations, they can rely on experimenting and counterfactual reasoning -- i.e. referring to an alternative course of events -- to identify causal relations and explain atypical situations. Different instances of control systems, such as smart homes, would benefit from having a similar causal model, as it would help the user understand the logic of the system and better react when needed. However, while data-driven methods achieve high levels of correlation detection, they mainly fall short of finding causal relations, notably being limited to observations only. Notably, they struggle to identify the cause from the effect when detecting a correlation between two variables. This paper introduces a new way to learn causal models from a mixture of experiments on the environment and observational data. The core of our method is the use of selected interventions, especially our learning takes into account the variables where it is impossible to intervene, unlike other approaches. The causal model we obtain is then used to generate Causal Bayesian Networks, which can be later used to perform diagnostic and predictive inference. We use our method on a smart home simulation, a use case where knowing causal relations pave the way towards explainable systems. Our algorithm succeeds in generating a Causal Bayesian Network close to the simulation's ground truth causal interactions, showing encouraging prospects for application in real-life systems.